statistics 1040, sections 007 009, quiz 1 (20 points)symanzik/teaching/2008_stat1040/... · 2008....
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Statistics 1040 Sections 007 amp 009 Quiz 1 (20 Points)
Friday August 31 2007
Your Name
Question 1 Controlled ExperimentsjObservational StudiesI (14 Points)
(hypothetica~ Does regularly taking vitamin C help protect people against flu
A ---- was conducted to answer this question The were 500 volunteering college students assigned to two groups of 250 students The students in the took regularly a tablet of vitamin C whereas those in the took an identically looking and tasting pill called _ Neither participating students nor personell administrating drugs to them knew who was
taking which pill in other words it was a ----- _ experiment After a couple of months the numbers of flu cases in both groups were compared
Fill the gaps in the paragraph above using the most appropriate words from the following list
placebo doublfr-blind haphazardly treatnaent group observational study randonaly singlfr-blindmiddot vaccine
confounding factor objects control group controlled experinaent subjects poliomiddot
Please turn over
1
middot Question 2 Controlled ExperimentsObservational Studies II (6 Points)
In 1990 four passengers were killed by crashes on commuter airlines compared to 39 killed on scheduled carriers (like United TWA and so forth) True or false Circle your answer and explain the data show that if you have to fly it is safer to do so on a commuter airline
2
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Statistics 1040 Sections 007 amp 009 Quiz 2 (20 Points)
Friday September 7 2007
Your Name
Question 1 Histograms (14 Points)
The following table is for the gestational age of 1210 babies
Gestational Age 230-250 250-270 270-290 290310 310-330
Number 47
206 731 199 27
Draw a histogram for these data on the graph paper provided Make sure to label the axes
I I I
bull WFF bull I - - -~-
bull -
f
I I I I T I i I I
bull I I
-= 0 I I
IT I I T I 11 I I I
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= 1m= I I
m I
I I I I I I
Please turn over
1
f
Question 2 Observational Studies Controlled Experiments (6 Points)
For each of the following studies determine whether the study in question was a randomshyized controlled experiment or an observational study (circle the correct answer)
bull Twenty male employees and twenty female employees participate in research deshysigned to compare attitudes towards the Social Security System of men and women Each individual responds to a series of questions on a survey Mean scores are computed for men and for women
randomized controlled experiment observational study
bull A researcher wants to learn whether regularly taking zinc supplements may reduce the risk of getting a cold Volunteers in this study chose to (or chose not to) take a zinc supplement
randomized controlled experiment observational study
bull A researcher wants to learn about whether computer simulations help students betshyter understand statistical concepts She puts the names of 20 volunteers into a box and randomly draws the names of 10 people who will use computer simulations to learn statistical concepts The other 10 study participants will use a conventional approach without computer simulations to learn the same concepts
randomized controlled experiment observational study
2
Statistics 1040 Sections 007 amp 009 Quiz 3 (20 Points)
Friday September 142007
Your Name ------------ shy
Question 1 The Average and the SDI (10 Points)
Here is a list of numbers
07 1698 32 54 08 77 63 22 41 81 65 37 06 69 99 88 31 57 91
1 Without doing any arithmetic guess whether the average is around (i) 1 (ii) 5 or (iii) 10 Circle your answer and explain
2 Without doing any arithmetic guess whether the SD is around (i) 1 (ii) 3 or (iii) 6 Circle your answer and explain
Question 2 The Average and the SD II (10 Points)
A study on college students found that the men had an average weight of about 66 kg and an SD of about 9 kg The women had an average weight of about 55kg and an SD of about 9 kg (Note that 1 kg = 221b)
1 Just roughly what percentage of the men weighted between 57 kg and 75 kg Answer Fill in your answer and exp~ain
2 If you took the men and women together would the SD of their weights be (i) smaller than 9 kg (ii) just about 9 kg or (iii) bigger than 9 kg Circle your answer and explain
1
Statistics 1040 Sections 007 amp 009 Quiz 4 (20 Points)
Friday September 21 2007
Your Name _------------- shy
Question 1 Normal Approximation for Data(20 Points)
The Graduate Record Examination (GRE) is a test taken by college students who intend to pursue a graduate degree in the United States For around 428000 examinees who took the General GRE Test in 2001-02 the mean for the verbal ability portion of the exam was around 470 and the standard deviation was around 125 We can assume that the histogram follows a normal curve Show your work
bull (7 Points) The percentage of examinees who scored less than 420 on the GRE test is roughly
bull (7 Points) The percentage of examinees who scored between 370 and 645 is about
bull (6 Points) In order to be among the top 4 a student must have obtained a minimum GRE score of about --- shy
) Please turn over
1
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Tablesmiddot )
A NORMAL TABLE
z Area z Area z Area
000 o 150 8664 300middot 99730 005shy 399 155 8789 30j 99771 010 797 160middot 8904 31099806 015 1192 165 9011 Jl~ 99837 020 1585 170 9109 320 99863
025 1914 175 9199 325 99885 030 2358 180 9281 330 99903 035 2137 185 9357 335 99919 040middot 3108 190middot 9426 340 99933 045 3473 195 9488 345 99944
050 3829 200 9545 350 99953 055 4177 205 9596 355 j 99961
I 060 4515 210 9643 360 99968 065 4843 215 9684 365 99974 070 5161 220 9122 370 99978
075 5467 225 9156 375 99982 080 5763 230 9786 380 99986 0~85 middot6(t47 235 9812 385 99988
~ bull~-- 090 6319 240 9836 390 99990 j
0~95 6579 245 9857 395 99992 I
100 6827 250 9816 400 999931 j 105 7063 255 9892 405 999949
110 7287 260 9907 410 999959 ~ 115 7499 265 9920 415 999967middot
I 120 7699 270 9931 420 999913f
I 125 7887 275 9940 425 999919 130 8064 i 280 9949 430 999983
) ~gt 135 8230 285 9956 435 1999986
440 middot999989middotmiddot140 i 8385 290 9963 145 ~8529 295 996middot8 445 99999-1
Statistics 1040 Sections 007 amp 009 Quiz 5 (20 Points)
Friday September 28 2007
Your Name ------------- shy
Questionmiddot 1 Measurement Error (8 Points)
You send a yardstick to a local laboratory for calibration asking that the procedure be repeated three times They report the following values
3596 inches 3601 inches 3603 inches
If you send the yardstick back for a fourth calibration you would expect to get 36 inches give or take
(a) 01 inches or so (b) 03 inches or so (c) 06inches or so
Circle your answer and explain
Question 2 Correlation (6 Points)
A teaching assistant gives a quiz to his section There are 10 questions on the quiz and no part credit is given After grading the papers the TA writes down for each student the number of questions the student got right and the number wrong The average number of right answers is 64 with an SD of 20 the average nUIILberof wrong answers is 36 with the same SD of 20
The correlation coefficient between the number of right answers andthe number of wrong answers is
(a) exactly 0 (b) -050 (c) +050 (d) -10 (e) +10 (f) -20 (g) +20
(h) cant tell without the data
Circle your answer and explain
Please turn over
1
Question 3 Correlation (6 Points)
For women age 25 and over in the US in 2005 the relationship between age and educashytionallevel (years of schooling completed) can be summarized as follows
average age ~ 50 years SD ~ 16 years average ed level ~ 132 years SD ~ 30 years r ~ -020
True or false and explain As you get older you become less educated If this statement is false what accounts for the negative correlation
Formulas
sum of all numbers avg = ----------shy
how many numbers )
SD = Javerage of [(deviations from avg) 2]
2
Statistics 1040 Sections 007 amp 009 Quiz 6 (20 Points)
Friday October 12 2007
Your Name -----~-----
Question 1 Regression (20 Points)
A selection of 65 varieties of cereal were tested for calories and sodium (in milligrams) for an one-cup serving The results can be summarized as follows
Average sodium - 240 mg SD = 131 mg Average calories = 149 calories SD = 62 calories r = 053
Show your work
1 (7 Points) Find the equation of the regression line for predicting number of mg sodium in an one-cup serving of cereals from calories
2 (4 Points) Predict the number of mg sodium in an one-cup serving of cereals that has 200 calories per cup
Please turn over
1
3 (5 Points) Find the rms error for predicting mg sodium from calories
4 (4 Points) Explain why it would not be a good idea to use the information in the question to estimate the amount of sodium for a cereal with 350 calories per cup
Formulas
rms error =Jl- r 2 x SDy
SD slope = r x --y intercept = avgy - slope x avgxSDx
)
2
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- - ~~~~~~_-
Statistics 1040 Sections 007 amp 009 Quiz 7 (20 Points)
Monday October 22 2007
Your Name
Question 1 ChanceProbability I (6 Points)
A deck of cards is shuffled and the top two cards are placed face down on a table Circle your answer
1 There is a 1 chance in 52 for the first card to be the ace of clubs True False
2 There is a 1 chance in 52 for the second card to be the ace of diamonds True False
3 The chance of getting the ace of clubs and then the ace of diamonds is 152 xl52 True False
~lt~J Question 2 ChanceProbability II (3 Points)
A coin is tossed six times Two possible sequences of results are
(i) H T T H T H (ii) H H H H H H
(The coin must land on H or T in the order given H = heads T = tails)
Which of the following is correct
Circle your answer
1 Sequence (i) is more likely
2 Sequence (ii) is more likely
3 Both sequences are equally likely
Please turn over
1
~ - -- _ -- -
Question 3 ChanceProbability III (3 Points)
Two cards will be dealt off the top of a well-shuffled deck You have a choice
(i) To win $1 if at least one of the two cards is a queen
(ii) To win $1 if the first card is a queen
Circle your answer
1 Option (i) is better for winning
2 Option (ii) is better for winning
3 Both options are equally good for winning
Question 4 ChanceProbability IV (4 Points)
One event has chance 12 another has chance 13 Fill in the blanks using one phrase from each pair below to make two true sentences Write out both sentences
If you want to find the chance that at least one of the two events both events will happen check to see if they are independent mutually exclusive If so you can add multiply the chances
Correct Sentence 1 If you want to find the chance that at least one of the two events will happen check to see if they are If so you can _ the chances
Correct Sentence 2 If you want to find the chance that both events will happen check to see if they are If so you can the chances
Question 5 ChanceProbability V (4 Points)
A coin is tossed 10 times Circle your answer
1 The chance of getting 10 heads in a row is 11024 True False
2 Given that the first 9 tosses were heads the chance of getting 10 heads in a row is -12 True False
2
Statistics 1040 Sections 007 amp 009 Quiz i (20 Points)
Friday October 26 2007
Your Name ~---------
Question 1 Law of Averages I (2 Points)
A box contains 10000 tickets 4000 [Q] s and 6000 [I] so And 10000 draws will be made at random with replacement from this box Which of the following best describes the situation Circle your answer You dont have to provide any explanations
1 The number of ls will be 6000 exactly
2 The number of ls is very likely to equal 6000 but there is also some small chance that it will not be equal to 6000
3 The number of ls is likely to be different from 6000 but the difference is likely to be small compared to 10000
Question 2 Law of Averages II (8 Points)
Circle your answer for each of the following four parts You dont have to provide any explanations
1 (2 Points) A die will be rolled some number of times and you win $1 if it shows an ace ( [J ) more than 20 of the time
Which is better 60 rolls or 600 rolls
2 (2 Points) As in 1) but you win the dollar if the percentage of aces is more than 15
Which is better 60 rolls or 600 rolls
3 (2 Points) As in 1) but you win the dollar if the percentage of aces is between 15 and 20
Which is better 60 rolls or 600 rolls
4 (2 Points) As in 1) but you win the dollar if the percentage of aces is exactly 16imiddot
Which is better 60 rolls or 600 rolls
1
Question 3 The Expected Value and Standard Error (10 Points)
One hundred draws are made at random with replacement from the box
1 (1 Point) If the sum of the draws is 321 what is their average
2 (1 Point) If the average of the draws is 378 what is the sum
3 (8 Points) Estimate the chance that the average of the draws is between 3 and 4 You have to make use of the normal curve to answer this part Show your work
Formulas
sum of all numbers in box box average =
how many numbers in box
box SD = Javerage of (deviations from box average)2]
EVsum = number of draws x box average
SEsum = vnumber of draws X box SD-)
2
Tablesmiddot
A NORMALTABLB
z iN- 1~ Ar~a
aoo f I (so 1 86Jj4 tQO- ~ ~13() 005 399 l 5S I 8789 31 ~ 99111 010 791 ltiOmiddot 89-04 3 fO- 99Jm6 015 IL92 165 ~ 9Ol1 3~J 99131 020 15amp5 170 9109 320 99~
O~2S 1914 L1S 9L99 3bull25 9988S O~30 2348 t80 92fU 339 99~903 035 t 21~31 t8S 93j1 335 J 99919
040 31JJ8 190 9426 ]40 99933 O~4S ]4I~13 ~ ~ ~ 195 MJ18 345 99944
1 O~SO 3829 200 9545 350 99953 O~5S 4177 1 2~05 9596 3S j 99961 O1jO i 4S~ I 210 43 36Q ~ 99968 o~6S GA3 215 middot9JiBe 3 99914 010 SI61 210 9112 J70 99~91
075 5467 225 9756 31S 99ta2 Z~30 ~ ~ 9186 1 380 99986 l~ 135 9812 middotjU 99bullbull
O~90 6319 240 983(i 390 99990 O~9S 6579 2~4S 917 3~9S 99991lt
100 6827 250 9816 400 999931los r 7063 25S 9892 405 999949 110 1JJ1 2M 9Ull 4(0 9999il
11amplt t Aft middot20 IIS 1499 2w 7~ 4 15 ~9961 120 bull 7699 210 ~11 420 9999ll
fmiddot2S 1881 t 27S 9940 130 8Oq4 i ~IO 9949 1~3S 8130 285 9956 140 imiddot aJss 190 9963 14S IS29 2+95 99611
3
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~- ~~ - - - bull - -- -- - shy
Statistics 1040 Sections 007 amp 009 Quiz 9 (20 Points)
Friday November 2 2007
Your Name
Question 1 Normal Approximation for Probability Histograms I (12 Points)
A programmer is working on a new program COIN to simulate tossing a coin As a preliminary test he sets up the programto do one million tosses The program returns with a count of 502015 heads The programmer looks at this and thinks Hmmm Two thousand and fifteen off Thats a lot No wait Compare it to the million Two thousand - forget the fifteen - out of a million is two out of a thousand Thats one in five hundred One fifth of a percent Very small Good COIN passes
Do you agree that COIN passes Answer yes or no and explain You should use box model calculations to support your answer
Please turn over
1
Question 2 Normal Approximation for Probability Histograms II (8 Points)
A coin is tossed 100 times True or false Just circle your answer You dont have to give any explanation Answer each of the following questions separately
1 The expected value for the number of heads is 50
True False
2 The expected value for the number of heads is 50 give or take 5 or so
True False
3 The number of heads will be 50
True False
4 The number of heads will be around 50 give or take 2 or so
True False
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets in the box
fraction fractionSD = (bigger - smaller) x
bigger x
smaller
Shortcut formulas for a box that contains only [Q] s and ITJ s
number of ITJ s average =
how many tIckets In the box
fraction fraction SD = of [] s x of [Q] s
2
Tablesmiddot
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155 160 165 170
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300 99730 3M ~ 99171 10lt 99806 3J 99337 )20 99~
02$ 030 03S 040 (tIS
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1914shy231 2731 3118 3473
11S 9199 180 2St L8S I 9351 190 9426 L95 9488 ~
325 3~30
335 340 345
99885 99~903
99919 99933
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t 4l11 i 4S IS
4843 s1~61
1~(JQ ~45 205 9596 2bull10 9643 215 9684210 ~ 9722
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9756 9186 9812
31~ 380 31S
999amp2 9Ct986 99918
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390 39S
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999931 999949
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9940 9949 99S()
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415 430 435 4lt40 4)1
middot 999919 i 99middot99~
99~ 999989 ~ 99~9991
3
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Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
~ J _ __ ~ bullbull
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Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
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middot Question 2 Controlled ExperimentsObservational Studies II (6 Points)
In 1990 four passengers were killed by crashes on commuter airlines compared to 39 killed on scheduled carriers (like United TWA and so forth) True or false Circle your answer and explain the data show that if you have to fly it is safer to do so on a commuter airline
2
----------
Statistics 1040 Sections 007 amp 009 Quiz 2 (20 Points)
Friday September 7 2007
Your Name
Question 1 Histograms (14 Points)
The following table is for the gestational age of 1210 babies
Gestational Age 230-250 250-270 270-290 290310 310-330
Number 47
206 731 199 27
Draw a histogram for these data on the graph paper provided Make sure to label the axes
I I I
bull WFF bull I - - -~-
bull -
f
I I I I T I i I I
bull I I
-= 0 I I
IT I I T I 11 I I I
mU
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II
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= 1m= I I
m I
I I I I I I
Please turn over
1
f
Question 2 Observational Studies Controlled Experiments (6 Points)
For each of the following studies determine whether the study in question was a randomshyized controlled experiment or an observational study (circle the correct answer)
bull Twenty male employees and twenty female employees participate in research deshysigned to compare attitudes towards the Social Security System of men and women Each individual responds to a series of questions on a survey Mean scores are computed for men and for women
randomized controlled experiment observational study
bull A researcher wants to learn whether regularly taking zinc supplements may reduce the risk of getting a cold Volunteers in this study chose to (or chose not to) take a zinc supplement
randomized controlled experiment observational study
bull A researcher wants to learn about whether computer simulations help students betshyter understand statistical concepts She puts the names of 20 volunteers into a box and randomly draws the names of 10 people who will use computer simulations to learn statistical concepts The other 10 study participants will use a conventional approach without computer simulations to learn the same concepts
randomized controlled experiment observational study
2
Statistics 1040 Sections 007 amp 009 Quiz 3 (20 Points)
Friday September 142007
Your Name ------------ shy
Question 1 The Average and the SDI (10 Points)
Here is a list of numbers
07 1698 32 54 08 77 63 22 41 81 65 37 06 69 99 88 31 57 91
1 Without doing any arithmetic guess whether the average is around (i) 1 (ii) 5 or (iii) 10 Circle your answer and explain
2 Without doing any arithmetic guess whether the SD is around (i) 1 (ii) 3 or (iii) 6 Circle your answer and explain
Question 2 The Average and the SD II (10 Points)
A study on college students found that the men had an average weight of about 66 kg and an SD of about 9 kg The women had an average weight of about 55kg and an SD of about 9 kg (Note that 1 kg = 221b)
1 Just roughly what percentage of the men weighted between 57 kg and 75 kg Answer Fill in your answer and exp~ain
2 If you took the men and women together would the SD of their weights be (i) smaller than 9 kg (ii) just about 9 kg or (iii) bigger than 9 kg Circle your answer and explain
1
Statistics 1040 Sections 007 amp 009 Quiz 4 (20 Points)
Friday September 21 2007
Your Name _------------- shy
Question 1 Normal Approximation for Data(20 Points)
The Graduate Record Examination (GRE) is a test taken by college students who intend to pursue a graduate degree in the United States For around 428000 examinees who took the General GRE Test in 2001-02 the mean for the verbal ability portion of the exam was around 470 and the standard deviation was around 125 We can assume that the histogram follows a normal curve Show your work
bull (7 Points) The percentage of examinees who scored less than 420 on the GRE test is roughly
bull (7 Points) The percentage of examinees who scored between 370 and 645 is about
bull (6 Points) In order to be among the top 4 a student must have obtained a minimum GRE score of about --- shy
) Please turn over
1
-I
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Tablesmiddot )
A NORMAL TABLE
z Area z Area z Area
000 o 150 8664 300middot 99730 005shy 399 155 8789 30j 99771 010 797 160middot 8904 31099806 015 1192 165 9011 Jl~ 99837 020 1585 170 9109 320 99863
025 1914 175 9199 325 99885 030 2358 180 9281 330 99903 035 2137 185 9357 335 99919 040middot 3108 190middot 9426 340 99933 045 3473 195 9488 345 99944
050 3829 200 9545 350 99953 055 4177 205 9596 355 j 99961
I 060 4515 210 9643 360 99968 065 4843 215 9684 365 99974 070 5161 220 9122 370 99978
075 5467 225 9156 375 99982 080 5763 230 9786 380 99986 0~85 middot6(t47 235 9812 385 99988
~ bull~-- 090 6319 240 9836 390 99990 j
0~95 6579 245 9857 395 99992 I
100 6827 250 9816 400 999931 j 105 7063 255 9892 405 999949
110 7287 260 9907 410 999959 ~ 115 7499 265 9920 415 999967middot
I 120 7699 270 9931 420 999913f
I 125 7887 275 9940 425 999919 130 8064 i 280 9949 430 999983
) ~gt 135 8230 285 9956 435 1999986
440 middot999989middotmiddot140 i 8385 290 9963 145 ~8529 295 996middot8 445 99999-1
Statistics 1040 Sections 007 amp 009 Quiz 5 (20 Points)
Friday September 28 2007
Your Name ------------- shy
Questionmiddot 1 Measurement Error (8 Points)
You send a yardstick to a local laboratory for calibration asking that the procedure be repeated three times They report the following values
3596 inches 3601 inches 3603 inches
If you send the yardstick back for a fourth calibration you would expect to get 36 inches give or take
(a) 01 inches or so (b) 03 inches or so (c) 06inches or so
Circle your answer and explain
Question 2 Correlation (6 Points)
A teaching assistant gives a quiz to his section There are 10 questions on the quiz and no part credit is given After grading the papers the TA writes down for each student the number of questions the student got right and the number wrong The average number of right answers is 64 with an SD of 20 the average nUIILberof wrong answers is 36 with the same SD of 20
The correlation coefficient between the number of right answers andthe number of wrong answers is
(a) exactly 0 (b) -050 (c) +050 (d) -10 (e) +10 (f) -20 (g) +20
(h) cant tell without the data
Circle your answer and explain
Please turn over
1
Question 3 Correlation (6 Points)
For women age 25 and over in the US in 2005 the relationship between age and educashytionallevel (years of schooling completed) can be summarized as follows
average age ~ 50 years SD ~ 16 years average ed level ~ 132 years SD ~ 30 years r ~ -020
True or false and explain As you get older you become less educated If this statement is false what accounts for the negative correlation
Formulas
sum of all numbers avg = ----------shy
how many numbers )
SD = Javerage of [(deviations from avg) 2]
2
Statistics 1040 Sections 007 amp 009 Quiz 6 (20 Points)
Friday October 12 2007
Your Name -----~-----
Question 1 Regression (20 Points)
A selection of 65 varieties of cereal were tested for calories and sodium (in milligrams) for an one-cup serving The results can be summarized as follows
Average sodium - 240 mg SD = 131 mg Average calories = 149 calories SD = 62 calories r = 053
Show your work
1 (7 Points) Find the equation of the regression line for predicting number of mg sodium in an one-cup serving of cereals from calories
2 (4 Points) Predict the number of mg sodium in an one-cup serving of cereals that has 200 calories per cup
Please turn over
1
3 (5 Points) Find the rms error for predicting mg sodium from calories
4 (4 Points) Explain why it would not be a good idea to use the information in the question to estimate the amount of sodium for a cereal with 350 calories per cup
Formulas
rms error =Jl- r 2 x SDy
SD slope = r x --y intercept = avgy - slope x avgxSDx
)
2
----------
- - ~~~~~~_-
Statistics 1040 Sections 007 amp 009 Quiz 7 (20 Points)
Monday October 22 2007
Your Name
Question 1 ChanceProbability I (6 Points)
A deck of cards is shuffled and the top two cards are placed face down on a table Circle your answer
1 There is a 1 chance in 52 for the first card to be the ace of clubs True False
2 There is a 1 chance in 52 for the second card to be the ace of diamonds True False
3 The chance of getting the ace of clubs and then the ace of diamonds is 152 xl52 True False
~lt~J Question 2 ChanceProbability II (3 Points)
A coin is tossed six times Two possible sequences of results are
(i) H T T H T H (ii) H H H H H H
(The coin must land on H or T in the order given H = heads T = tails)
Which of the following is correct
Circle your answer
1 Sequence (i) is more likely
2 Sequence (ii) is more likely
3 Both sequences are equally likely
Please turn over
1
~ - -- _ -- -
Question 3 ChanceProbability III (3 Points)
Two cards will be dealt off the top of a well-shuffled deck You have a choice
(i) To win $1 if at least one of the two cards is a queen
(ii) To win $1 if the first card is a queen
Circle your answer
1 Option (i) is better for winning
2 Option (ii) is better for winning
3 Both options are equally good for winning
Question 4 ChanceProbability IV (4 Points)
One event has chance 12 another has chance 13 Fill in the blanks using one phrase from each pair below to make two true sentences Write out both sentences
If you want to find the chance that at least one of the two events both events will happen check to see if they are independent mutually exclusive If so you can add multiply the chances
Correct Sentence 1 If you want to find the chance that at least one of the two events will happen check to see if they are If so you can _ the chances
Correct Sentence 2 If you want to find the chance that both events will happen check to see if they are If so you can the chances
Question 5 ChanceProbability V (4 Points)
A coin is tossed 10 times Circle your answer
1 The chance of getting 10 heads in a row is 11024 True False
2 Given that the first 9 tosses were heads the chance of getting 10 heads in a row is -12 True False
2
Statistics 1040 Sections 007 amp 009 Quiz i (20 Points)
Friday October 26 2007
Your Name ~---------
Question 1 Law of Averages I (2 Points)
A box contains 10000 tickets 4000 [Q] s and 6000 [I] so And 10000 draws will be made at random with replacement from this box Which of the following best describes the situation Circle your answer You dont have to provide any explanations
1 The number of ls will be 6000 exactly
2 The number of ls is very likely to equal 6000 but there is also some small chance that it will not be equal to 6000
3 The number of ls is likely to be different from 6000 but the difference is likely to be small compared to 10000
Question 2 Law of Averages II (8 Points)
Circle your answer for each of the following four parts You dont have to provide any explanations
1 (2 Points) A die will be rolled some number of times and you win $1 if it shows an ace ( [J ) more than 20 of the time
Which is better 60 rolls or 600 rolls
2 (2 Points) As in 1) but you win the dollar if the percentage of aces is more than 15
Which is better 60 rolls or 600 rolls
3 (2 Points) As in 1) but you win the dollar if the percentage of aces is between 15 and 20
Which is better 60 rolls or 600 rolls
4 (2 Points) As in 1) but you win the dollar if the percentage of aces is exactly 16imiddot
Which is better 60 rolls or 600 rolls
1
Question 3 The Expected Value and Standard Error (10 Points)
One hundred draws are made at random with replacement from the box
1 (1 Point) If the sum of the draws is 321 what is their average
2 (1 Point) If the average of the draws is 378 what is the sum
3 (8 Points) Estimate the chance that the average of the draws is between 3 and 4 You have to make use of the normal curve to answer this part Show your work
Formulas
sum of all numbers in box box average =
how many numbers in box
box SD = Javerage of (deviations from box average)2]
EVsum = number of draws x box average
SEsum = vnumber of draws X box SD-)
2
Tablesmiddot
A NORMALTABLB
z iN- 1~ Ar~a
aoo f I (so 1 86Jj4 tQO- ~ ~13() 005 399 l 5S I 8789 31 ~ 99111 010 791 ltiOmiddot 89-04 3 fO- 99Jm6 015 IL92 165 ~ 9Ol1 3~J 99131 020 15amp5 170 9109 320 99~
O~2S 1914 L1S 9L99 3bull25 9988S O~30 2348 t80 92fU 339 99~903 035 t 21~31 t8S 93j1 335 J 99919
040 31JJ8 190 9426 ]40 99933 O~4S ]4I~13 ~ ~ ~ 195 MJ18 345 99944
1 O~SO 3829 200 9545 350 99953 O~5S 4177 1 2~05 9596 3S j 99961 O1jO i 4S~ I 210 43 36Q ~ 99968 o~6S GA3 215 middot9JiBe 3 99914 010 SI61 210 9112 J70 99~91
075 5467 225 9756 31S 99ta2 Z~30 ~ ~ 9186 1 380 99986 l~ 135 9812 middotjU 99bullbull
O~90 6319 240 983(i 390 99990 O~9S 6579 2~4S 917 3~9S 99991lt
100 6827 250 9816 400 999931los r 7063 25S 9892 405 999949 110 1JJ1 2M 9Ull 4(0 9999il
11amplt t Aft middot20 IIS 1499 2w 7~ 4 15 ~9961 120 bull 7699 210 ~11 420 9999ll
fmiddot2S 1881 t 27S 9940 130 8Oq4 i ~IO 9949 1~3S 8130 285 9956 140 imiddot aJss 190 9963 14S IS29 2+95 99611
3
-----------
~- ~~ - - - bull - -- -- - shy
Statistics 1040 Sections 007 amp 009 Quiz 9 (20 Points)
Friday November 2 2007
Your Name
Question 1 Normal Approximation for Probability Histograms I (12 Points)
A programmer is working on a new program COIN to simulate tossing a coin As a preliminary test he sets up the programto do one million tosses The program returns with a count of 502015 heads The programmer looks at this and thinks Hmmm Two thousand and fifteen off Thats a lot No wait Compare it to the million Two thousand - forget the fifteen - out of a million is two out of a thousand Thats one in five hundred One fifth of a percent Very small Good COIN passes
Do you agree that COIN passes Answer yes or no and explain You should use box model calculations to support your answer
Please turn over
1
Question 2 Normal Approximation for Probability Histograms II (8 Points)
A coin is tossed 100 times True or false Just circle your answer You dont have to give any explanation Answer each of the following questions separately
1 The expected value for the number of heads is 50
True False
2 The expected value for the number of heads is 50 give or take 5 or so
True False
3 The number of heads will be 50
True False
4 The number of heads will be around 50 give or take 2 or so
True False
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets in the box
fraction fractionSD = (bigger - smaller) x
bigger x
smaller
Shortcut formulas for a box that contains only [Q] s and ITJ s
number of ITJ s average =
how many tIckets In the box
fraction fraction SD = of [] s x of [Q] s
2
Tablesmiddot
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OU~l 8189 ~ 89JJ4 4)011
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300 99730 3M ~ 99171 10lt 99806 3J 99337 )20 99~
02$ 030 03S 040 (tIS
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11S 9199 180 2St L8S I 9351 190 9426 L95 9488 ~
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99~918
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22S 130shy23S
~ middot
9756 9186 9812
31~ 380 31S
999amp2 9Ct986 99918
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19 248
2~4S 9836 9857
390 39S
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110 1187 ltS bullbull 74~ft 120 7699
250 20SS
260265 270
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999931 999949
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290 293
9940 9949 99S()
63 9968 ~
415 430 435 4lt40 4)1
middot 999919 i 99middot99~
99~ 999989 ~ 99~9991
3
-----------
)
Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
~ J _ __ ~ bullbull
-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
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Statistics 1040 Sections 007 amp 009 Quiz 2 (20 Points)
Friday September 7 2007
Your Name
Question 1 Histograms (14 Points)
The following table is for the gestational age of 1210 babies
Gestational Age 230-250 250-270 270-290 290310 310-330
Number 47
206 731 199 27
Draw a histogram for these data on the graph paper provided Make sure to label the axes
I I I
bull WFF bull I - - -~-
bull -
f
I I I I T I i I I
bull I I
-= 0 I I
IT I I T I 11 I I I
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m I
I I I I I I
Please turn over
1
f
Question 2 Observational Studies Controlled Experiments (6 Points)
For each of the following studies determine whether the study in question was a randomshyized controlled experiment or an observational study (circle the correct answer)
bull Twenty male employees and twenty female employees participate in research deshysigned to compare attitudes towards the Social Security System of men and women Each individual responds to a series of questions on a survey Mean scores are computed for men and for women
randomized controlled experiment observational study
bull A researcher wants to learn whether regularly taking zinc supplements may reduce the risk of getting a cold Volunteers in this study chose to (or chose not to) take a zinc supplement
randomized controlled experiment observational study
bull A researcher wants to learn about whether computer simulations help students betshyter understand statistical concepts She puts the names of 20 volunteers into a box and randomly draws the names of 10 people who will use computer simulations to learn statistical concepts The other 10 study participants will use a conventional approach without computer simulations to learn the same concepts
randomized controlled experiment observational study
2
Statistics 1040 Sections 007 amp 009 Quiz 3 (20 Points)
Friday September 142007
Your Name ------------ shy
Question 1 The Average and the SDI (10 Points)
Here is a list of numbers
07 1698 32 54 08 77 63 22 41 81 65 37 06 69 99 88 31 57 91
1 Without doing any arithmetic guess whether the average is around (i) 1 (ii) 5 or (iii) 10 Circle your answer and explain
2 Without doing any arithmetic guess whether the SD is around (i) 1 (ii) 3 or (iii) 6 Circle your answer and explain
Question 2 The Average and the SD II (10 Points)
A study on college students found that the men had an average weight of about 66 kg and an SD of about 9 kg The women had an average weight of about 55kg and an SD of about 9 kg (Note that 1 kg = 221b)
1 Just roughly what percentage of the men weighted between 57 kg and 75 kg Answer Fill in your answer and exp~ain
2 If you took the men and women together would the SD of their weights be (i) smaller than 9 kg (ii) just about 9 kg or (iii) bigger than 9 kg Circle your answer and explain
1
Statistics 1040 Sections 007 amp 009 Quiz 4 (20 Points)
Friday September 21 2007
Your Name _------------- shy
Question 1 Normal Approximation for Data(20 Points)
The Graduate Record Examination (GRE) is a test taken by college students who intend to pursue a graduate degree in the United States For around 428000 examinees who took the General GRE Test in 2001-02 the mean for the verbal ability portion of the exam was around 470 and the standard deviation was around 125 We can assume that the histogram follows a normal curve Show your work
bull (7 Points) The percentage of examinees who scored less than 420 on the GRE test is roughly
bull (7 Points) The percentage of examinees who scored between 370 and 645 is about
bull (6 Points) In order to be among the top 4 a student must have obtained a minimum GRE score of about --- shy
) Please turn over
1
-I
Flt~=~~~~~-~~~~gt~jmiddotCpound~l~~~dili
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z Area z Area z Area
000 o 150 8664 300middot 99730 005shy 399 155 8789 30j 99771 010 797 160middot 8904 31099806 015 1192 165 9011 Jl~ 99837 020 1585 170 9109 320 99863
025 1914 175 9199 325 99885 030 2358 180 9281 330 99903 035 2137 185 9357 335 99919 040middot 3108 190middot 9426 340 99933 045 3473 195 9488 345 99944
050 3829 200 9545 350 99953 055 4177 205 9596 355 j 99961
I 060 4515 210 9643 360 99968 065 4843 215 9684 365 99974 070 5161 220 9122 370 99978
075 5467 225 9156 375 99982 080 5763 230 9786 380 99986 0~85 middot6(t47 235 9812 385 99988
~ bull~-- 090 6319 240 9836 390 99990 j
0~95 6579 245 9857 395 99992 I
100 6827 250 9816 400 999931 j 105 7063 255 9892 405 999949
110 7287 260 9907 410 999959 ~ 115 7499 265 9920 415 999967middot
I 120 7699 270 9931 420 999913f
I 125 7887 275 9940 425 999919 130 8064 i 280 9949 430 999983
) ~gt 135 8230 285 9956 435 1999986
440 middot999989middotmiddot140 i 8385 290 9963 145 ~8529 295 996middot8 445 99999-1
Statistics 1040 Sections 007 amp 009 Quiz 5 (20 Points)
Friday September 28 2007
Your Name ------------- shy
Questionmiddot 1 Measurement Error (8 Points)
You send a yardstick to a local laboratory for calibration asking that the procedure be repeated three times They report the following values
3596 inches 3601 inches 3603 inches
If you send the yardstick back for a fourth calibration you would expect to get 36 inches give or take
(a) 01 inches or so (b) 03 inches or so (c) 06inches or so
Circle your answer and explain
Question 2 Correlation (6 Points)
A teaching assistant gives a quiz to his section There are 10 questions on the quiz and no part credit is given After grading the papers the TA writes down for each student the number of questions the student got right and the number wrong The average number of right answers is 64 with an SD of 20 the average nUIILberof wrong answers is 36 with the same SD of 20
The correlation coefficient between the number of right answers andthe number of wrong answers is
(a) exactly 0 (b) -050 (c) +050 (d) -10 (e) +10 (f) -20 (g) +20
(h) cant tell without the data
Circle your answer and explain
Please turn over
1
Question 3 Correlation (6 Points)
For women age 25 and over in the US in 2005 the relationship between age and educashytionallevel (years of schooling completed) can be summarized as follows
average age ~ 50 years SD ~ 16 years average ed level ~ 132 years SD ~ 30 years r ~ -020
True or false and explain As you get older you become less educated If this statement is false what accounts for the negative correlation
Formulas
sum of all numbers avg = ----------shy
how many numbers )
SD = Javerage of [(deviations from avg) 2]
2
Statistics 1040 Sections 007 amp 009 Quiz 6 (20 Points)
Friday October 12 2007
Your Name -----~-----
Question 1 Regression (20 Points)
A selection of 65 varieties of cereal were tested for calories and sodium (in milligrams) for an one-cup serving The results can be summarized as follows
Average sodium - 240 mg SD = 131 mg Average calories = 149 calories SD = 62 calories r = 053
Show your work
1 (7 Points) Find the equation of the regression line for predicting number of mg sodium in an one-cup serving of cereals from calories
2 (4 Points) Predict the number of mg sodium in an one-cup serving of cereals that has 200 calories per cup
Please turn over
1
3 (5 Points) Find the rms error for predicting mg sodium from calories
4 (4 Points) Explain why it would not be a good idea to use the information in the question to estimate the amount of sodium for a cereal with 350 calories per cup
Formulas
rms error =Jl- r 2 x SDy
SD slope = r x --y intercept = avgy - slope x avgxSDx
)
2
----------
- - ~~~~~~_-
Statistics 1040 Sections 007 amp 009 Quiz 7 (20 Points)
Monday October 22 2007
Your Name
Question 1 ChanceProbability I (6 Points)
A deck of cards is shuffled and the top two cards are placed face down on a table Circle your answer
1 There is a 1 chance in 52 for the first card to be the ace of clubs True False
2 There is a 1 chance in 52 for the second card to be the ace of diamonds True False
3 The chance of getting the ace of clubs and then the ace of diamonds is 152 xl52 True False
~lt~J Question 2 ChanceProbability II (3 Points)
A coin is tossed six times Two possible sequences of results are
(i) H T T H T H (ii) H H H H H H
(The coin must land on H or T in the order given H = heads T = tails)
Which of the following is correct
Circle your answer
1 Sequence (i) is more likely
2 Sequence (ii) is more likely
3 Both sequences are equally likely
Please turn over
1
~ - -- _ -- -
Question 3 ChanceProbability III (3 Points)
Two cards will be dealt off the top of a well-shuffled deck You have a choice
(i) To win $1 if at least one of the two cards is a queen
(ii) To win $1 if the first card is a queen
Circle your answer
1 Option (i) is better for winning
2 Option (ii) is better for winning
3 Both options are equally good for winning
Question 4 ChanceProbability IV (4 Points)
One event has chance 12 another has chance 13 Fill in the blanks using one phrase from each pair below to make two true sentences Write out both sentences
If you want to find the chance that at least one of the two events both events will happen check to see if they are independent mutually exclusive If so you can add multiply the chances
Correct Sentence 1 If you want to find the chance that at least one of the two events will happen check to see if they are If so you can _ the chances
Correct Sentence 2 If you want to find the chance that both events will happen check to see if they are If so you can the chances
Question 5 ChanceProbability V (4 Points)
A coin is tossed 10 times Circle your answer
1 The chance of getting 10 heads in a row is 11024 True False
2 Given that the first 9 tosses were heads the chance of getting 10 heads in a row is -12 True False
2
Statistics 1040 Sections 007 amp 009 Quiz i (20 Points)
Friday October 26 2007
Your Name ~---------
Question 1 Law of Averages I (2 Points)
A box contains 10000 tickets 4000 [Q] s and 6000 [I] so And 10000 draws will be made at random with replacement from this box Which of the following best describes the situation Circle your answer You dont have to provide any explanations
1 The number of ls will be 6000 exactly
2 The number of ls is very likely to equal 6000 but there is also some small chance that it will not be equal to 6000
3 The number of ls is likely to be different from 6000 but the difference is likely to be small compared to 10000
Question 2 Law of Averages II (8 Points)
Circle your answer for each of the following four parts You dont have to provide any explanations
1 (2 Points) A die will be rolled some number of times and you win $1 if it shows an ace ( [J ) more than 20 of the time
Which is better 60 rolls or 600 rolls
2 (2 Points) As in 1) but you win the dollar if the percentage of aces is more than 15
Which is better 60 rolls or 600 rolls
3 (2 Points) As in 1) but you win the dollar if the percentage of aces is between 15 and 20
Which is better 60 rolls or 600 rolls
4 (2 Points) As in 1) but you win the dollar if the percentage of aces is exactly 16imiddot
Which is better 60 rolls or 600 rolls
1
Question 3 The Expected Value and Standard Error (10 Points)
One hundred draws are made at random with replacement from the box
1 (1 Point) If the sum of the draws is 321 what is their average
2 (1 Point) If the average of the draws is 378 what is the sum
3 (8 Points) Estimate the chance that the average of the draws is between 3 and 4 You have to make use of the normal curve to answer this part Show your work
Formulas
sum of all numbers in box box average =
how many numbers in box
box SD = Javerage of (deviations from box average)2]
EVsum = number of draws x box average
SEsum = vnumber of draws X box SD-)
2
Tablesmiddot
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O~2S 1914 L1S 9L99 3bull25 9988S O~30 2348 t80 92fU 339 99~903 035 t 21~31 t8S 93j1 335 J 99919
040 31JJ8 190 9426 ]40 99933 O~4S ]4I~13 ~ ~ ~ 195 MJ18 345 99944
1 O~SO 3829 200 9545 350 99953 O~5S 4177 1 2~05 9596 3S j 99961 O1jO i 4S~ I 210 43 36Q ~ 99968 o~6S GA3 215 middot9JiBe 3 99914 010 SI61 210 9112 J70 99~91
075 5467 225 9756 31S 99ta2 Z~30 ~ ~ 9186 1 380 99986 l~ 135 9812 middotjU 99bullbull
O~90 6319 240 983(i 390 99990 O~9S 6579 2~4S 917 3~9S 99991lt
100 6827 250 9816 400 999931los r 7063 25S 9892 405 999949 110 1JJ1 2M 9Ull 4(0 9999il
11amplt t Aft middot20 IIS 1499 2w 7~ 4 15 ~9961 120 bull 7699 210 ~11 420 9999ll
fmiddot2S 1881 t 27S 9940 130 8Oq4 i ~IO 9949 1~3S 8130 285 9956 140 imiddot aJss 190 9963 14S IS29 2+95 99611
3
-----------
~- ~~ - - - bull - -- -- - shy
Statistics 1040 Sections 007 amp 009 Quiz 9 (20 Points)
Friday November 2 2007
Your Name
Question 1 Normal Approximation for Probability Histograms I (12 Points)
A programmer is working on a new program COIN to simulate tossing a coin As a preliminary test he sets up the programto do one million tosses The program returns with a count of 502015 heads The programmer looks at this and thinks Hmmm Two thousand and fifteen off Thats a lot No wait Compare it to the million Two thousand - forget the fifteen - out of a million is two out of a thousand Thats one in five hundred One fifth of a percent Very small Good COIN passes
Do you agree that COIN passes Answer yes or no and explain You should use box model calculations to support your answer
Please turn over
1
Question 2 Normal Approximation for Probability Histograms II (8 Points)
A coin is tossed 100 times True or false Just circle your answer You dont have to give any explanation Answer each of the following questions separately
1 The expected value for the number of heads is 50
True False
2 The expected value for the number of heads is 50 give or take 5 or so
True False
3 The number of heads will be 50
True False
4 The number of heads will be around 50 give or take 2 or so
True False
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets in the box
fraction fractionSD = (bigger - smaller) x
bigger x
smaller
Shortcut formulas for a box that contains only [Q] s and ITJ s
number of ITJ s average =
how many tIckets In the box
fraction fraction SD = of [] s x of [Q] s
2
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-----------
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Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
~ J _ __ ~ bullbull
-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
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Question 2 Observational Studies Controlled Experiments (6 Points)
For each of the following studies determine whether the study in question was a randomshyized controlled experiment or an observational study (circle the correct answer)
bull Twenty male employees and twenty female employees participate in research deshysigned to compare attitudes towards the Social Security System of men and women Each individual responds to a series of questions on a survey Mean scores are computed for men and for women
randomized controlled experiment observational study
bull A researcher wants to learn whether regularly taking zinc supplements may reduce the risk of getting a cold Volunteers in this study chose to (or chose not to) take a zinc supplement
randomized controlled experiment observational study
bull A researcher wants to learn about whether computer simulations help students betshyter understand statistical concepts She puts the names of 20 volunteers into a box and randomly draws the names of 10 people who will use computer simulations to learn statistical concepts The other 10 study participants will use a conventional approach without computer simulations to learn the same concepts
randomized controlled experiment observational study
2
Statistics 1040 Sections 007 amp 009 Quiz 3 (20 Points)
Friday September 142007
Your Name ------------ shy
Question 1 The Average and the SDI (10 Points)
Here is a list of numbers
07 1698 32 54 08 77 63 22 41 81 65 37 06 69 99 88 31 57 91
1 Without doing any arithmetic guess whether the average is around (i) 1 (ii) 5 or (iii) 10 Circle your answer and explain
2 Without doing any arithmetic guess whether the SD is around (i) 1 (ii) 3 or (iii) 6 Circle your answer and explain
Question 2 The Average and the SD II (10 Points)
A study on college students found that the men had an average weight of about 66 kg and an SD of about 9 kg The women had an average weight of about 55kg and an SD of about 9 kg (Note that 1 kg = 221b)
1 Just roughly what percentage of the men weighted between 57 kg and 75 kg Answer Fill in your answer and exp~ain
2 If you took the men and women together would the SD of their weights be (i) smaller than 9 kg (ii) just about 9 kg or (iii) bigger than 9 kg Circle your answer and explain
1
Statistics 1040 Sections 007 amp 009 Quiz 4 (20 Points)
Friday September 21 2007
Your Name _------------- shy
Question 1 Normal Approximation for Data(20 Points)
The Graduate Record Examination (GRE) is a test taken by college students who intend to pursue a graduate degree in the United States For around 428000 examinees who took the General GRE Test in 2001-02 the mean for the verbal ability portion of the exam was around 470 and the standard deviation was around 125 We can assume that the histogram follows a normal curve Show your work
bull (7 Points) The percentage of examinees who scored less than 420 on the GRE test is roughly
bull (7 Points) The percentage of examinees who scored between 370 and 645 is about
bull (6 Points) In order to be among the top 4 a student must have obtained a minimum GRE score of about --- shy
) Please turn over
1
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z Area z Area z Area
000 o 150 8664 300middot 99730 005shy 399 155 8789 30j 99771 010 797 160middot 8904 31099806 015 1192 165 9011 Jl~ 99837 020 1585 170 9109 320 99863
025 1914 175 9199 325 99885 030 2358 180 9281 330 99903 035 2137 185 9357 335 99919 040middot 3108 190middot 9426 340 99933 045 3473 195 9488 345 99944
050 3829 200 9545 350 99953 055 4177 205 9596 355 j 99961
I 060 4515 210 9643 360 99968 065 4843 215 9684 365 99974 070 5161 220 9122 370 99978
075 5467 225 9156 375 99982 080 5763 230 9786 380 99986 0~85 middot6(t47 235 9812 385 99988
~ bull~-- 090 6319 240 9836 390 99990 j
0~95 6579 245 9857 395 99992 I
100 6827 250 9816 400 999931 j 105 7063 255 9892 405 999949
110 7287 260 9907 410 999959 ~ 115 7499 265 9920 415 999967middot
I 120 7699 270 9931 420 999913f
I 125 7887 275 9940 425 999919 130 8064 i 280 9949 430 999983
) ~gt 135 8230 285 9956 435 1999986
440 middot999989middotmiddot140 i 8385 290 9963 145 ~8529 295 996middot8 445 99999-1
Statistics 1040 Sections 007 amp 009 Quiz 5 (20 Points)
Friday September 28 2007
Your Name ------------- shy
Questionmiddot 1 Measurement Error (8 Points)
You send a yardstick to a local laboratory for calibration asking that the procedure be repeated three times They report the following values
3596 inches 3601 inches 3603 inches
If you send the yardstick back for a fourth calibration you would expect to get 36 inches give or take
(a) 01 inches or so (b) 03 inches or so (c) 06inches or so
Circle your answer and explain
Question 2 Correlation (6 Points)
A teaching assistant gives a quiz to his section There are 10 questions on the quiz and no part credit is given After grading the papers the TA writes down for each student the number of questions the student got right and the number wrong The average number of right answers is 64 with an SD of 20 the average nUIILberof wrong answers is 36 with the same SD of 20
The correlation coefficient between the number of right answers andthe number of wrong answers is
(a) exactly 0 (b) -050 (c) +050 (d) -10 (e) +10 (f) -20 (g) +20
(h) cant tell without the data
Circle your answer and explain
Please turn over
1
Question 3 Correlation (6 Points)
For women age 25 and over in the US in 2005 the relationship between age and educashytionallevel (years of schooling completed) can be summarized as follows
average age ~ 50 years SD ~ 16 years average ed level ~ 132 years SD ~ 30 years r ~ -020
True or false and explain As you get older you become less educated If this statement is false what accounts for the negative correlation
Formulas
sum of all numbers avg = ----------shy
how many numbers )
SD = Javerage of [(deviations from avg) 2]
2
Statistics 1040 Sections 007 amp 009 Quiz 6 (20 Points)
Friday October 12 2007
Your Name -----~-----
Question 1 Regression (20 Points)
A selection of 65 varieties of cereal were tested for calories and sodium (in milligrams) for an one-cup serving The results can be summarized as follows
Average sodium - 240 mg SD = 131 mg Average calories = 149 calories SD = 62 calories r = 053
Show your work
1 (7 Points) Find the equation of the regression line for predicting number of mg sodium in an one-cup serving of cereals from calories
2 (4 Points) Predict the number of mg sodium in an one-cup serving of cereals that has 200 calories per cup
Please turn over
1
3 (5 Points) Find the rms error for predicting mg sodium from calories
4 (4 Points) Explain why it would not be a good idea to use the information in the question to estimate the amount of sodium for a cereal with 350 calories per cup
Formulas
rms error =Jl- r 2 x SDy
SD slope = r x --y intercept = avgy - slope x avgxSDx
)
2
----------
- - ~~~~~~_-
Statistics 1040 Sections 007 amp 009 Quiz 7 (20 Points)
Monday October 22 2007
Your Name
Question 1 ChanceProbability I (6 Points)
A deck of cards is shuffled and the top two cards are placed face down on a table Circle your answer
1 There is a 1 chance in 52 for the first card to be the ace of clubs True False
2 There is a 1 chance in 52 for the second card to be the ace of diamonds True False
3 The chance of getting the ace of clubs and then the ace of diamonds is 152 xl52 True False
~lt~J Question 2 ChanceProbability II (3 Points)
A coin is tossed six times Two possible sequences of results are
(i) H T T H T H (ii) H H H H H H
(The coin must land on H or T in the order given H = heads T = tails)
Which of the following is correct
Circle your answer
1 Sequence (i) is more likely
2 Sequence (ii) is more likely
3 Both sequences are equally likely
Please turn over
1
~ - -- _ -- -
Question 3 ChanceProbability III (3 Points)
Two cards will be dealt off the top of a well-shuffled deck You have a choice
(i) To win $1 if at least one of the two cards is a queen
(ii) To win $1 if the first card is a queen
Circle your answer
1 Option (i) is better for winning
2 Option (ii) is better for winning
3 Both options are equally good for winning
Question 4 ChanceProbability IV (4 Points)
One event has chance 12 another has chance 13 Fill in the blanks using one phrase from each pair below to make two true sentences Write out both sentences
If you want to find the chance that at least one of the two events both events will happen check to see if they are independent mutually exclusive If so you can add multiply the chances
Correct Sentence 1 If you want to find the chance that at least one of the two events will happen check to see if they are If so you can _ the chances
Correct Sentence 2 If you want to find the chance that both events will happen check to see if they are If so you can the chances
Question 5 ChanceProbability V (4 Points)
A coin is tossed 10 times Circle your answer
1 The chance of getting 10 heads in a row is 11024 True False
2 Given that the first 9 tosses were heads the chance of getting 10 heads in a row is -12 True False
2
Statistics 1040 Sections 007 amp 009 Quiz i (20 Points)
Friday October 26 2007
Your Name ~---------
Question 1 Law of Averages I (2 Points)
A box contains 10000 tickets 4000 [Q] s and 6000 [I] so And 10000 draws will be made at random with replacement from this box Which of the following best describes the situation Circle your answer You dont have to provide any explanations
1 The number of ls will be 6000 exactly
2 The number of ls is very likely to equal 6000 but there is also some small chance that it will not be equal to 6000
3 The number of ls is likely to be different from 6000 but the difference is likely to be small compared to 10000
Question 2 Law of Averages II (8 Points)
Circle your answer for each of the following four parts You dont have to provide any explanations
1 (2 Points) A die will be rolled some number of times and you win $1 if it shows an ace ( [J ) more than 20 of the time
Which is better 60 rolls or 600 rolls
2 (2 Points) As in 1) but you win the dollar if the percentage of aces is more than 15
Which is better 60 rolls or 600 rolls
3 (2 Points) As in 1) but you win the dollar if the percentage of aces is between 15 and 20
Which is better 60 rolls or 600 rolls
4 (2 Points) As in 1) but you win the dollar if the percentage of aces is exactly 16imiddot
Which is better 60 rolls or 600 rolls
1
Question 3 The Expected Value and Standard Error (10 Points)
One hundred draws are made at random with replacement from the box
1 (1 Point) If the sum of the draws is 321 what is their average
2 (1 Point) If the average of the draws is 378 what is the sum
3 (8 Points) Estimate the chance that the average of the draws is between 3 and 4 You have to make use of the normal curve to answer this part Show your work
Formulas
sum of all numbers in box box average =
how many numbers in box
box SD = Javerage of (deviations from box average)2]
EVsum = number of draws x box average
SEsum = vnumber of draws X box SD-)
2
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3
-----------
~- ~~ - - - bull - -- -- - shy
Statistics 1040 Sections 007 amp 009 Quiz 9 (20 Points)
Friday November 2 2007
Your Name
Question 1 Normal Approximation for Probability Histograms I (12 Points)
A programmer is working on a new program COIN to simulate tossing a coin As a preliminary test he sets up the programto do one million tosses The program returns with a count of 502015 heads The programmer looks at this and thinks Hmmm Two thousand and fifteen off Thats a lot No wait Compare it to the million Two thousand - forget the fifteen - out of a million is two out of a thousand Thats one in five hundred One fifth of a percent Very small Good COIN passes
Do you agree that COIN passes Answer yes or no and explain You should use box model calculations to support your answer
Please turn over
1
Question 2 Normal Approximation for Probability Histograms II (8 Points)
A coin is tossed 100 times True or false Just circle your answer You dont have to give any explanation Answer each of the following questions separately
1 The expected value for the number of heads is 50
True False
2 The expected value for the number of heads is 50 give or take 5 or so
True False
3 The number of heads will be 50
True False
4 The number of heads will be around 50 give or take 2 or so
True False
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets in the box
fraction fractionSD = (bigger - smaller) x
bigger x
smaller
Shortcut formulas for a box that contains only [Q] s and ITJ s
number of ITJ s average =
how many tIckets In the box
fraction fraction SD = of [] s x of [Q] s
2
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3
-----------
)
Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
~ J _ __ ~ bullbull
-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
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Statistics 1040 Sections 007 amp 009 Quiz 3 (20 Points)
Friday September 142007
Your Name ------------ shy
Question 1 The Average and the SDI (10 Points)
Here is a list of numbers
07 1698 32 54 08 77 63 22 41 81 65 37 06 69 99 88 31 57 91
1 Without doing any arithmetic guess whether the average is around (i) 1 (ii) 5 or (iii) 10 Circle your answer and explain
2 Without doing any arithmetic guess whether the SD is around (i) 1 (ii) 3 or (iii) 6 Circle your answer and explain
Question 2 The Average and the SD II (10 Points)
A study on college students found that the men had an average weight of about 66 kg and an SD of about 9 kg The women had an average weight of about 55kg and an SD of about 9 kg (Note that 1 kg = 221b)
1 Just roughly what percentage of the men weighted between 57 kg and 75 kg Answer Fill in your answer and exp~ain
2 If you took the men and women together would the SD of their weights be (i) smaller than 9 kg (ii) just about 9 kg or (iii) bigger than 9 kg Circle your answer and explain
1
Statistics 1040 Sections 007 amp 009 Quiz 4 (20 Points)
Friday September 21 2007
Your Name _------------- shy
Question 1 Normal Approximation for Data(20 Points)
The Graduate Record Examination (GRE) is a test taken by college students who intend to pursue a graduate degree in the United States For around 428000 examinees who took the General GRE Test in 2001-02 the mean for the verbal ability portion of the exam was around 470 and the standard deviation was around 125 We can assume that the histogram follows a normal curve Show your work
bull (7 Points) The percentage of examinees who scored less than 420 on the GRE test is roughly
bull (7 Points) The percentage of examinees who scored between 370 and 645 is about
bull (6 Points) In order to be among the top 4 a student must have obtained a minimum GRE score of about --- shy
) Please turn over
1
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A NORMAL TABLE
z Area z Area z Area
000 o 150 8664 300middot 99730 005shy 399 155 8789 30j 99771 010 797 160middot 8904 31099806 015 1192 165 9011 Jl~ 99837 020 1585 170 9109 320 99863
025 1914 175 9199 325 99885 030 2358 180 9281 330 99903 035 2137 185 9357 335 99919 040middot 3108 190middot 9426 340 99933 045 3473 195 9488 345 99944
050 3829 200 9545 350 99953 055 4177 205 9596 355 j 99961
I 060 4515 210 9643 360 99968 065 4843 215 9684 365 99974 070 5161 220 9122 370 99978
075 5467 225 9156 375 99982 080 5763 230 9786 380 99986 0~85 middot6(t47 235 9812 385 99988
~ bull~-- 090 6319 240 9836 390 99990 j
0~95 6579 245 9857 395 99992 I
100 6827 250 9816 400 999931 j 105 7063 255 9892 405 999949
110 7287 260 9907 410 999959 ~ 115 7499 265 9920 415 999967middot
I 120 7699 270 9931 420 999913f
I 125 7887 275 9940 425 999919 130 8064 i 280 9949 430 999983
) ~gt 135 8230 285 9956 435 1999986
440 middot999989middotmiddot140 i 8385 290 9963 145 ~8529 295 996middot8 445 99999-1
Statistics 1040 Sections 007 amp 009 Quiz 5 (20 Points)
Friday September 28 2007
Your Name ------------- shy
Questionmiddot 1 Measurement Error (8 Points)
You send a yardstick to a local laboratory for calibration asking that the procedure be repeated three times They report the following values
3596 inches 3601 inches 3603 inches
If you send the yardstick back for a fourth calibration you would expect to get 36 inches give or take
(a) 01 inches or so (b) 03 inches or so (c) 06inches or so
Circle your answer and explain
Question 2 Correlation (6 Points)
A teaching assistant gives a quiz to his section There are 10 questions on the quiz and no part credit is given After grading the papers the TA writes down for each student the number of questions the student got right and the number wrong The average number of right answers is 64 with an SD of 20 the average nUIILberof wrong answers is 36 with the same SD of 20
The correlation coefficient between the number of right answers andthe number of wrong answers is
(a) exactly 0 (b) -050 (c) +050 (d) -10 (e) +10 (f) -20 (g) +20
(h) cant tell without the data
Circle your answer and explain
Please turn over
1
Question 3 Correlation (6 Points)
For women age 25 and over in the US in 2005 the relationship between age and educashytionallevel (years of schooling completed) can be summarized as follows
average age ~ 50 years SD ~ 16 years average ed level ~ 132 years SD ~ 30 years r ~ -020
True or false and explain As you get older you become less educated If this statement is false what accounts for the negative correlation
Formulas
sum of all numbers avg = ----------shy
how many numbers )
SD = Javerage of [(deviations from avg) 2]
2
Statistics 1040 Sections 007 amp 009 Quiz 6 (20 Points)
Friday October 12 2007
Your Name -----~-----
Question 1 Regression (20 Points)
A selection of 65 varieties of cereal were tested for calories and sodium (in milligrams) for an one-cup serving The results can be summarized as follows
Average sodium - 240 mg SD = 131 mg Average calories = 149 calories SD = 62 calories r = 053
Show your work
1 (7 Points) Find the equation of the regression line for predicting number of mg sodium in an one-cup serving of cereals from calories
2 (4 Points) Predict the number of mg sodium in an one-cup serving of cereals that has 200 calories per cup
Please turn over
1
3 (5 Points) Find the rms error for predicting mg sodium from calories
4 (4 Points) Explain why it would not be a good idea to use the information in the question to estimate the amount of sodium for a cereal with 350 calories per cup
Formulas
rms error =Jl- r 2 x SDy
SD slope = r x --y intercept = avgy - slope x avgxSDx
)
2
----------
- - ~~~~~~_-
Statistics 1040 Sections 007 amp 009 Quiz 7 (20 Points)
Monday October 22 2007
Your Name
Question 1 ChanceProbability I (6 Points)
A deck of cards is shuffled and the top two cards are placed face down on a table Circle your answer
1 There is a 1 chance in 52 for the first card to be the ace of clubs True False
2 There is a 1 chance in 52 for the second card to be the ace of diamonds True False
3 The chance of getting the ace of clubs and then the ace of diamonds is 152 xl52 True False
~lt~J Question 2 ChanceProbability II (3 Points)
A coin is tossed six times Two possible sequences of results are
(i) H T T H T H (ii) H H H H H H
(The coin must land on H or T in the order given H = heads T = tails)
Which of the following is correct
Circle your answer
1 Sequence (i) is more likely
2 Sequence (ii) is more likely
3 Both sequences are equally likely
Please turn over
1
~ - -- _ -- -
Question 3 ChanceProbability III (3 Points)
Two cards will be dealt off the top of a well-shuffled deck You have a choice
(i) To win $1 if at least one of the two cards is a queen
(ii) To win $1 if the first card is a queen
Circle your answer
1 Option (i) is better for winning
2 Option (ii) is better for winning
3 Both options are equally good for winning
Question 4 ChanceProbability IV (4 Points)
One event has chance 12 another has chance 13 Fill in the blanks using one phrase from each pair below to make two true sentences Write out both sentences
If you want to find the chance that at least one of the two events both events will happen check to see if they are independent mutually exclusive If so you can add multiply the chances
Correct Sentence 1 If you want to find the chance that at least one of the two events will happen check to see if they are If so you can _ the chances
Correct Sentence 2 If you want to find the chance that both events will happen check to see if they are If so you can the chances
Question 5 ChanceProbability V (4 Points)
A coin is tossed 10 times Circle your answer
1 The chance of getting 10 heads in a row is 11024 True False
2 Given that the first 9 tosses were heads the chance of getting 10 heads in a row is -12 True False
2
Statistics 1040 Sections 007 amp 009 Quiz i (20 Points)
Friday October 26 2007
Your Name ~---------
Question 1 Law of Averages I (2 Points)
A box contains 10000 tickets 4000 [Q] s and 6000 [I] so And 10000 draws will be made at random with replacement from this box Which of the following best describes the situation Circle your answer You dont have to provide any explanations
1 The number of ls will be 6000 exactly
2 The number of ls is very likely to equal 6000 but there is also some small chance that it will not be equal to 6000
3 The number of ls is likely to be different from 6000 but the difference is likely to be small compared to 10000
Question 2 Law of Averages II (8 Points)
Circle your answer for each of the following four parts You dont have to provide any explanations
1 (2 Points) A die will be rolled some number of times and you win $1 if it shows an ace ( [J ) more than 20 of the time
Which is better 60 rolls or 600 rolls
2 (2 Points) As in 1) but you win the dollar if the percentage of aces is more than 15
Which is better 60 rolls or 600 rolls
3 (2 Points) As in 1) but you win the dollar if the percentage of aces is between 15 and 20
Which is better 60 rolls or 600 rolls
4 (2 Points) As in 1) but you win the dollar if the percentage of aces is exactly 16imiddot
Which is better 60 rolls or 600 rolls
1
Question 3 The Expected Value and Standard Error (10 Points)
One hundred draws are made at random with replacement from the box
1 (1 Point) If the sum of the draws is 321 what is their average
2 (1 Point) If the average of the draws is 378 what is the sum
3 (8 Points) Estimate the chance that the average of the draws is between 3 and 4 You have to make use of the normal curve to answer this part Show your work
Formulas
sum of all numbers in box box average =
how many numbers in box
box SD = Javerage of (deviations from box average)2]
EVsum = number of draws x box average
SEsum = vnumber of draws X box SD-)
2
Tablesmiddot
A NORMALTABLB
z iN- 1~ Ar~a
aoo f I (so 1 86Jj4 tQO- ~ ~13() 005 399 l 5S I 8789 31 ~ 99111 010 791 ltiOmiddot 89-04 3 fO- 99Jm6 015 IL92 165 ~ 9Ol1 3~J 99131 020 15amp5 170 9109 320 99~
O~2S 1914 L1S 9L99 3bull25 9988S O~30 2348 t80 92fU 339 99~903 035 t 21~31 t8S 93j1 335 J 99919
040 31JJ8 190 9426 ]40 99933 O~4S ]4I~13 ~ ~ ~ 195 MJ18 345 99944
1 O~SO 3829 200 9545 350 99953 O~5S 4177 1 2~05 9596 3S j 99961 O1jO i 4S~ I 210 43 36Q ~ 99968 o~6S GA3 215 middot9JiBe 3 99914 010 SI61 210 9112 J70 99~91
075 5467 225 9756 31S 99ta2 Z~30 ~ ~ 9186 1 380 99986 l~ 135 9812 middotjU 99bullbull
O~90 6319 240 983(i 390 99990 O~9S 6579 2~4S 917 3~9S 99991lt
100 6827 250 9816 400 999931los r 7063 25S 9892 405 999949 110 1JJ1 2M 9Ull 4(0 9999il
11amplt t Aft middot20 IIS 1499 2w 7~ 4 15 ~9961 120 bull 7699 210 ~11 420 9999ll
fmiddot2S 1881 t 27S 9940 130 8Oq4 i ~IO 9949 1~3S 8130 285 9956 140 imiddot aJss 190 9963 14S IS29 2+95 99611
3
-----------
~- ~~ - - - bull - -- -- - shy
Statistics 1040 Sections 007 amp 009 Quiz 9 (20 Points)
Friday November 2 2007
Your Name
Question 1 Normal Approximation for Probability Histograms I (12 Points)
A programmer is working on a new program COIN to simulate tossing a coin As a preliminary test he sets up the programto do one million tosses The program returns with a count of 502015 heads The programmer looks at this and thinks Hmmm Two thousand and fifteen off Thats a lot No wait Compare it to the million Two thousand - forget the fifteen - out of a million is two out of a thousand Thats one in five hundred One fifth of a percent Very small Good COIN passes
Do you agree that COIN passes Answer yes or no and explain You should use box model calculations to support your answer
Please turn over
1
Question 2 Normal Approximation for Probability Histograms II (8 Points)
A coin is tossed 100 times True or false Just circle your answer You dont have to give any explanation Answer each of the following questions separately
1 The expected value for the number of heads is 50
True False
2 The expected value for the number of heads is 50 give or take 5 or so
True False
3 The number of heads will be 50
True False
4 The number of heads will be around 50 give or take 2 or so
True False
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets in the box
fraction fractionSD = (bigger - smaller) x
bigger x
smaller
Shortcut formulas for a box that contains only [Q] s and ITJ s
number of ITJ s average =
how many tIckets In the box
fraction fraction SD = of [] s x of [Q] s
2
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3
-----------
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Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
~ J _ __ ~ bullbull
-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
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Statistics 1040 Sections 007 amp 009 Quiz 4 (20 Points)
Friday September 21 2007
Your Name _------------- shy
Question 1 Normal Approximation for Data(20 Points)
The Graduate Record Examination (GRE) is a test taken by college students who intend to pursue a graduate degree in the United States For around 428000 examinees who took the General GRE Test in 2001-02 the mean for the verbal ability portion of the exam was around 470 and the standard deviation was around 125 We can assume that the histogram follows a normal curve Show your work
bull (7 Points) The percentage of examinees who scored less than 420 on the GRE test is roughly
bull (7 Points) The percentage of examinees who scored between 370 and 645 is about
bull (6 Points) In order to be among the top 4 a student must have obtained a minimum GRE score of about --- shy
) Please turn over
1
-I
Flt~=~~~~~-~~~~gt~jmiddotCpound~l~~~dili
Tablesmiddot )
A NORMAL TABLE
z Area z Area z Area
000 o 150 8664 300middot 99730 005shy 399 155 8789 30j 99771 010 797 160middot 8904 31099806 015 1192 165 9011 Jl~ 99837 020 1585 170 9109 320 99863
025 1914 175 9199 325 99885 030 2358 180 9281 330 99903 035 2137 185 9357 335 99919 040middot 3108 190middot 9426 340 99933 045 3473 195 9488 345 99944
050 3829 200 9545 350 99953 055 4177 205 9596 355 j 99961
I 060 4515 210 9643 360 99968 065 4843 215 9684 365 99974 070 5161 220 9122 370 99978
075 5467 225 9156 375 99982 080 5763 230 9786 380 99986 0~85 middot6(t47 235 9812 385 99988
~ bull~-- 090 6319 240 9836 390 99990 j
0~95 6579 245 9857 395 99992 I
100 6827 250 9816 400 999931 j 105 7063 255 9892 405 999949
110 7287 260 9907 410 999959 ~ 115 7499 265 9920 415 999967middot
I 120 7699 270 9931 420 999913f
I 125 7887 275 9940 425 999919 130 8064 i 280 9949 430 999983
) ~gt 135 8230 285 9956 435 1999986
440 middot999989middotmiddot140 i 8385 290 9963 145 ~8529 295 996middot8 445 99999-1
Statistics 1040 Sections 007 amp 009 Quiz 5 (20 Points)
Friday September 28 2007
Your Name ------------- shy
Questionmiddot 1 Measurement Error (8 Points)
You send a yardstick to a local laboratory for calibration asking that the procedure be repeated three times They report the following values
3596 inches 3601 inches 3603 inches
If you send the yardstick back for a fourth calibration you would expect to get 36 inches give or take
(a) 01 inches or so (b) 03 inches or so (c) 06inches or so
Circle your answer and explain
Question 2 Correlation (6 Points)
A teaching assistant gives a quiz to his section There are 10 questions on the quiz and no part credit is given After grading the papers the TA writes down for each student the number of questions the student got right and the number wrong The average number of right answers is 64 with an SD of 20 the average nUIILberof wrong answers is 36 with the same SD of 20
The correlation coefficient between the number of right answers andthe number of wrong answers is
(a) exactly 0 (b) -050 (c) +050 (d) -10 (e) +10 (f) -20 (g) +20
(h) cant tell without the data
Circle your answer and explain
Please turn over
1
Question 3 Correlation (6 Points)
For women age 25 and over in the US in 2005 the relationship between age and educashytionallevel (years of schooling completed) can be summarized as follows
average age ~ 50 years SD ~ 16 years average ed level ~ 132 years SD ~ 30 years r ~ -020
True or false and explain As you get older you become less educated If this statement is false what accounts for the negative correlation
Formulas
sum of all numbers avg = ----------shy
how many numbers )
SD = Javerage of [(deviations from avg) 2]
2
Statistics 1040 Sections 007 amp 009 Quiz 6 (20 Points)
Friday October 12 2007
Your Name -----~-----
Question 1 Regression (20 Points)
A selection of 65 varieties of cereal were tested for calories and sodium (in milligrams) for an one-cup serving The results can be summarized as follows
Average sodium - 240 mg SD = 131 mg Average calories = 149 calories SD = 62 calories r = 053
Show your work
1 (7 Points) Find the equation of the regression line for predicting number of mg sodium in an one-cup serving of cereals from calories
2 (4 Points) Predict the number of mg sodium in an one-cup serving of cereals that has 200 calories per cup
Please turn over
1
3 (5 Points) Find the rms error for predicting mg sodium from calories
4 (4 Points) Explain why it would not be a good idea to use the information in the question to estimate the amount of sodium for a cereal with 350 calories per cup
Formulas
rms error =Jl- r 2 x SDy
SD slope = r x --y intercept = avgy - slope x avgxSDx
)
2
----------
- - ~~~~~~_-
Statistics 1040 Sections 007 amp 009 Quiz 7 (20 Points)
Monday October 22 2007
Your Name
Question 1 ChanceProbability I (6 Points)
A deck of cards is shuffled and the top two cards are placed face down on a table Circle your answer
1 There is a 1 chance in 52 for the first card to be the ace of clubs True False
2 There is a 1 chance in 52 for the second card to be the ace of diamonds True False
3 The chance of getting the ace of clubs and then the ace of diamonds is 152 xl52 True False
~lt~J Question 2 ChanceProbability II (3 Points)
A coin is tossed six times Two possible sequences of results are
(i) H T T H T H (ii) H H H H H H
(The coin must land on H or T in the order given H = heads T = tails)
Which of the following is correct
Circle your answer
1 Sequence (i) is more likely
2 Sequence (ii) is more likely
3 Both sequences are equally likely
Please turn over
1
~ - -- _ -- -
Question 3 ChanceProbability III (3 Points)
Two cards will be dealt off the top of a well-shuffled deck You have a choice
(i) To win $1 if at least one of the two cards is a queen
(ii) To win $1 if the first card is a queen
Circle your answer
1 Option (i) is better for winning
2 Option (ii) is better for winning
3 Both options are equally good for winning
Question 4 ChanceProbability IV (4 Points)
One event has chance 12 another has chance 13 Fill in the blanks using one phrase from each pair below to make two true sentences Write out both sentences
If you want to find the chance that at least one of the two events both events will happen check to see if they are independent mutually exclusive If so you can add multiply the chances
Correct Sentence 1 If you want to find the chance that at least one of the two events will happen check to see if they are If so you can _ the chances
Correct Sentence 2 If you want to find the chance that both events will happen check to see if they are If so you can the chances
Question 5 ChanceProbability V (4 Points)
A coin is tossed 10 times Circle your answer
1 The chance of getting 10 heads in a row is 11024 True False
2 Given that the first 9 tosses were heads the chance of getting 10 heads in a row is -12 True False
2
Statistics 1040 Sections 007 amp 009 Quiz i (20 Points)
Friday October 26 2007
Your Name ~---------
Question 1 Law of Averages I (2 Points)
A box contains 10000 tickets 4000 [Q] s and 6000 [I] so And 10000 draws will be made at random with replacement from this box Which of the following best describes the situation Circle your answer You dont have to provide any explanations
1 The number of ls will be 6000 exactly
2 The number of ls is very likely to equal 6000 but there is also some small chance that it will not be equal to 6000
3 The number of ls is likely to be different from 6000 but the difference is likely to be small compared to 10000
Question 2 Law of Averages II (8 Points)
Circle your answer for each of the following four parts You dont have to provide any explanations
1 (2 Points) A die will be rolled some number of times and you win $1 if it shows an ace ( [J ) more than 20 of the time
Which is better 60 rolls or 600 rolls
2 (2 Points) As in 1) but you win the dollar if the percentage of aces is more than 15
Which is better 60 rolls or 600 rolls
3 (2 Points) As in 1) but you win the dollar if the percentage of aces is between 15 and 20
Which is better 60 rolls or 600 rolls
4 (2 Points) As in 1) but you win the dollar if the percentage of aces is exactly 16imiddot
Which is better 60 rolls or 600 rolls
1
Question 3 The Expected Value and Standard Error (10 Points)
One hundred draws are made at random with replacement from the box
1 (1 Point) If the sum of the draws is 321 what is their average
2 (1 Point) If the average of the draws is 378 what is the sum
3 (8 Points) Estimate the chance that the average of the draws is between 3 and 4 You have to make use of the normal curve to answer this part Show your work
Formulas
sum of all numbers in box box average =
how many numbers in box
box SD = Javerage of (deviations from box average)2]
EVsum = number of draws x box average
SEsum = vnumber of draws X box SD-)
2
Tablesmiddot
A NORMALTABLB
z iN- 1~ Ar~a
aoo f I (so 1 86Jj4 tQO- ~ ~13() 005 399 l 5S I 8789 31 ~ 99111 010 791 ltiOmiddot 89-04 3 fO- 99Jm6 015 IL92 165 ~ 9Ol1 3~J 99131 020 15amp5 170 9109 320 99~
O~2S 1914 L1S 9L99 3bull25 9988S O~30 2348 t80 92fU 339 99~903 035 t 21~31 t8S 93j1 335 J 99919
040 31JJ8 190 9426 ]40 99933 O~4S ]4I~13 ~ ~ ~ 195 MJ18 345 99944
1 O~SO 3829 200 9545 350 99953 O~5S 4177 1 2~05 9596 3S j 99961 O1jO i 4S~ I 210 43 36Q ~ 99968 o~6S GA3 215 middot9JiBe 3 99914 010 SI61 210 9112 J70 99~91
075 5467 225 9756 31S 99ta2 Z~30 ~ ~ 9186 1 380 99986 l~ 135 9812 middotjU 99bullbull
O~90 6319 240 983(i 390 99990 O~9S 6579 2~4S 917 3~9S 99991lt
100 6827 250 9816 400 999931los r 7063 25S 9892 405 999949 110 1JJ1 2M 9Ull 4(0 9999il
11amplt t Aft middot20 IIS 1499 2w 7~ 4 15 ~9961 120 bull 7699 210 ~11 420 9999ll
fmiddot2S 1881 t 27S 9940 130 8Oq4 i ~IO 9949 1~3S 8130 285 9956 140 imiddot aJss 190 9963 14S IS29 2+95 99611
3
-----------
~- ~~ - - - bull - -- -- - shy
Statistics 1040 Sections 007 amp 009 Quiz 9 (20 Points)
Friday November 2 2007
Your Name
Question 1 Normal Approximation for Probability Histograms I (12 Points)
A programmer is working on a new program COIN to simulate tossing a coin As a preliminary test he sets up the programto do one million tosses The program returns with a count of 502015 heads The programmer looks at this and thinks Hmmm Two thousand and fifteen off Thats a lot No wait Compare it to the million Two thousand - forget the fifteen - out of a million is two out of a thousand Thats one in five hundred One fifth of a percent Very small Good COIN passes
Do you agree that COIN passes Answer yes or no and explain You should use box model calculations to support your answer
Please turn over
1
Question 2 Normal Approximation for Probability Histograms II (8 Points)
A coin is tossed 100 times True or false Just circle your answer You dont have to give any explanation Answer each of the following questions separately
1 The expected value for the number of heads is 50
True False
2 The expected value for the number of heads is 50 give or take 5 or so
True False
3 The number of heads will be 50
True False
4 The number of heads will be around 50 give or take 2 or so
True False
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets in the box
fraction fractionSD = (bigger - smaller) x
bigger x
smaller
Shortcut formulas for a box that contains only [Q] s and ITJ s
number of ITJ s average =
how many tIckets In the box
fraction fraction SD = of [] s x of [Q] s
2
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3
-----------
)
Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
~ J _ __ ~ bullbull
-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
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A NORMAL TABLE
z Area z Area z Area
000 o 150 8664 300middot 99730 005shy 399 155 8789 30j 99771 010 797 160middot 8904 31099806 015 1192 165 9011 Jl~ 99837 020 1585 170 9109 320 99863
025 1914 175 9199 325 99885 030 2358 180 9281 330 99903 035 2137 185 9357 335 99919 040middot 3108 190middot 9426 340 99933 045 3473 195 9488 345 99944
050 3829 200 9545 350 99953 055 4177 205 9596 355 j 99961
I 060 4515 210 9643 360 99968 065 4843 215 9684 365 99974 070 5161 220 9122 370 99978
075 5467 225 9156 375 99982 080 5763 230 9786 380 99986 0~85 middot6(t47 235 9812 385 99988
~ bull~-- 090 6319 240 9836 390 99990 j
0~95 6579 245 9857 395 99992 I
100 6827 250 9816 400 999931 j 105 7063 255 9892 405 999949
110 7287 260 9907 410 999959 ~ 115 7499 265 9920 415 999967middot
I 120 7699 270 9931 420 999913f
I 125 7887 275 9940 425 999919 130 8064 i 280 9949 430 999983
) ~gt 135 8230 285 9956 435 1999986
440 middot999989middotmiddot140 i 8385 290 9963 145 ~8529 295 996middot8 445 99999-1
Statistics 1040 Sections 007 amp 009 Quiz 5 (20 Points)
Friday September 28 2007
Your Name ------------- shy
Questionmiddot 1 Measurement Error (8 Points)
You send a yardstick to a local laboratory for calibration asking that the procedure be repeated three times They report the following values
3596 inches 3601 inches 3603 inches
If you send the yardstick back for a fourth calibration you would expect to get 36 inches give or take
(a) 01 inches or so (b) 03 inches or so (c) 06inches or so
Circle your answer and explain
Question 2 Correlation (6 Points)
A teaching assistant gives a quiz to his section There are 10 questions on the quiz and no part credit is given After grading the papers the TA writes down for each student the number of questions the student got right and the number wrong The average number of right answers is 64 with an SD of 20 the average nUIILberof wrong answers is 36 with the same SD of 20
The correlation coefficient between the number of right answers andthe number of wrong answers is
(a) exactly 0 (b) -050 (c) +050 (d) -10 (e) +10 (f) -20 (g) +20
(h) cant tell without the data
Circle your answer and explain
Please turn over
1
Question 3 Correlation (6 Points)
For women age 25 and over in the US in 2005 the relationship between age and educashytionallevel (years of schooling completed) can be summarized as follows
average age ~ 50 years SD ~ 16 years average ed level ~ 132 years SD ~ 30 years r ~ -020
True or false and explain As you get older you become less educated If this statement is false what accounts for the negative correlation
Formulas
sum of all numbers avg = ----------shy
how many numbers )
SD = Javerage of [(deviations from avg) 2]
2
Statistics 1040 Sections 007 amp 009 Quiz 6 (20 Points)
Friday October 12 2007
Your Name -----~-----
Question 1 Regression (20 Points)
A selection of 65 varieties of cereal were tested for calories and sodium (in milligrams) for an one-cup serving The results can be summarized as follows
Average sodium - 240 mg SD = 131 mg Average calories = 149 calories SD = 62 calories r = 053
Show your work
1 (7 Points) Find the equation of the regression line for predicting number of mg sodium in an one-cup serving of cereals from calories
2 (4 Points) Predict the number of mg sodium in an one-cup serving of cereals that has 200 calories per cup
Please turn over
1
3 (5 Points) Find the rms error for predicting mg sodium from calories
4 (4 Points) Explain why it would not be a good idea to use the information in the question to estimate the amount of sodium for a cereal with 350 calories per cup
Formulas
rms error =Jl- r 2 x SDy
SD slope = r x --y intercept = avgy - slope x avgxSDx
)
2
----------
- - ~~~~~~_-
Statistics 1040 Sections 007 amp 009 Quiz 7 (20 Points)
Monday October 22 2007
Your Name
Question 1 ChanceProbability I (6 Points)
A deck of cards is shuffled and the top two cards are placed face down on a table Circle your answer
1 There is a 1 chance in 52 for the first card to be the ace of clubs True False
2 There is a 1 chance in 52 for the second card to be the ace of diamonds True False
3 The chance of getting the ace of clubs and then the ace of diamonds is 152 xl52 True False
~lt~J Question 2 ChanceProbability II (3 Points)
A coin is tossed six times Two possible sequences of results are
(i) H T T H T H (ii) H H H H H H
(The coin must land on H or T in the order given H = heads T = tails)
Which of the following is correct
Circle your answer
1 Sequence (i) is more likely
2 Sequence (ii) is more likely
3 Both sequences are equally likely
Please turn over
1
~ - -- _ -- -
Question 3 ChanceProbability III (3 Points)
Two cards will be dealt off the top of a well-shuffled deck You have a choice
(i) To win $1 if at least one of the two cards is a queen
(ii) To win $1 if the first card is a queen
Circle your answer
1 Option (i) is better for winning
2 Option (ii) is better for winning
3 Both options are equally good for winning
Question 4 ChanceProbability IV (4 Points)
One event has chance 12 another has chance 13 Fill in the blanks using one phrase from each pair below to make two true sentences Write out both sentences
If you want to find the chance that at least one of the two events both events will happen check to see if they are independent mutually exclusive If so you can add multiply the chances
Correct Sentence 1 If you want to find the chance that at least one of the two events will happen check to see if they are If so you can _ the chances
Correct Sentence 2 If you want to find the chance that both events will happen check to see if they are If so you can the chances
Question 5 ChanceProbability V (4 Points)
A coin is tossed 10 times Circle your answer
1 The chance of getting 10 heads in a row is 11024 True False
2 Given that the first 9 tosses were heads the chance of getting 10 heads in a row is -12 True False
2
Statistics 1040 Sections 007 amp 009 Quiz i (20 Points)
Friday October 26 2007
Your Name ~---------
Question 1 Law of Averages I (2 Points)
A box contains 10000 tickets 4000 [Q] s and 6000 [I] so And 10000 draws will be made at random with replacement from this box Which of the following best describes the situation Circle your answer You dont have to provide any explanations
1 The number of ls will be 6000 exactly
2 The number of ls is very likely to equal 6000 but there is also some small chance that it will not be equal to 6000
3 The number of ls is likely to be different from 6000 but the difference is likely to be small compared to 10000
Question 2 Law of Averages II (8 Points)
Circle your answer for each of the following four parts You dont have to provide any explanations
1 (2 Points) A die will be rolled some number of times and you win $1 if it shows an ace ( [J ) more than 20 of the time
Which is better 60 rolls or 600 rolls
2 (2 Points) As in 1) but you win the dollar if the percentage of aces is more than 15
Which is better 60 rolls or 600 rolls
3 (2 Points) As in 1) but you win the dollar if the percentage of aces is between 15 and 20
Which is better 60 rolls or 600 rolls
4 (2 Points) As in 1) but you win the dollar if the percentage of aces is exactly 16imiddot
Which is better 60 rolls or 600 rolls
1
Question 3 The Expected Value and Standard Error (10 Points)
One hundred draws are made at random with replacement from the box
1 (1 Point) If the sum of the draws is 321 what is their average
2 (1 Point) If the average of the draws is 378 what is the sum
3 (8 Points) Estimate the chance that the average of the draws is between 3 and 4 You have to make use of the normal curve to answer this part Show your work
Formulas
sum of all numbers in box box average =
how many numbers in box
box SD = Javerage of (deviations from box average)2]
EVsum = number of draws x box average
SEsum = vnumber of draws X box SD-)
2
Tablesmiddot
A NORMALTABLB
z iN- 1~ Ar~a
aoo f I (so 1 86Jj4 tQO- ~ ~13() 005 399 l 5S I 8789 31 ~ 99111 010 791 ltiOmiddot 89-04 3 fO- 99Jm6 015 IL92 165 ~ 9Ol1 3~J 99131 020 15amp5 170 9109 320 99~
O~2S 1914 L1S 9L99 3bull25 9988S O~30 2348 t80 92fU 339 99~903 035 t 21~31 t8S 93j1 335 J 99919
040 31JJ8 190 9426 ]40 99933 O~4S ]4I~13 ~ ~ ~ 195 MJ18 345 99944
1 O~SO 3829 200 9545 350 99953 O~5S 4177 1 2~05 9596 3S j 99961 O1jO i 4S~ I 210 43 36Q ~ 99968 o~6S GA3 215 middot9JiBe 3 99914 010 SI61 210 9112 J70 99~91
075 5467 225 9756 31S 99ta2 Z~30 ~ ~ 9186 1 380 99986 l~ 135 9812 middotjU 99bullbull
O~90 6319 240 983(i 390 99990 O~9S 6579 2~4S 917 3~9S 99991lt
100 6827 250 9816 400 999931los r 7063 25S 9892 405 999949 110 1JJ1 2M 9Ull 4(0 9999il
11amplt t Aft middot20 IIS 1499 2w 7~ 4 15 ~9961 120 bull 7699 210 ~11 420 9999ll
fmiddot2S 1881 t 27S 9940 130 8Oq4 i ~IO 9949 1~3S 8130 285 9956 140 imiddot aJss 190 9963 14S IS29 2+95 99611
3
-----------
~- ~~ - - - bull - -- -- - shy
Statistics 1040 Sections 007 amp 009 Quiz 9 (20 Points)
Friday November 2 2007
Your Name
Question 1 Normal Approximation for Probability Histograms I (12 Points)
A programmer is working on a new program COIN to simulate tossing a coin As a preliminary test he sets up the programto do one million tosses The program returns with a count of 502015 heads The programmer looks at this and thinks Hmmm Two thousand and fifteen off Thats a lot No wait Compare it to the million Two thousand - forget the fifteen - out of a million is two out of a thousand Thats one in five hundred One fifth of a percent Very small Good COIN passes
Do you agree that COIN passes Answer yes or no and explain You should use box model calculations to support your answer
Please turn over
1
Question 2 Normal Approximation for Probability Histograms II (8 Points)
A coin is tossed 100 times True or false Just circle your answer You dont have to give any explanation Answer each of the following questions separately
1 The expected value for the number of heads is 50
True False
2 The expected value for the number of heads is 50 give or take 5 or so
True False
3 The number of heads will be 50
True False
4 The number of heads will be around 50 give or take 2 or so
True False
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets in the box
fraction fractionSD = (bigger - smaller) x
bigger x
smaller
Shortcut formulas for a box that contains only [Q] s and ITJ s
number of ITJ s average =
how many tIckets In the box
fraction fraction SD = of [] s x of [Q] s
2
Tablesmiddot
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300 99730 3M ~ 99171 10lt 99806 3J 99337 )20 99~
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11S 9199 180 2St L8S I 9351 190 9426 L95 9488 ~
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3
-----------
)
Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
~ J _ __ ~ bullbull
-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
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Statistics 1040 Sections 007 amp 009 Quiz 5 (20 Points)
Friday September 28 2007
Your Name ------------- shy
Questionmiddot 1 Measurement Error (8 Points)
You send a yardstick to a local laboratory for calibration asking that the procedure be repeated three times They report the following values
3596 inches 3601 inches 3603 inches
If you send the yardstick back for a fourth calibration you would expect to get 36 inches give or take
(a) 01 inches or so (b) 03 inches or so (c) 06inches or so
Circle your answer and explain
Question 2 Correlation (6 Points)
A teaching assistant gives a quiz to his section There are 10 questions on the quiz and no part credit is given After grading the papers the TA writes down for each student the number of questions the student got right and the number wrong The average number of right answers is 64 with an SD of 20 the average nUIILberof wrong answers is 36 with the same SD of 20
The correlation coefficient between the number of right answers andthe number of wrong answers is
(a) exactly 0 (b) -050 (c) +050 (d) -10 (e) +10 (f) -20 (g) +20
(h) cant tell without the data
Circle your answer and explain
Please turn over
1
Question 3 Correlation (6 Points)
For women age 25 and over in the US in 2005 the relationship between age and educashytionallevel (years of schooling completed) can be summarized as follows
average age ~ 50 years SD ~ 16 years average ed level ~ 132 years SD ~ 30 years r ~ -020
True or false and explain As you get older you become less educated If this statement is false what accounts for the negative correlation
Formulas
sum of all numbers avg = ----------shy
how many numbers )
SD = Javerage of [(deviations from avg) 2]
2
Statistics 1040 Sections 007 amp 009 Quiz 6 (20 Points)
Friday October 12 2007
Your Name -----~-----
Question 1 Regression (20 Points)
A selection of 65 varieties of cereal were tested for calories and sodium (in milligrams) for an one-cup serving The results can be summarized as follows
Average sodium - 240 mg SD = 131 mg Average calories = 149 calories SD = 62 calories r = 053
Show your work
1 (7 Points) Find the equation of the regression line for predicting number of mg sodium in an one-cup serving of cereals from calories
2 (4 Points) Predict the number of mg sodium in an one-cup serving of cereals that has 200 calories per cup
Please turn over
1
3 (5 Points) Find the rms error for predicting mg sodium from calories
4 (4 Points) Explain why it would not be a good idea to use the information in the question to estimate the amount of sodium for a cereal with 350 calories per cup
Formulas
rms error =Jl- r 2 x SDy
SD slope = r x --y intercept = avgy - slope x avgxSDx
)
2
----------
- - ~~~~~~_-
Statistics 1040 Sections 007 amp 009 Quiz 7 (20 Points)
Monday October 22 2007
Your Name
Question 1 ChanceProbability I (6 Points)
A deck of cards is shuffled and the top two cards are placed face down on a table Circle your answer
1 There is a 1 chance in 52 for the first card to be the ace of clubs True False
2 There is a 1 chance in 52 for the second card to be the ace of diamonds True False
3 The chance of getting the ace of clubs and then the ace of diamonds is 152 xl52 True False
~lt~J Question 2 ChanceProbability II (3 Points)
A coin is tossed six times Two possible sequences of results are
(i) H T T H T H (ii) H H H H H H
(The coin must land on H or T in the order given H = heads T = tails)
Which of the following is correct
Circle your answer
1 Sequence (i) is more likely
2 Sequence (ii) is more likely
3 Both sequences are equally likely
Please turn over
1
~ - -- _ -- -
Question 3 ChanceProbability III (3 Points)
Two cards will be dealt off the top of a well-shuffled deck You have a choice
(i) To win $1 if at least one of the two cards is a queen
(ii) To win $1 if the first card is a queen
Circle your answer
1 Option (i) is better for winning
2 Option (ii) is better for winning
3 Both options are equally good for winning
Question 4 ChanceProbability IV (4 Points)
One event has chance 12 another has chance 13 Fill in the blanks using one phrase from each pair below to make two true sentences Write out both sentences
If you want to find the chance that at least one of the two events both events will happen check to see if they are independent mutually exclusive If so you can add multiply the chances
Correct Sentence 1 If you want to find the chance that at least one of the two events will happen check to see if they are If so you can _ the chances
Correct Sentence 2 If you want to find the chance that both events will happen check to see if they are If so you can the chances
Question 5 ChanceProbability V (4 Points)
A coin is tossed 10 times Circle your answer
1 The chance of getting 10 heads in a row is 11024 True False
2 Given that the first 9 tosses were heads the chance of getting 10 heads in a row is -12 True False
2
Statistics 1040 Sections 007 amp 009 Quiz i (20 Points)
Friday October 26 2007
Your Name ~---------
Question 1 Law of Averages I (2 Points)
A box contains 10000 tickets 4000 [Q] s and 6000 [I] so And 10000 draws will be made at random with replacement from this box Which of the following best describes the situation Circle your answer You dont have to provide any explanations
1 The number of ls will be 6000 exactly
2 The number of ls is very likely to equal 6000 but there is also some small chance that it will not be equal to 6000
3 The number of ls is likely to be different from 6000 but the difference is likely to be small compared to 10000
Question 2 Law of Averages II (8 Points)
Circle your answer for each of the following four parts You dont have to provide any explanations
1 (2 Points) A die will be rolled some number of times and you win $1 if it shows an ace ( [J ) more than 20 of the time
Which is better 60 rolls or 600 rolls
2 (2 Points) As in 1) but you win the dollar if the percentage of aces is more than 15
Which is better 60 rolls or 600 rolls
3 (2 Points) As in 1) but you win the dollar if the percentage of aces is between 15 and 20
Which is better 60 rolls or 600 rolls
4 (2 Points) As in 1) but you win the dollar if the percentage of aces is exactly 16imiddot
Which is better 60 rolls or 600 rolls
1
Question 3 The Expected Value and Standard Error (10 Points)
One hundred draws are made at random with replacement from the box
1 (1 Point) If the sum of the draws is 321 what is their average
2 (1 Point) If the average of the draws is 378 what is the sum
3 (8 Points) Estimate the chance that the average of the draws is between 3 and 4 You have to make use of the normal curve to answer this part Show your work
Formulas
sum of all numbers in box box average =
how many numbers in box
box SD = Javerage of (deviations from box average)2]
EVsum = number of draws x box average
SEsum = vnumber of draws X box SD-)
2
Tablesmiddot
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040 31JJ8 190 9426 ]40 99933 O~4S ]4I~13 ~ ~ ~ 195 MJ18 345 99944
1 O~SO 3829 200 9545 350 99953 O~5S 4177 1 2~05 9596 3S j 99961 O1jO i 4S~ I 210 43 36Q ~ 99968 o~6S GA3 215 middot9JiBe 3 99914 010 SI61 210 9112 J70 99~91
075 5467 225 9756 31S 99ta2 Z~30 ~ ~ 9186 1 380 99986 l~ 135 9812 middotjU 99bullbull
O~90 6319 240 983(i 390 99990 O~9S 6579 2~4S 917 3~9S 99991lt
100 6827 250 9816 400 999931los r 7063 25S 9892 405 999949 110 1JJ1 2M 9Ull 4(0 9999il
11amplt t Aft middot20 IIS 1499 2w 7~ 4 15 ~9961 120 bull 7699 210 ~11 420 9999ll
fmiddot2S 1881 t 27S 9940 130 8Oq4 i ~IO 9949 1~3S 8130 285 9956 140 imiddot aJss 190 9963 14S IS29 2+95 99611
3
-----------
~- ~~ - - - bull - -- -- - shy
Statistics 1040 Sections 007 amp 009 Quiz 9 (20 Points)
Friday November 2 2007
Your Name
Question 1 Normal Approximation for Probability Histograms I (12 Points)
A programmer is working on a new program COIN to simulate tossing a coin As a preliminary test he sets up the programto do one million tosses The program returns with a count of 502015 heads The programmer looks at this and thinks Hmmm Two thousand and fifteen off Thats a lot No wait Compare it to the million Two thousand - forget the fifteen - out of a million is two out of a thousand Thats one in five hundred One fifth of a percent Very small Good COIN passes
Do you agree that COIN passes Answer yes or no and explain You should use box model calculations to support your answer
Please turn over
1
Question 2 Normal Approximation for Probability Histograms II (8 Points)
A coin is tossed 100 times True or false Just circle your answer You dont have to give any explanation Answer each of the following questions separately
1 The expected value for the number of heads is 50
True False
2 The expected value for the number of heads is 50 give or take 5 or so
True False
3 The number of heads will be 50
True False
4 The number of heads will be around 50 give or take 2 or so
True False
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets in the box
fraction fractionSD = (bigger - smaller) x
bigger x
smaller
Shortcut formulas for a box that contains only [Q] s and ITJ s
number of ITJ s average =
how many tIckets In the box
fraction fraction SD = of [] s x of [Q] s
2
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3
-----------
)
Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
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~ J _ __ ~ bullbull
-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
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Question 3 Correlation (6 Points)
For women age 25 and over in the US in 2005 the relationship between age and educashytionallevel (years of schooling completed) can be summarized as follows
average age ~ 50 years SD ~ 16 years average ed level ~ 132 years SD ~ 30 years r ~ -020
True or false and explain As you get older you become less educated If this statement is false what accounts for the negative correlation
Formulas
sum of all numbers avg = ----------shy
how many numbers )
SD = Javerage of [(deviations from avg) 2]
2
Statistics 1040 Sections 007 amp 009 Quiz 6 (20 Points)
Friday October 12 2007
Your Name -----~-----
Question 1 Regression (20 Points)
A selection of 65 varieties of cereal were tested for calories and sodium (in milligrams) for an one-cup serving The results can be summarized as follows
Average sodium - 240 mg SD = 131 mg Average calories = 149 calories SD = 62 calories r = 053
Show your work
1 (7 Points) Find the equation of the regression line for predicting number of mg sodium in an one-cup serving of cereals from calories
2 (4 Points) Predict the number of mg sodium in an one-cup serving of cereals that has 200 calories per cup
Please turn over
1
3 (5 Points) Find the rms error for predicting mg sodium from calories
4 (4 Points) Explain why it would not be a good idea to use the information in the question to estimate the amount of sodium for a cereal with 350 calories per cup
Formulas
rms error =Jl- r 2 x SDy
SD slope = r x --y intercept = avgy - slope x avgxSDx
)
2
----------
- - ~~~~~~_-
Statistics 1040 Sections 007 amp 009 Quiz 7 (20 Points)
Monday October 22 2007
Your Name
Question 1 ChanceProbability I (6 Points)
A deck of cards is shuffled and the top two cards are placed face down on a table Circle your answer
1 There is a 1 chance in 52 for the first card to be the ace of clubs True False
2 There is a 1 chance in 52 for the second card to be the ace of diamonds True False
3 The chance of getting the ace of clubs and then the ace of diamonds is 152 xl52 True False
~lt~J Question 2 ChanceProbability II (3 Points)
A coin is tossed six times Two possible sequences of results are
(i) H T T H T H (ii) H H H H H H
(The coin must land on H or T in the order given H = heads T = tails)
Which of the following is correct
Circle your answer
1 Sequence (i) is more likely
2 Sequence (ii) is more likely
3 Both sequences are equally likely
Please turn over
1
~ - -- _ -- -
Question 3 ChanceProbability III (3 Points)
Two cards will be dealt off the top of a well-shuffled deck You have a choice
(i) To win $1 if at least one of the two cards is a queen
(ii) To win $1 if the first card is a queen
Circle your answer
1 Option (i) is better for winning
2 Option (ii) is better for winning
3 Both options are equally good for winning
Question 4 ChanceProbability IV (4 Points)
One event has chance 12 another has chance 13 Fill in the blanks using one phrase from each pair below to make two true sentences Write out both sentences
If you want to find the chance that at least one of the two events both events will happen check to see if they are independent mutually exclusive If so you can add multiply the chances
Correct Sentence 1 If you want to find the chance that at least one of the two events will happen check to see if they are If so you can _ the chances
Correct Sentence 2 If you want to find the chance that both events will happen check to see if they are If so you can the chances
Question 5 ChanceProbability V (4 Points)
A coin is tossed 10 times Circle your answer
1 The chance of getting 10 heads in a row is 11024 True False
2 Given that the first 9 tosses were heads the chance of getting 10 heads in a row is -12 True False
2
Statistics 1040 Sections 007 amp 009 Quiz i (20 Points)
Friday October 26 2007
Your Name ~---------
Question 1 Law of Averages I (2 Points)
A box contains 10000 tickets 4000 [Q] s and 6000 [I] so And 10000 draws will be made at random with replacement from this box Which of the following best describes the situation Circle your answer You dont have to provide any explanations
1 The number of ls will be 6000 exactly
2 The number of ls is very likely to equal 6000 but there is also some small chance that it will not be equal to 6000
3 The number of ls is likely to be different from 6000 but the difference is likely to be small compared to 10000
Question 2 Law of Averages II (8 Points)
Circle your answer for each of the following four parts You dont have to provide any explanations
1 (2 Points) A die will be rolled some number of times and you win $1 if it shows an ace ( [J ) more than 20 of the time
Which is better 60 rolls or 600 rolls
2 (2 Points) As in 1) but you win the dollar if the percentage of aces is more than 15
Which is better 60 rolls or 600 rolls
3 (2 Points) As in 1) but you win the dollar if the percentage of aces is between 15 and 20
Which is better 60 rolls or 600 rolls
4 (2 Points) As in 1) but you win the dollar if the percentage of aces is exactly 16imiddot
Which is better 60 rolls or 600 rolls
1
Question 3 The Expected Value and Standard Error (10 Points)
One hundred draws are made at random with replacement from the box
1 (1 Point) If the sum of the draws is 321 what is their average
2 (1 Point) If the average of the draws is 378 what is the sum
3 (8 Points) Estimate the chance that the average of the draws is between 3 and 4 You have to make use of the normal curve to answer this part Show your work
Formulas
sum of all numbers in box box average =
how many numbers in box
box SD = Javerage of (deviations from box average)2]
EVsum = number of draws x box average
SEsum = vnumber of draws X box SD-)
2
Tablesmiddot
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040 31JJ8 190 9426 ]40 99933 O~4S ]4I~13 ~ ~ ~ 195 MJ18 345 99944
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3
-----------
~- ~~ - - - bull - -- -- - shy
Statistics 1040 Sections 007 amp 009 Quiz 9 (20 Points)
Friday November 2 2007
Your Name
Question 1 Normal Approximation for Probability Histograms I (12 Points)
A programmer is working on a new program COIN to simulate tossing a coin As a preliminary test he sets up the programto do one million tosses The program returns with a count of 502015 heads The programmer looks at this and thinks Hmmm Two thousand and fifteen off Thats a lot No wait Compare it to the million Two thousand - forget the fifteen - out of a million is two out of a thousand Thats one in five hundred One fifth of a percent Very small Good COIN passes
Do you agree that COIN passes Answer yes or no and explain You should use box model calculations to support your answer
Please turn over
1
Question 2 Normal Approximation for Probability Histograms II (8 Points)
A coin is tossed 100 times True or false Just circle your answer You dont have to give any explanation Answer each of the following questions separately
1 The expected value for the number of heads is 50
True False
2 The expected value for the number of heads is 50 give or take 5 or so
True False
3 The number of heads will be 50
True False
4 The number of heads will be around 50 give or take 2 or so
True False
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets in the box
fraction fractionSD = (bigger - smaller) x
bigger x
smaller
Shortcut formulas for a box that contains only [Q] s and ITJ s
number of ITJ s average =
how many tIckets In the box
fraction fraction SD = of [] s x of [Q] s
2
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3
-----------
)
Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
~ J _ __ ~ bullbull
-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
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Statistics 1040 Sections 007 amp 009 Quiz 6 (20 Points)
Friday October 12 2007
Your Name -----~-----
Question 1 Regression (20 Points)
A selection of 65 varieties of cereal were tested for calories and sodium (in milligrams) for an one-cup serving The results can be summarized as follows
Average sodium - 240 mg SD = 131 mg Average calories = 149 calories SD = 62 calories r = 053
Show your work
1 (7 Points) Find the equation of the regression line for predicting number of mg sodium in an one-cup serving of cereals from calories
2 (4 Points) Predict the number of mg sodium in an one-cup serving of cereals that has 200 calories per cup
Please turn over
1
3 (5 Points) Find the rms error for predicting mg sodium from calories
4 (4 Points) Explain why it would not be a good idea to use the information in the question to estimate the amount of sodium for a cereal with 350 calories per cup
Formulas
rms error =Jl- r 2 x SDy
SD slope = r x --y intercept = avgy - slope x avgxSDx
)
2
----------
- - ~~~~~~_-
Statistics 1040 Sections 007 amp 009 Quiz 7 (20 Points)
Monday October 22 2007
Your Name
Question 1 ChanceProbability I (6 Points)
A deck of cards is shuffled and the top two cards are placed face down on a table Circle your answer
1 There is a 1 chance in 52 for the first card to be the ace of clubs True False
2 There is a 1 chance in 52 for the second card to be the ace of diamonds True False
3 The chance of getting the ace of clubs and then the ace of diamonds is 152 xl52 True False
~lt~J Question 2 ChanceProbability II (3 Points)
A coin is tossed six times Two possible sequences of results are
(i) H T T H T H (ii) H H H H H H
(The coin must land on H or T in the order given H = heads T = tails)
Which of the following is correct
Circle your answer
1 Sequence (i) is more likely
2 Sequence (ii) is more likely
3 Both sequences are equally likely
Please turn over
1
~ - -- _ -- -
Question 3 ChanceProbability III (3 Points)
Two cards will be dealt off the top of a well-shuffled deck You have a choice
(i) To win $1 if at least one of the two cards is a queen
(ii) To win $1 if the first card is a queen
Circle your answer
1 Option (i) is better for winning
2 Option (ii) is better for winning
3 Both options are equally good for winning
Question 4 ChanceProbability IV (4 Points)
One event has chance 12 another has chance 13 Fill in the blanks using one phrase from each pair below to make two true sentences Write out both sentences
If you want to find the chance that at least one of the two events both events will happen check to see if they are independent mutually exclusive If so you can add multiply the chances
Correct Sentence 1 If you want to find the chance that at least one of the two events will happen check to see if they are If so you can _ the chances
Correct Sentence 2 If you want to find the chance that both events will happen check to see if they are If so you can the chances
Question 5 ChanceProbability V (4 Points)
A coin is tossed 10 times Circle your answer
1 The chance of getting 10 heads in a row is 11024 True False
2 Given that the first 9 tosses were heads the chance of getting 10 heads in a row is -12 True False
2
Statistics 1040 Sections 007 amp 009 Quiz i (20 Points)
Friday October 26 2007
Your Name ~---------
Question 1 Law of Averages I (2 Points)
A box contains 10000 tickets 4000 [Q] s and 6000 [I] so And 10000 draws will be made at random with replacement from this box Which of the following best describes the situation Circle your answer You dont have to provide any explanations
1 The number of ls will be 6000 exactly
2 The number of ls is very likely to equal 6000 but there is also some small chance that it will not be equal to 6000
3 The number of ls is likely to be different from 6000 but the difference is likely to be small compared to 10000
Question 2 Law of Averages II (8 Points)
Circle your answer for each of the following four parts You dont have to provide any explanations
1 (2 Points) A die will be rolled some number of times and you win $1 if it shows an ace ( [J ) more than 20 of the time
Which is better 60 rolls or 600 rolls
2 (2 Points) As in 1) but you win the dollar if the percentage of aces is more than 15
Which is better 60 rolls or 600 rolls
3 (2 Points) As in 1) but you win the dollar if the percentage of aces is between 15 and 20
Which is better 60 rolls or 600 rolls
4 (2 Points) As in 1) but you win the dollar if the percentage of aces is exactly 16imiddot
Which is better 60 rolls or 600 rolls
1
Question 3 The Expected Value and Standard Error (10 Points)
One hundred draws are made at random with replacement from the box
1 (1 Point) If the sum of the draws is 321 what is their average
2 (1 Point) If the average of the draws is 378 what is the sum
3 (8 Points) Estimate the chance that the average of the draws is between 3 and 4 You have to make use of the normal curve to answer this part Show your work
Formulas
sum of all numbers in box box average =
how many numbers in box
box SD = Javerage of (deviations from box average)2]
EVsum = number of draws x box average
SEsum = vnumber of draws X box SD-)
2
Tablesmiddot
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3
-----------
~- ~~ - - - bull - -- -- - shy
Statistics 1040 Sections 007 amp 009 Quiz 9 (20 Points)
Friday November 2 2007
Your Name
Question 1 Normal Approximation for Probability Histograms I (12 Points)
A programmer is working on a new program COIN to simulate tossing a coin As a preliminary test he sets up the programto do one million tosses The program returns with a count of 502015 heads The programmer looks at this and thinks Hmmm Two thousand and fifteen off Thats a lot No wait Compare it to the million Two thousand - forget the fifteen - out of a million is two out of a thousand Thats one in five hundred One fifth of a percent Very small Good COIN passes
Do you agree that COIN passes Answer yes or no and explain You should use box model calculations to support your answer
Please turn over
1
Question 2 Normal Approximation for Probability Histograms II (8 Points)
A coin is tossed 100 times True or false Just circle your answer You dont have to give any explanation Answer each of the following questions separately
1 The expected value for the number of heads is 50
True False
2 The expected value for the number of heads is 50 give or take 5 or so
True False
3 The number of heads will be 50
True False
4 The number of heads will be around 50 give or take 2 or so
True False
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets in the box
fraction fractionSD = (bigger - smaller) x
bigger x
smaller
Shortcut formulas for a box that contains only [Q] s and ITJ s
number of ITJ s average =
how many tIckets In the box
fraction fraction SD = of [] s x of [Q] s
2
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-----------
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Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
~ J _ __ ~ bullbull
-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
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3 (5 Points) Find the rms error for predicting mg sodium from calories
4 (4 Points) Explain why it would not be a good idea to use the information in the question to estimate the amount of sodium for a cereal with 350 calories per cup
Formulas
rms error =Jl- r 2 x SDy
SD slope = r x --y intercept = avgy - slope x avgxSDx
)
2
----------
- - ~~~~~~_-
Statistics 1040 Sections 007 amp 009 Quiz 7 (20 Points)
Monday October 22 2007
Your Name
Question 1 ChanceProbability I (6 Points)
A deck of cards is shuffled and the top two cards are placed face down on a table Circle your answer
1 There is a 1 chance in 52 for the first card to be the ace of clubs True False
2 There is a 1 chance in 52 for the second card to be the ace of diamonds True False
3 The chance of getting the ace of clubs and then the ace of diamonds is 152 xl52 True False
~lt~J Question 2 ChanceProbability II (3 Points)
A coin is tossed six times Two possible sequences of results are
(i) H T T H T H (ii) H H H H H H
(The coin must land on H or T in the order given H = heads T = tails)
Which of the following is correct
Circle your answer
1 Sequence (i) is more likely
2 Sequence (ii) is more likely
3 Both sequences are equally likely
Please turn over
1
~ - -- _ -- -
Question 3 ChanceProbability III (3 Points)
Two cards will be dealt off the top of a well-shuffled deck You have a choice
(i) To win $1 if at least one of the two cards is a queen
(ii) To win $1 if the first card is a queen
Circle your answer
1 Option (i) is better for winning
2 Option (ii) is better for winning
3 Both options are equally good for winning
Question 4 ChanceProbability IV (4 Points)
One event has chance 12 another has chance 13 Fill in the blanks using one phrase from each pair below to make two true sentences Write out both sentences
If you want to find the chance that at least one of the two events both events will happen check to see if they are independent mutually exclusive If so you can add multiply the chances
Correct Sentence 1 If you want to find the chance that at least one of the two events will happen check to see if they are If so you can _ the chances
Correct Sentence 2 If you want to find the chance that both events will happen check to see if they are If so you can the chances
Question 5 ChanceProbability V (4 Points)
A coin is tossed 10 times Circle your answer
1 The chance of getting 10 heads in a row is 11024 True False
2 Given that the first 9 tosses were heads the chance of getting 10 heads in a row is -12 True False
2
Statistics 1040 Sections 007 amp 009 Quiz i (20 Points)
Friday October 26 2007
Your Name ~---------
Question 1 Law of Averages I (2 Points)
A box contains 10000 tickets 4000 [Q] s and 6000 [I] so And 10000 draws will be made at random with replacement from this box Which of the following best describes the situation Circle your answer You dont have to provide any explanations
1 The number of ls will be 6000 exactly
2 The number of ls is very likely to equal 6000 but there is also some small chance that it will not be equal to 6000
3 The number of ls is likely to be different from 6000 but the difference is likely to be small compared to 10000
Question 2 Law of Averages II (8 Points)
Circle your answer for each of the following four parts You dont have to provide any explanations
1 (2 Points) A die will be rolled some number of times and you win $1 if it shows an ace ( [J ) more than 20 of the time
Which is better 60 rolls or 600 rolls
2 (2 Points) As in 1) but you win the dollar if the percentage of aces is more than 15
Which is better 60 rolls or 600 rolls
3 (2 Points) As in 1) but you win the dollar if the percentage of aces is between 15 and 20
Which is better 60 rolls or 600 rolls
4 (2 Points) As in 1) but you win the dollar if the percentage of aces is exactly 16imiddot
Which is better 60 rolls or 600 rolls
1
Question 3 The Expected Value and Standard Error (10 Points)
One hundred draws are made at random with replacement from the box
1 (1 Point) If the sum of the draws is 321 what is their average
2 (1 Point) If the average of the draws is 378 what is the sum
3 (8 Points) Estimate the chance that the average of the draws is between 3 and 4 You have to make use of the normal curve to answer this part Show your work
Formulas
sum of all numbers in box box average =
how many numbers in box
box SD = Javerage of (deviations from box average)2]
EVsum = number of draws x box average
SEsum = vnumber of draws X box SD-)
2
Tablesmiddot
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3
-----------
~- ~~ - - - bull - -- -- - shy
Statistics 1040 Sections 007 amp 009 Quiz 9 (20 Points)
Friday November 2 2007
Your Name
Question 1 Normal Approximation for Probability Histograms I (12 Points)
A programmer is working on a new program COIN to simulate tossing a coin As a preliminary test he sets up the programto do one million tosses The program returns with a count of 502015 heads The programmer looks at this and thinks Hmmm Two thousand and fifteen off Thats a lot No wait Compare it to the million Two thousand - forget the fifteen - out of a million is two out of a thousand Thats one in five hundred One fifth of a percent Very small Good COIN passes
Do you agree that COIN passes Answer yes or no and explain You should use box model calculations to support your answer
Please turn over
1
Question 2 Normal Approximation for Probability Histograms II (8 Points)
A coin is tossed 100 times True or false Just circle your answer You dont have to give any explanation Answer each of the following questions separately
1 The expected value for the number of heads is 50
True False
2 The expected value for the number of heads is 50 give or take 5 or so
True False
3 The number of heads will be 50
True False
4 The number of heads will be around 50 give or take 2 or so
True False
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets in the box
fraction fractionSD = (bigger - smaller) x
bigger x
smaller
Shortcut formulas for a box that contains only [Q] s and ITJ s
number of ITJ s average =
how many tIckets In the box
fraction fraction SD = of [] s x of [Q] s
2
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Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
~ J _ __ ~ bullbull
-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
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Statistics 1040 Sections 007 amp 009 Quiz 7 (20 Points)
Monday October 22 2007
Your Name
Question 1 ChanceProbability I (6 Points)
A deck of cards is shuffled and the top two cards are placed face down on a table Circle your answer
1 There is a 1 chance in 52 for the first card to be the ace of clubs True False
2 There is a 1 chance in 52 for the second card to be the ace of diamonds True False
3 The chance of getting the ace of clubs and then the ace of diamonds is 152 xl52 True False
~lt~J Question 2 ChanceProbability II (3 Points)
A coin is tossed six times Two possible sequences of results are
(i) H T T H T H (ii) H H H H H H
(The coin must land on H or T in the order given H = heads T = tails)
Which of the following is correct
Circle your answer
1 Sequence (i) is more likely
2 Sequence (ii) is more likely
3 Both sequences are equally likely
Please turn over
1
~ - -- _ -- -
Question 3 ChanceProbability III (3 Points)
Two cards will be dealt off the top of a well-shuffled deck You have a choice
(i) To win $1 if at least one of the two cards is a queen
(ii) To win $1 if the first card is a queen
Circle your answer
1 Option (i) is better for winning
2 Option (ii) is better for winning
3 Both options are equally good for winning
Question 4 ChanceProbability IV (4 Points)
One event has chance 12 another has chance 13 Fill in the blanks using one phrase from each pair below to make two true sentences Write out both sentences
If you want to find the chance that at least one of the two events both events will happen check to see if they are independent mutually exclusive If so you can add multiply the chances
Correct Sentence 1 If you want to find the chance that at least one of the two events will happen check to see if they are If so you can _ the chances
Correct Sentence 2 If you want to find the chance that both events will happen check to see if they are If so you can the chances
Question 5 ChanceProbability V (4 Points)
A coin is tossed 10 times Circle your answer
1 The chance of getting 10 heads in a row is 11024 True False
2 Given that the first 9 tosses were heads the chance of getting 10 heads in a row is -12 True False
2
Statistics 1040 Sections 007 amp 009 Quiz i (20 Points)
Friday October 26 2007
Your Name ~---------
Question 1 Law of Averages I (2 Points)
A box contains 10000 tickets 4000 [Q] s and 6000 [I] so And 10000 draws will be made at random with replacement from this box Which of the following best describes the situation Circle your answer You dont have to provide any explanations
1 The number of ls will be 6000 exactly
2 The number of ls is very likely to equal 6000 but there is also some small chance that it will not be equal to 6000
3 The number of ls is likely to be different from 6000 but the difference is likely to be small compared to 10000
Question 2 Law of Averages II (8 Points)
Circle your answer for each of the following four parts You dont have to provide any explanations
1 (2 Points) A die will be rolled some number of times and you win $1 if it shows an ace ( [J ) more than 20 of the time
Which is better 60 rolls or 600 rolls
2 (2 Points) As in 1) but you win the dollar if the percentage of aces is more than 15
Which is better 60 rolls or 600 rolls
3 (2 Points) As in 1) but you win the dollar if the percentage of aces is between 15 and 20
Which is better 60 rolls or 600 rolls
4 (2 Points) As in 1) but you win the dollar if the percentage of aces is exactly 16imiddot
Which is better 60 rolls or 600 rolls
1
Question 3 The Expected Value and Standard Error (10 Points)
One hundred draws are made at random with replacement from the box
1 (1 Point) If the sum of the draws is 321 what is their average
2 (1 Point) If the average of the draws is 378 what is the sum
3 (8 Points) Estimate the chance that the average of the draws is between 3 and 4 You have to make use of the normal curve to answer this part Show your work
Formulas
sum of all numbers in box box average =
how many numbers in box
box SD = Javerage of (deviations from box average)2]
EVsum = number of draws x box average
SEsum = vnumber of draws X box SD-)
2
Tablesmiddot
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040 31JJ8 190 9426 ]40 99933 O~4S ]4I~13 ~ ~ ~ 195 MJ18 345 99944
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3
-----------
~- ~~ - - - bull - -- -- - shy
Statistics 1040 Sections 007 amp 009 Quiz 9 (20 Points)
Friday November 2 2007
Your Name
Question 1 Normal Approximation for Probability Histograms I (12 Points)
A programmer is working on a new program COIN to simulate tossing a coin As a preliminary test he sets up the programto do one million tosses The program returns with a count of 502015 heads The programmer looks at this and thinks Hmmm Two thousand and fifteen off Thats a lot No wait Compare it to the million Two thousand - forget the fifteen - out of a million is two out of a thousand Thats one in five hundred One fifth of a percent Very small Good COIN passes
Do you agree that COIN passes Answer yes or no and explain You should use box model calculations to support your answer
Please turn over
1
Question 2 Normal Approximation for Probability Histograms II (8 Points)
A coin is tossed 100 times True or false Just circle your answer You dont have to give any explanation Answer each of the following questions separately
1 The expected value for the number of heads is 50
True False
2 The expected value for the number of heads is 50 give or take 5 or so
True False
3 The number of heads will be 50
True False
4 The number of heads will be around 50 give or take 2 or so
True False
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets in the box
fraction fractionSD = (bigger - smaller) x
bigger x
smaller
Shortcut formulas for a box that contains only [Q] s and ITJ s
number of ITJ s average =
how many tIckets In the box
fraction fraction SD = of [] s x of [Q] s
2
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Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
~ J _ __ ~ bullbull
-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
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~ - -- _ -- -
Question 3 ChanceProbability III (3 Points)
Two cards will be dealt off the top of a well-shuffled deck You have a choice
(i) To win $1 if at least one of the two cards is a queen
(ii) To win $1 if the first card is a queen
Circle your answer
1 Option (i) is better for winning
2 Option (ii) is better for winning
3 Both options are equally good for winning
Question 4 ChanceProbability IV (4 Points)
One event has chance 12 another has chance 13 Fill in the blanks using one phrase from each pair below to make two true sentences Write out both sentences
If you want to find the chance that at least one of the two events both events will happen check to see if they are independent mutually exclusive If so you can add multiply the chances
Correct Sentence 1 If you want to find the chance that at least one of the two events will happen check to see if they are If so you can _ the chances
Correct Sentence 2 If you want to find the chance that both events will happen check to see if they are If so you can the chances
Question 5 ChanceProbability V (4 Points)
A coin is tossed 10 times Circle your answer
1 The chance of getting 10 heads in a row is 11024 True False
2 Given that the first 9 tosses were heads the chance of getting 10 heads in a row is -12 True False
2
Statistics 1040 Sections 007 amp 009 Quiz i (20 Points)
Friday October 26 2007
Your Name ~---------
Question 1 Law of Averages I (2 Points)
A box contains 10000 tickets 4000 [Q] s and 6000 [I] so And 10000 draws will be made at random with replacement from this box Which of the following best describes the situation Circle your answer You dont have to provide any explanations
1 The number of ls will be 6000 exactly
2 The number of ls is very likely to equal 6000 but there is also some small chance that it will not be equal to 6000
3 The number of ls is likely to be different from 6000 but the difference is likely to be small compared to 10000
Question 2 Law of Averages II (8 Points)
Circle your answer for each of the following four parts You dont have to provide any explanations
1 (2 Points) A die will be rolled some number of times and you win $1 if it shows an ace ( [J ) more than 20 of the time
Which is better 60 rolls or 600 rolls
2 (2 Points) As in 1) but you win the dollar if the percentage of aces is more than 15
Which is better 60 rolls or 600 rolls
3 (2 Points) As in 1) but you win the dollar if the percentage of aces is between 15 and 20
Which is better 60 rolls or 600 rolls
4 (2 Points) As in 1) but you win the dollar if the percentage of aces is exactly 16imiddot
Which is better 60 rolls or 600 rolls
1
Question 3 The Expected Value and Standard Error (10 Points)
One hundred draws are made at random with replacement from the box
1 (1 Point) If the sum of the draws is 321 what is their average
2 (1 Point) If the average of the draws is 378 what is the sum
3 (8 Points) Estimate the chance that the average of the draws is between 3 and 4 You have to make use of the normal curve to answer this part Show your work
Formulas
sum of all numbers in box box average =
how many numbers in box
box SD = Javerage of (deviations from box average)2]
EVsum = number of draws x box average
SEsum = vnumber of draws X box SD-)
2
Tablesmiddot
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040 31JJ8 190 9426 ]40 99933 O~4S ]4I~13 ~ ~ ~ 195 MJ18 345 99944
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3
-----------
~- ~~ - - - bull - -- -- - shy
Statistics 1040 Sections 007 amp 009 Quiz 9 (20 Points)
Friday November 2 2007
Your Name
Question 1 Normal Approximation for Probability Histograms I (12 Points)
A programmer is working on a new program COIN to simulate tossing a coin As a preliminary test he sets up the programto do one million tosses The program returns with a count of 502015 heads The programmer looks at this and thinks Hmmm Two thousand and fifteen off Thats a lot No wait Compare it to the million Two thousand - forget the fifteen - out of a million is two out of a thousand Thats one in five hundred One fifth of a percent Very small Good COIN passes
Do you agree that COIN passes Answer yes or no and explain You should use box model calculations to support your answer
Please turn over
1
Question 2 Normal Approximation for Probability Histograms II (8 Points)
A coin is tossed 100 times True or false Just circle your answer You dont have to give any explanation Answer each of the following questions separately
1 The expected value for the number of heads is 50
True False
2 The expected value for the number of heads is 50 give or take 5 or so
True False
3 The number of heads will be 50
True False
4 The number of heads will be around 50 give or take 2 or so
True False
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets in the box
fraction fractionSD = (bigger - smaller) x
bigger x
smaller
Shortcut formulas for a box that contains only [Q] s and ITJ s
number of ITJ s average =
how many tIckets In the box
fraction fraction SD = of [] s x of [Q] s
2
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Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
~ J _ __ ~ bullbull
-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
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Statistics 1040 Sections 007 amp 009 Quiz i (20 Points)
Friday October 26 2007
Your Name ~---------
Question 1 Law of Averages I (2 Points)
A box contains 10000 tickets 4000 [Q] s and 6000 [I] so And 10000 draws will be made at random with replacement from this box Which of the following best describes the situation Circle your answer You dont have to provide any explanations
1 The number of ls will be 6000 exactly
2 The number of ls is very likely to equal 6000 but there is also some small chance that it will not be equal to 6000
3 The number of ls is likely to be different from 6000 but the difference is likely to be small compared to 10000
Question 2 Law of Averages II (8 Points)
Circle your answer for each of the following four parts You dont have to provide any explanations
1 (2 Points) A die will be rolled some number of times and you win $1 if it shows an ace ( [J ) more than 20 of the time
Which is better 60 rolls or 600 rolls
2 (2 Points) As in 1) but you win the dollar if the percentage of aces is more than 15
Which is better 60 rolls or 600 rolls
3 (2 Points) As in 1) but you win the dollar if the percentage of aces is between 15 and 20
Which is better 60 rolls or 600 rolls
4 (2 Points) As in 1) but you win the dollar if the percentage of aces is exactly 16imiddot
Which is better 60 rolls or 600 rolls
1
Question 3 The Expected Value and Standard Error (10 Points)
One hundred draws are made at random with replacement from the box
1 (1 Point) If the sum of the draws is 321 what is their average
2 (1 Point) If the average of the draws is 378 what is the sum
3 (8 Points) Estimate the chance that the average of the draws is between 3 and 4 You have to make use of the normal curve to answer this part Show your work
Formulas
sum of all numbers in box box average =
how many numbers in box
box SD = Javerage of (deviations from box average)2]
EVsum = number of draws x box average
SEsum = vnumber of draws X box SD-)
2
Tablesmiddot
A NORMALTABLB
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040 31JJ8 190 9426 ]40 99933 O~4S ]4I~13 ~ ~ ~ 195 MJ18 345 99944
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075 5467 225 9756 31S 99ta2 Z~30 ~ ~ 9186 1 380 99986 l~ 135 9812 middotjU 99bullbull
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fmiddot2S 1881 t 27S 9940 130 8Oq4 i ~IO 9949 1~3S 8130 285 9956 140 imiddot aJss 190 9963 14S IS29 2+95 99611
3
-----------
~- ~~ - - - bull - -- -- - shy
Statistics 1040 Sections 007 amp 009 Quiz 9 (20 Points)
Friday November 2 2007
Your Name
Question 1 Normal Approximation for Probability Histograms I (12 Points)
A programmer is working on a new program COIN to simulate tossing a coin As a preliminary test he sets up the programto do one million tosses The program returns with a count of 502015 heads The programmer looks at this and thinks Hmmm Two thousand and fifteen off Thats a lot No wait Compare it to the million Two thousand - forget the fifteen - out of a million is two out of a thousand Thats one in five hundred One fifth of a percent Very small Good COIN passes
Do you agree that COIN passes Answer yes or no and explain You should use box model calculations to support your answer
Please turn over
1
Question 2 Normal Approximation for Probability Histograms II (8 Points)
A coin is tossed 100 times True or false Just circle your answer You dont have to give any explanation Answer each of the following questions separately
1 The expected value for the number of heads is 50
True False
2 The expected value for the number of heads is 50 give or take 5 or so
True False
3 The number of heads will be 50
True False
4 The number of heads will be around 50 give or take 2 or so
True False
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets in the box
fraction fractionSD = (bigger - smaller) x
bigger x
smaller
Shortcut formulas for a box that contains only [Q] s and ITJ s
number of ITJ s average =
how many tIckets In the box
fraction fraction SD = of [] s x of [Q] s
2
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3
-----------
)
Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
~ J _ __ ~ bullbull
-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
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Question 3 The Expected Value and Standard Error (10 Points)
One hundred draws are made at random with replacement from the box
1 (1 Point) If the sum of the draws is 321 what is their average
2 (1 Point) If the average of the draws is 378 what is the sum
3 (8 Points) Estimate the chance that the average of the draws is between 3 and 4 You have to make use of the normal curve to answer this part Show your work
Formulas
sum of all numbers in box box average =
how many numbers in box
box SD = Javerage of (deviations from box average)2]
EVsum = number of draws x box average
SEsum = vnumber of draws X box SD-)
2
Tablesmiddot
A NORMALTABLB
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040 31JJ8 190 9426 ]40 99933 O~4S ]4I~13 ~ ~ ~ 195 MJ18 345 99944
1 O~SO 3829 200 9545 350 99953 O~5S 4177 1 2~05 9596 3S j 99961 O1jO i 4S~ I 210 43 36Q ~ 99968 o~6S GA3 215 middot9JiBe 3 99914 010 SI61 210 9112 J70 99~91
075 5467 225 9756 31S 99ta2 Z~30 ~ ~ 9186 1 380 99986 l~ 135 9812 middotjU 99bullbull
O~90 6319 240 983(i 390 99990 O~9S 6579 2~4S 917 3~9S 99991lt
100 6827 250 9816 400 999931los r 7063 25S 9892 405 999949 110 1JJ1 2M 9Ull 4(0 9999il
11amplt t Aft middot20 IIS 1499 2w 7~ 4 15 ~9961 120 bull 7699 210 ~11 420 9999ll
fmiddot2S 1881 t 27S 9940 130 8Oq4 i ~IO 9949 1~3S 8130 285 9956 140 imiddot aJss 190 9963 14S IS29 2+95 99611
3
-----------
~- ~~ - - - bull - -- -- - shy
Statistics 1040 Sections 007 amp 009 Quiz 9 (20 Points)
Friday November 2 2007
Your Name
Question 1 Normal Approximation for Probability Histograms I (12 Points)
A programmer is working on a new program COIN to simulate tossing a coin As a preliminary test he sets up the programto do one million tosses The program returns with a count of 502015 heads The programmer looks at this and thinks Hmmm Two thousand and fifteen off Thats a lot No wait Compare it to the million Two thousand - forget the fifteen - out of a million is two out of a thousand Thats one in five hundred One fifth of a percent Very small Good COIN passes
Do you agree that COIN passes Answer yes or no and explain You should use box model calculations to support your answer
Please turn over
1
Question 2 Normal Approximation for Probability Histograms II (8 Points)
A coin is tossed 100 times True or false Just circle your answer You dont have to give any explanation Answer each of the following questions separately
1 The expected value for the number of heads is 50
True False
2 The expected value for the number of heads is 50 give or take 5 or so
True False
3 The number of heads will be 50
True False
4 The number of heads will be around 50 give or take 2 or so
True False
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets in the box
fraction fractionSD = (bigger - smaller) x
bigger x
smaller
Shortcut formulas for a box that contains only [Q] s and ITJ s
number of ITJ s average =
how many tIckets In the box
fraction fraction SD = of [] s x of [Q] s
2
Tablesmiddot
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3
-----------
)
Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
~ J _ __ ~ bullbull
-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
Show your workmiddot
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040 31JJ8 190 9426 ]40 99933 O~4S ]4I~13 ~ ~ ~ 195 MJ18 345 99944
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3
-----------
~- ~~ - - - bull - -- -- - shy
Statistics 1040 Sections 007 amp 009 Quiz 9 (20 Points)
Friday November 2 2007
Your Name
Question 1 Normal Approximation for Probability Histograms I (12 Points)
A programmer is working on a new program COIN to simulate tossing a coin As a preliminary test he sets up the programto do one million tosses The program returns with a count of 502015 heads The programmer looks at this and thinks Hmmm Two thousand and fifteen off Thats a lot No wait Compare it to the million Two thousand - forget the fifteen - out of a million is two out of a thousand Thats one in five hundred One fifth of a percent Very small Good COIN passes
Do you agree that COIN passes Answer yes or no and explain You should use box model calculations to support your answer
Please turn over
1
Question 2 Normal Approximation for Probability Histograms II (8 Points)
A coin is tossed 100 times True or false Just circle your answer You dont have to give any explanation Answer each of the following questions separately
1 The expected value for the number of heads is 50
True False
2 The expected value for the number of heads is 50 give or take 5 or so
True False
3 The number of heads will be 50
True False
4 The number of heads will be around 50 give or take 2 or so
True False
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets in the box
fraction fractionSD = (bigger - smaller) x
bigger x
smaller
Shortcut formulas for a box that contains only [Q] s and ITJ s
number of ITJ s average =
how many tIckets In the box
fraction fraction SD = of [] s x of [Q] s
2
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3
-----------
)
Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
~ J _ __ ~ bullbull
-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
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Statistics 1040 Sections 007 amp 009 Quiz 9 (20 Points)
Friday November 2 2007
Your Name
Question 1 Normal Approximation for Probability Histograms I (12 Points)
A programmer is working on a new program COIN to simulate tossing a coin As a preliminary test he sets up the programto do one million tosses The program returns with a count of 502015 heads The programmer looks at this and thinks Hmmm Two thousand and fifteen off Thats a lot No wait Compare it to the million Two thousand - forget the fifteen - out of a million is two out of a thousand Thats one in five hundred One fifth of a percent Very small Good COIN passes
Do you agree that COIN passes Answer yes or no and explain You should use box model calculations to support your answer
Please turn over
1
Question 2 Normal Approximation for Probability Histograms II (8 Points)
A coin is tossed 100 times True or false Just circle your answer You dont have to give any explanation Answer each of the following questions separately
1 The expected value for the number of heads is 50
True False
2 The expected value for the number of heads is 50 give or take 5 or so
True False
3 The number of heads will be 50
True False
4 The number of heads will be around 50 give or take 2 or so
True False
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets in the box
fraction fractionSD = (bigger - smaller) x
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Shortcut formulas for a box that contains only [Q] s and ITJ s
number of ITJ s average =
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fraction fraction SD = of [] s x of [Q] s
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Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
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number of IT] s average =
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fraction fraction SD
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EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
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-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
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EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
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number of ill s average = h k h b ow many tIc ets III t e ox
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EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
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Question 2 Normal Approximation for Probability Histograms II (8 Points)
A coin is tossed 100 times True or false Just circle your answer You dont have to give any explanation Answer each of the following questions separately
1 The expected value for the number of heads is 50
True False
2 The expected value for the number of heads is 50 give or take 5 or so
True False
3 The number of heads will be 50
True False
4 The number of heads will be around 50 give or take 2 or so
True False
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets in the box
fraction fractionSD = (bigger - smaller) x
bigger x
smaller
Shortcut formulas for a box that contains only [Q] s and ITJ s
number of ITJ s average =
how many tIckets In the box
fraction fraction SD = of [] s x of [Q] s
2
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-----------
)
Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
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-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
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3
-----------
)
Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
~ J _ __ ~ bullbull
-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
Show your workmiddot
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-----------
)
Statistics 1040 Sections 007 amp 009 Quiz 10 (20 Points)
Frida~ November 16 2007
Your Name
Question 1 The Accuracy of Percentages (20 Points)
The National Assessment of Educational Progress administers standardized achievement tests to nationwide samples of 17-year-olds in school One year the tests covered history and literature You may assume that a simple random sample of size 6000 was taken Only 361 of the students in the sample knew that Chaucer wrote The Canterbury Tales but 952 knew that Edison invented the light bulb
1 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Chaucer wrote The Canterbury Tales Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
2 (10 Points) Is it possible to find a 95 confidence interval for the percentage of all 17-year-olds in school who knew that Edison invented the light bulb Yes or No - Circle your answer If yes calculate this CI (and show your work) If no clearly indicate why this is not possible
Please turn over
1
Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
~ J _ __ ~ bullbull
-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
Show your workmiddot
1
~ 1
1
k
Mem
ory
A~ds
ANO
RM
AL T
AB
LE
~~)
Piea
se n
ote
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[ese a
r~prov
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gtr yo
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enl~~c
el ~ut
it is
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res
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ibili
ty to
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w h~~j
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igh
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r =
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rea
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Formulas
sum of all numbers in box box average =
how many numbers In box
box SD = Javerage of [(deviations from box ~erage)2]
EVsum = number of draws x box average
SEsum = vnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average =
how many tickets In the box
fraction fractionSD = (bigger - smaller) x x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and IT] s
number of IT] s average =
how many tickets in the box
fraction fraction SD
of IT] s x of [Q] s
EV = of[J s in the box
SEsumSEor = x 100 o number of draws
2
~ J _ __ ~ bullbull
-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
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-----------
Statistics 1040 Sections 007 amp 009 Quiz 11 (20 Points)
Wednesday November 282007
Your Name
Question 1 The Accuracy of Averages (20 Points)
One year there were about 3000 institutions of higher learning in the US (including junior colleges and community colleges) As part of a continuing study of higher educashytion the Carnegie Commission took a simple random sample of 400 of these institutions The average enrollment in the 400 sample schools was 3700 and the SD was 6500 The Commission estimates the average enrollment at all 3000 institutions to be around 3700 they put a give-or-take number of 325 on this estimate
Say whether each of the following statements is true or false and explain If you need more information to decide say what you need and why
1 (4 Points) An approximate 68-confidence interval for the average enrollment of all 3000 institutions runs from 3375 to 4025
Yes No or Need more information Circle your answer and explain
2 (4 Points) If a statistician takes a simple random sample of 400 institutions out of 3000 and goes one SE either way from the average enrollment of the 400 samshyple schools there is about a 68 chance that this interval will cover the average enrollment of all 3000 schools
Yes No or Need more information Circle your answer and explain
Please turn over
1
3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
Show your workmiddot
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3 (4 Points) About 68 of the schools in the sample had enrollments in the range 3700 plusmn 6500
Yes No or Need more information Circle your answer and explain
4 (4 Points) It is estimated that 68 of the 3000 institutions of higher learning in the US enrolled between 3700 - 325 = 3375 and 3700 + 325 = 4025 students
Yes No or Need more information Circle your answer and explain
5 (4 Points) The normal curve cant be used to figure confidence levels here at all because the data dont follow the normal curve
Yes No or Need more information Circle your answer and explain
2
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
Show your workmiddot
1
~ 1
1
k
Mem
ory
A~ds
ANO
RM
AL T
AB
LE
~~)
Piea
se n
ote
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[ese a
r~prov
~dedfc
gtr yo
~rcOnv
enl~~c
el ~ut
it is
youi
res
pons
ibili
ty to
kno
w h~~j
J
and
whe
n to
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the
m
middotAr
a
He
igh
t
rnis
erro
r =
vl=1
1 x
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ac
errt
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e =
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Dy
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0
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rea
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ea
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rea
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um
=
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t ~
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y -
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SD
box
=
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s )(
frac
tion
of 1
s
num
ber
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raw
s ~
llo
Iebo
x
vnumb~r
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s x
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x
num
ber
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s
x S
D
zmm
ber
of d
raw
s shy
1 sn
+
00
0 0
005
3
99
019
7
97
015
11
92
020
15
85
025
19
74
030
23
58
035
27
37
0
40
310
8 00
45
347
3
050
38
29
055
41
77
060
45
15
065
48
43
070
5
161
1 ~SO
8
664
155
87
89
1
60
89~04
165
90
-11
170
91
09
175
91
99
180
9
281
1
85
935
7
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94
26
195
94
88
200
95
45
205
9S9~
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96
43
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20
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30
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335
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919
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61
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ve =
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ox
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sum
shy~lUmber
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54
67
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3
085
60
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95
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56
2
30
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6
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98
12
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AO
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245
98
57
375
99
982
3
80
999
86
38
5
999
88
390
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90
39
5
999
92
EV
=
SE
=
of
ls
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the
box
( SE~um)
num
ber
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raw
s gtlt
10
0
100
682
7 1
05
706
3 L
lO
728
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15
749
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12
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99
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98
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255
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here
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s th
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firs
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orth
e se
cond
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ntitY
i an
d t~e
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ntiti
es a
re i
ndep
ende
nt
125
78~87
130
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230
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O
83 ~ ~
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56
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63
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99
79
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ree
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71
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66
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00
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152
082
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101
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71
38
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66
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292
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2
20
27
2 3
11
11
305
4~8
5
58
81S
1
034
12
90
172
812
0
70
136
178
2
18
268
3
05
12
196
8 24
73
305
7 5
23
6~0
9
03
113
4 1
40
j 18
55
210
313
0
69
135
1
77
216
2
65
301
26
22
13
411
5
8914
0
69
135
70
4 9
93
123
4
151
2 19
81
223
6 27
69
176
2
14
262
2
98
14
466
6
57
10
82IS
0
69
134
1
75
213
2
60
295
7
79
1~34
16
22
21
06
23
69
291
4IS
5
23
726
8
55
117
2
143
4 17
32
~231
25
00
30
58
16
0
69
134
1
75
212
2
58
292
16
5
8117
0
69
133
1
74
2
11
796
931
126~
15
34
(8
42
23
54
26
30
3
200
25
7 2
90
17
641
IH
06
9
13
3 1
73
210
2
55
28
8 8
67
100
9 13
53
163
4 19
51
24
77
27
59
33
41
1-819
0
69
133
1
73
209
2
S4
286
7
00
93
9 10
87
144
4
173
4 2
060
2
59
9 2
887
3
48
I
19
63
20
069
1
33
172
2
09
25
3 2
85
101
2 1L
6s
fS3
S
183
4 2L
69
27
20
30J
4 36
19
20
8
26
108
5 12
44
16
27
193
4 2
278
2
841
3
i41
J7
S7
21
069
1
32
17
2 2
08
252
2
83
SO
lirtC
Ada
ptcd
fro
in P
O 11
2 o(
Sir
R A
Fi
shcr
SIQtiIN~QI
Mth
Qlb
orR
mQ
rh
Wor
km
22
06
9
132
1
7
207
251
2
82
lte
dinb
ursh
01
1 vcr
amp B
oyd
195~)
23
06
9
1
32
1
71
~ 07
2S
0
~81
24
0
68
1
32
l
71
2
06
2
49
2
80
25
1
32
24
9 0
68
1
71
~06
2
79
~
~~
shy
Formulas
sum of all numbers in boxbox average = ----------shy
how many numbers in box
box SD = Javerage of [(deviations from box average)2]
EVsum = number of draws x box average
SEsum = Jnumber of draws x box SD
SEsumSE =EVavg = box average av 9 number of draws
Shortcut formulas for a box that contains only two different numbers
(smaller x how many) + (bigger x how many) average = h k h bow many tIc ets In t e ox
fraction x fractionSD = (bigger - smaller) x
bigger smaller
Shortcut formulas for a box that contains only [Q] s and [I] s
number of ill s average = h k h b ow many tIc ets III t e ox
fraction fraction SD
of II] s x of] s
EV = of [I] s in the box
SE = SEsum x 100 number of draws
3
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
Show your workmiddot
1
~ 1
1
k
Mem
ory
A~ds
ANO
RM
AL T
AB
LE
~~)
Piea
se n
ote
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gtr yo
~rcOnv
enl~~c
el ~ut
it is
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res
pons
ibili
ty to
kno
w h~~j
J
and
whe
n to
use
the
m
middotAr
a
He
igh
t
rnis
erro
r =
vl=1
1 x
SDy
(r~~
-=
=(p
ac
errt
)
slop
e =
r S
Dy
x S
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-z
0
z A
rea
z Ar
ea
z A
rea
EYsu~
SS
um
=
inte
rcep
t ~
ave
y -
s1o
p~ x
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SD
box
=
rra~tlon
bfo
s )(
frac
tion
of 1
s
num
ber
of d
raw
s ~
llo
Iebo
x
vnumb~r
of
draw
s x
SDbo
x
num
ber
of d
raw
s
x S
D
zmm
ber
of d
raw
s shy
1 sn
+
00
0 0
005
3
99
019
7
97
015
11
92
020
15
85
025
19
74
030
23
58
035
27
37
0
40
310
8 00
45
347
3
050
38
29
055
41
77
060
45
15
065
48
43
070
5
161
1 ~SO
8
664
155
87
89
1
60
89~04
165
90
-11
170
91
09
175
91
99
180
9
281
1
85
935
7
190
94
26
195
94
88
200
95
45
205
9S9~
210
96
43
215
9
684
2
20
972
2
30
0 99
730
3
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997
71
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806
3
15
998
37
320
99
863
325
99
885
3
30
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03
335
99
919
3
40
999
33
345
9-
994
4
350
99~9S3
35
59
99
61
3
60
999
68
3~65
99
974
3
70
999
78
EV~ve=
SEa
ve =
aveb
ox
SE
sum
shy~lUmber
otdraw~
07S
54
67
08
0 5
76
3
085
60
47
09
0
631
9 0
95
657
9
~25
97
56
2
30
978
6
~35
98
12
2
AO
middot98
36
245
98
57
375
99
982
3
80
999
86
38
5
999
88
390
-99~ 9
90
39
5
999
92
EV
=
SE
=
of
ls
in
the
box
( SE~um)
num
ber
0pound d
raw
s gtlt
10
0
100
682
7 1
05
706
3 L
lO
728
7 1
15
749
9
12
0 76
99
250
98
76
255
9
892
26
0 99
07
2~65
99
20
27
0 99~1
40
0 9
9~9937
4
05
9
999
49
4
10middot
-99
995
9 4
15
99
9967
42
0 99
997
3
SE
difi
=
02
+ b
2 w
here
0 i
s th
e S
Efo
rthe
firs
t q~antltr
b Is
the
SE f
orth
e se
cond
qua
ntitY
i an
d t~e
two
qua
ntiti
es a
re i
ndep
ende
nt
125
78~87
130
~O64
1-3-5
8
230
lA
O
83 ~ ~
5
145
852
9
2
75middot
99AO
2
80
~99~49
28
5 99
56
~90
99
63
2
95
996
8
42
5 99
99
79
4 3
0 99
99$
3 4
35
99
9986
~40
99
9989
4
45
999
991
(gt
)
Q~r
j ~
C
I
A~106
TA
BLES
TA
BLE
S A~
TO(
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AB
LE
AC
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QU
AR
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BLE
StU
dlZ
lltll
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he ~had
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e t
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le
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ree
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95
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50
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a
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12
71
318
2 63
66
I
00
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0
0039
0
016
0
152
082
0
46
101
2
71
38
4
66
41
89
292
430
6
96
992
2
002
0 0
10
021
0
71
middot13
9 2
41
460
5
993
076
1
64
235
3
18
4
54
584
9
213
012
03
05
05
8
14
2 2
37
3~7
625
7
824
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1
53
f1
3
278
3
75
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11
34
4 0
30
071
1
06
220
3
36
488
7
78
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S 0
73
148
20
l 2
57
336
4
03
132
85
055
1
14
161
3
00
435
6Q
6 9
24
110
7 15
09
6 0
72-
144
1
94
2AS
31
4 3
71
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87
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2
20
38
3 7
237
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1
41
189
2
36
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3
50
53
1
06
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59
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2
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67
63
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120~
8 0
71
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1
86
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90
336
140
7 18
48
8
165
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70
L38
~183
2
26
282
3
25
raquo 2
73
349
5
53
734
9
52
133
6 IS
51
20
09
9 2
09
333
4
17
639
8
34
1016
6 14
68
16
9210
0
70
137
1
81
223
2
76
216
710
2
563
17
394
4
86
72
7 9
34
11
78
159
9 18
31
232
1 II
0
70
13
6
180
2
20
27
2 3
11
11
305
4~8
5
58
81S
1
034
12
90
172
812
0
70
136
178
2
18
268
3
05
12
196
8 24
73
305
7 5
23
6~0
9
03
113
4 1
40
j 18
55
210
313
0
69
135
1
77
216
2
65
301
26
22
13
411
5
8914
0
69
135
70
4 9
93
123
4
151
2 19
81
223
6 27
69
176
2
14
262
2
98
14
466
6
57
10
82IS
0
69
134
1
75
213
2
60
295
7
79
1~34
16
22
21
06
23
69
291
4IS
5
23
726
8
55
117
2
143
4 17
32
~231
25
00
30
58
16
0
69
134
1
75
212
2
58
292
16
5
8117
0
69
133
1
74
2
11
796
931
126~
15
34
(8
42
23
54
26
30
3
200
25
7 2
90
17
641
IH
06
9
13
3 1
73
210
2
55
28
8 8
67
100
9 13
53
163
4 19
51
24
77
27
59
33
41
1-819
0
69
133
1
73
209
2
S4
286
7
00
93
9 10
87
144
4
173
4 2
060
2
59
9 2
887
3
48
I
19
63
20
069
1
33
172
2
09
25
3 2
85
101
2 1L
6s
fS3
S
183
4 2L
69
27
20
30J
4 36
19
20
8
26
108
5 12
44
16
27
193
4 2
278
2
841
3
i41
J7
S7
21
069
1
32
17
2 2
08
252
2
83
SO
lirtC
Ada
ptcd
fro
in P
O 11
2 o(
Sir
R A
Fi
shcr
SIQtiIN~QI
Mth
Qlb
orR
mQ
rh
Wor
km
22
06
9
132
1
7
207
251
2
82
lte
dinb
ursh
01
1 vcr
amp B
oyd
195~)
23
06
9
1
32
1
71
~ 07
2S
0
~81
24
0
68
1
32
l
71
2
06
2
49
2
80
25
1
32
24
9 0
68
1
71
~06
2
79
~
~~
shy
- ~- -- ~~-~--
Statistics 1040 Sections 007 amp 009 Quiz 12 (20 Points)
Wednesday December 5 2007
Your Name ---------- shy
Question 1 Tests of Significance I (20 Points)
A random sample of 18 Penn State students was selected The nose length of each student was measured in millimeters and was recorded in the following data set
41 57 43 42 55 35 36 40 45 55 55 36 45 44 45 47 37 48
A student thinks that the average nose length of Penn State students is fairly large He thinks that the average nose length could be more than 44 millimeters Does this sample of 18 students provide evidence to suggest that the average nose length is more than 44 millimeters State the null and the alternative hypothesis calculate the test statistic (after finding the average and SD of the sample) obtain the P-value and clearly state your conclusions Assume that the nose lengths follow the normal curve
Indicate whether this is a z-test t-test or 2-sample z-test Circle your answer and explain why you have chosen that test (If we cannot conduct a test state so and explain why not)
Show your workmiddot
1
~ 1
1
k
Mem
ory
A~ds
ANO
RM
AL T
AB
LE
~~)
Piea
se n
ote
~Lc
[ese a
r~prov
~dedfc
gtr yo
~rcOnv
enl~~c
el ~ut
it is
youi
res
pons
ibili
ty to
kno
w h~~j
J
and
whe
n to
use
the
m
middotAr
a
He
igh
t
rnis
erro
r =
vl=1
1 x
SDy
(r~~
-=
=(p
ac
errt
)
slop
e =
r S
Dy
x S
Dx
-z
0
z A
rea
z Ar
ea
z A
rea
EYsu~
SS
um
=
inte
rcep
t ~
ave
y -
s1o
p~ x
avex
SD
box
=
rra~tlon
bfo
s )(
frac
tion
of 1
s
num
ber
of d
raw
s ~
llo
Iebo
x
vnumb~r
of
draw
s x
SDbo
x
num
ber
of d
raw
s
x S
D
zmm
ber
of d
raw
s shy
1 sn
+
00
0 0
005
3
99
019
7
97
015
11
92
020
15
85
025
19
74
030
23
58
035
27
37
0
40
310
8 00
45
347
3
050
38
29
055
41
77
060
45
15
065
48
43
070
5
161
1 ~SO
8
664
155
87
89
1
60
89~04
165
90
-11
170
91
09
175
91
99
180
9
281
1
85
935
7
190
94
26
195
94
88
200
95
45
205
9S9~
210
96
43
215
9
684
2
20
972
2
30
0 99
730
3
05
997
71
310
99
806
3
15
998
37
320
99
863
325
99
885
3
30
999
03
335
99
919
3
40
999
33
345
9-
994
4
350
99~9S3
35
59
99
61
3
60
999
68
3~65
99
974
3
70
999
78
EV~ve=
SEa
ve =
aveb
ox
SE
sum
shy~lUmber
otdraw~
07S
54
67
08
0 5
76
3
085
60
47
09
0
631
9 0
95
657
9
~25
97
56
2
30
978
6
~35
98
12
2
AO
middot98
36
245
98
57
375
99
982
3
80
999
86
38
5
999
88
390
-99~ 9
90
39
5
999
92
EV
=
SE
=
of
ls
in
the
box
( SE~um)
num
ber
0pound d
raw
s gtlt
10
0
100
682
7 1
05
706
3 L
lO
728
7 1
15
749
9
12
0 76
99
250
98
76
255
9
892
26
0 99
07
2~65
99
20
27
0 99~1
40
0 9
9~9937
4
05
9
999
49
4
10middot
-99
995
9 4
15
99
9967
42
0 99
997
3
SE
difi
=
02
+ b
2 w
here
0 i
s th
e S
Efo
rthe
firs
t q~antltr
b Is
the
SE f
orth
e se
cond
qua
ntitY
i an
d t~e
two
qua
ntiti
es a
re i
ndep
ende
nt
125
78~87
130
~O64
1-3-5
8
230
lA
O
83 ~ ~
5
145
852
9
2
75middot
99AO
2
80
~99~49
28
5 99
56
~90
99
63
2
95
996
8
42
5 99
99
79
4 3
0 99
99$
3 4
35
99
9986
~40
99
9989
4
45
999
991
(gt
)
Q~r
j ~
C
I
A~106
TA
BLES
TA
BLE
S A~
TO(
At-T
AB
LE
AC
HI-S
QU
AR
ETA
BLE
StU
dlZ
lltll
ll carv~1
wit
h T
he ~had
d
are_ I
e
Th~
chimiddot~q~Nr
eU
tV
amp1
~9re~
of rreed~m
how
sho
Wn
alo
ns -
tMc
tcp
wl~hdet8lbull
bullbull o
f
i
lie h
adQ
c1
)f
aa
js
at th~
leFt
ert
heo
bb
le
or
tnCll
tab
le
fe
ed
om
hol
oUn
show
n ~IO$
th
e t
op
8Ion~
th~
leF
t OT
of
th
e
tal
gtl~
the -
tab
le ~
1i
~j
sM
own
in t
he
b
Cd
yer
tnc
tli
ble
ibullbull
ho
wn
in
th
e
bod)
o
t th
e i
ab
le
lgtg
rtts
of
D
egru
sof
ree
a9m
25
IO~
59
0
25
0
5
fr~edom
99
95
90
Ofcent
50
JO
a
05
11
100
3
08
631
12
71
318
2 63
66
I
00
0016
0
0039
0
016
0
152
082
0
46
101
2
71
38
4
66
41
89
292
430
6
96
992
2
002
0 0
10
021
0
71
middot13
9 2
41
460
5
993
076
1
64
235
3
18
4
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