integrating the computer and the calculator in the statistics classroom international conference on...

Integrating the Computer and the Integrating the Computer and the Calculator in the Statistics ClassroomCalculator in the Statistics Classroom

International Conference on Technology in International Conference on Technology in Collegiate MathematicsCollegiate Mathematics

Friday, November 5, 1999Friday, November 5, 1999

Session: S11 Location: Boardroom IVSession: S11 Location: Boardroom IV8:00 -8:45 AM San Francisco8:00 -8:45 AM San Francisco

11/1/9911/1/99 [email protected]@mc3.edu 22##

Integrating the Computer and the Integrating the Computer and the Calculator in the Statistics ClassroomCalculator in the Statistics Classroom

Roseanne HofmannRoseanne Hofmann

Montgomery County Community CollegeMontgomery County Community College

[email protected]@mc3.edu


Special Thanks to:

MCCC Foundation

Dean Brad Gottfried

Shayne Clark Wallis

Students who used the materials


Talking isn’t

Teaching


Listening isn’t Learning


Use a Constructivist Approach in Teaching.Use a Constructivist Approach in Teaching.

Give up the role of “sage on Give up the role of “sage on the stage” to become “guide the stage” to become “guide on the side.”on the side.”

Research encourages teachers toResearch encourages teachers to


Changes in Teaching FocusChanges in Teaching Focus

TeacherTeacherCenteredCentered

StudentStudentCenteredCentered


Give a fish and they eat for a day;

teach them to fish and they eat for a lifetime.


“Lure” students into Mathematics by getting them to “play” with interesting application problems.


VisualizationVisualizationin the broadest sense has always in the broadest sense has always

been important in mathematics.been important in mathematics.

Teaching based on visualization requires us Teaching based on visualization requires us

to relearn many of our pedagogical skills.to relearn many of our pedagogical skills.

Dock and TeachDock and Teach

Borrowing a term from the business Borrowing a term from the business world that uses portable computersworld that uses portable computers


Purpose of Internal GrantPurpose of Internal Grant

• Use of Notebook Computer in Use of Notebook Computer in

Classroom, Office, and HomeClassroom, Office, and Home

• Writing of Multimedia modules for Writing of Multimedia modules for

Elementary AlgebraElementary Algebra


Bonus

•Use computer for PowerPoint presentations supplied by Statistics textbook

•Use computer for Statistics CD authored by Velleman


Hardware - ObviousHardware - Obvious

• ProjectorProjector

• Portable ComputerPortable Computer

• Connection to NetworkConnection to Network

• TI-83 Plus CalculatorTI-83 Plus Calculator


SoftwareSoftware

• Velleman CD diskVelleman CD disk

• Triola PowerPoint SlidesTriola PowerPoint Slides


Cost ConcernsCost Concerns

• SoftwareSoftware

• TextbookTextbook

• CalculatorCalculator


• Balance of PowerPoint and Velleman CDBalance of PowerPoint and Velleman CD

• Graphics CalculatorGraphics Calculator

• Group LearningGroup Learning

• Simulations in ClassSimulations in Class

TeachingTeaching


MONTGOMERY COUNTY COMMUNITY COLLEGEIntroduction to Statistics I

Fall, 1999

MAT 131 BC 9:05-10:00 a.m.PH Room 116

Roseanne Hofmann, Ed.D.

MAT 131 CC 10:10-11:05 A.M.PH Room 116

[email protected]

CATALOG DESCRIPTION

A basic course designed for students in all fields. Topics include organization of data,measures of central tendency, measures of variation, statistical inference and correlation.This is a self-contained course. With MAT 132, it is a course with greater depth andapplications. A graphing calculator is required for class, homework, and testing.Classroom instruction and programs will be presented using a TI-83+ graphingcalculator.

PREREQUISITES

Math placement test recommendation of “ABV 100” (above MAT 100) or MAT 100,with a minimum grade of “C”.


OBJECTIVES/OUTCOMES

Upon completion of this course, students should be able to

1. Understand descriptive statistics by being able to find by hand and using the TIcalculator, mean, median, mode, midrange, range, variance and standard deviation fora given set of data.

2. Make frequency tables, histograms, frequency polygrams, ogives, pie charts, stem andleaf plots and box plots.

3. Solve probability problems using the addition and multiplication rules andcomplementary events.

4. Understand probability distribution, random variable, mean, variance, and expectationfor the binomial and normal distributions.

5. Understand the normal distribution as an approximation to the binomial distributionand the Central Limit Theorem.

6. Estimate sample sizes of means and sample sizes of proportions.7. Test hypotheses: test a claim about a mean, understand p-values, a t-test, and tests of

proportions.8. Make inferences from two samples using means and proportions.9. Understand correlation and regression.10. Understand multinomial experiments and contingency tables.11. Use the TI graphing calculator to do many of the statistical tests described above.


REQUIRED MATERIALS

Required Text: Elementary Statistics, 7th edition, Mario F. Triola, Addison-WesleyPublishing Company, 1998.

1. A TI-83+ graphing calculator2. ActivStats, CD-ROM, Paul Velleman

SUGGESTED TEXTBOOKS

1. Student’s Solution Manual to accompany the textbook, Milton Loyer2. TI-83 Companion to Elementary Statistics, 7th edition, Larry Morgan

Student projects will be required.


TENTATIVE SCHEDULESeptember 1 1.1, 1.2; V3.1 October 25 7.1, 7.2; V17.1

3 1.3, 1.4; V8.1 27 7.38 2.1, 2.2; V3.2 29 7.3

10 2.3; V4.1November 1 7.4

13 2.4; V4.2 3 7.5; V19.115 2.5; V5.1 5 Review17 2.6

8 Test 3 Chs. 5 and 720 2.7; V2.7 10 6.1, 6.2; V15.122 Review 12 6.3; V16.124 Test 1 Chs. 1 and 227 3.1, 3.2 Project Due; V10.1 15 6.4; V19.129 3.3 17 9.1, 9.2; V21.1

October 1 3.4; V9.1, 11.1 19 9.3; V22.1, 23.1

4 4.1, 4.2; V13.1 22 10.1, 10.2 Project Due; V24.16 4.38 4.4 29 10.3

11 Review December 1 8.1, 8.2; V20.113 Test 2 Chs. 3 and 4 3 8.3, 8.415 5.1, 5.2; V12.1

6 Review18 5.3, 5.4; V14.1 8 Test 4 Chs. 6, 9, 10, 820 5.5 10 Review22 5.5 13 Last Class


Data Sheet

1. _______Sex2. _______Married/Single3. _______Height(In)4. _______Number of Brother and Sisters5. _______Number of Children6. _______Birth Month7. _______Number of Credits currently enrolled for8. _______Average Number of hours of Sleep per night9. _______Number of Pierced Ears10. _______Watch Soaps regularly – yes/no11. _______Pulse Rate12. _______Amount of change in pocket or purse

First Day Data SheetFirst Day Data Sheet


MAT 131 Fall 1999 Statistics Project (50 points)PART I Due date: Monday, September 27, 1999Remember neatness counts and there is a grade reduction for lateness.

1. (10 pts.) Randomly survey 32 people over 18 years of age. Use either all males or all females.Obtain the following data for each:a. their hand size, measured to the nearest 1/4 inchb. their shoe size, to the nearest 1/2 inch (Do not include width.)List the data in the pairs obtained:i.e. person 1 hand size shoe size

person 2 hand size shoe size 2. (5 pts.) State a purpose for this project. This means you must invent a reason for wanting the

required data. (Use your imagination.) Also state a specific population. (Think about who yoursample represents.)

3. (18 pts.) For the hand size data: find: MEAN, MEDIAN, MODE, RANGE, VARIANCE,STANDARD DEVIATION, Q1, Q3. Show any work or explain what you did to get your answers.ALSO, explain what information Q1 gives you in terms of your numbers.

4. (6 pts.) Arrange the hand size data into grouped data. Use 4 or 5 classes. Find: MEAN, MEDIAN,VARIANCE, STANDARD DEVIATION for this grouped data. Explain what you did or show howyou got your answers.

5. (5 pts.) Compare the common parts of question #3 and #4. What do you conclude? 6. (6 pts.) Arrange the show sizes into a frequency distribution (grouped data) and again use 4 or 5groups. Make a histogram for this grouped data, carefully labeling each axis with numbers and names.The histogram should also have a title.


PART II Due date: Monday, November 22, 1999For Part II of the project, use the raw data, not the grouped data. Attach a copy of your original data. Then summarizeyour data in a table like the following:

HAND SIZE SHOE SIZESample mean, xSample standard deviation, sSample size, nYou must show all work (not just answers). If you use your calculator to find an answer, explain carefully what youdid. Again, neatness counts and there is a grade reduction for lateness. 7. (18 pts.) For the HAND SIZE data:

a. Give the best point estimate for the average hand size based on your sample results;b. Depending on whether your sample was composed of males or females, test the claim that:

AVERAGE HAND SIZE FOR MEN IS 7 1/2AVERAGE HAND SIZE FOR WOMEN IS 6 1/2In either case, assume that the population is normally distributed and state your conclusion for = 0.05.Give the P-value for the test.

c. Determine a 98% confidence interval for . Again, assume the population is normally distributed.8. (8 pts.) For the SHOE SIZE data:

a. Determine the best point estimate for the proportion of women with shoe size 6 or of men with shoe size 9,depending on your sample;

b. Determine a 99% confidence interval for this point estimate. 9. (6 pts.) Referring back to the paired data (#1), draw a scatter diagram. Label each axis carefully with names and

numbers. Your scatter diagram should have a title.

10. (8 pts.) Find "r," explaining how you did it. Determine if there is a linear correlation between shoe sizes and handsizes. ( = 0.05)

11. (8 pts.) Regardless of your answer to the previous question, determine the equation for the regression line andgraph the line on the scatter diagram done in #10. Be sure to give the points you used to graph the line.

12. (2 pts.) Use the regression line found in #11 to predict the shoe size of a person whose hand size is 6 1/4".


Mat 131 Jigsaw

1. Complete collection of elements to bestudied

Population

2. A subset of a population Sample3. Numerical measurement describing

some characteristic of a populationParameter

4. Numerical measurement describingsome characteristic of a sample

Statistic

5. Zip code - level of measurement Nominal6. Cars described as subcompact,

compact, intermediate - level ofmeasurement

Ordinal

7. Temperatures of irate Mat 131 studentsover price of book - level ofmeasurement

Interval

Grouping ToolGrouping Tool


8. Annual income of doctors - level ofmeasurement

Ratio

9. Number of Siblings - discrete orcontinuous

Discrete

10. Heights of Students - discrete orcontinuous

Continuous

11. Equal chance of being selected -numbers in hat

Random sample

12. A sociologist at the CC Collegesurveys all students from each of 20randomly selected 4 English Classes

Cluster

13. A sociologist at the CC College selects12 men and 12 women from each of 4English classes

Stratified sample

Grouping ToolGrouping Tool


DATA SETS

Given the following data sets find the mean, mode, median, and standarddeviation. Make a table with the data sets in rows and the mean, modemedian, and standard deviation in columns. Draw a box plot and a histogramfor each.

A = 2,3,4,5,6,14,15,16,17,18

B = 2,10,10,10,10,10,10,10,10,18C= 2,2,2,2,3,16,18,18,18,18D = 2,3,5,5,6,10,15,18,18,18E = 2,4,10,10,10,10,10,10,16,18F = 2,4,8,9,10,10,12,16,18G = 8,9,9,9,10,10,10,10,11,11,12,13H = 52,53,55,55,56,60,65,68,68,68J = 8,8,9,9,9,11,11,11,11,11


Input the data in L1, L2, L3, etc. Share the list with your partner by havingyour partner use GetCalc from the catalogue. Then use One Variablestatistics on each list.


Source:http://m-ms.com/factory/history/faq1.html

Hofmann


M A T 1 3 1 M u l t i p l e C h o i c e T e s t N a m e _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _1 . T h e p e r i o d o f t i m e d u r in g w h i c h r e p t i l e s f i r s t a p p e a r e d o n e a r th i s t h e _ _ _ _ _ p e r i o d .

a . J u r a s s i cb . D e v o n i a nc . T r i a s s i c

d . C a m b r i a ne . L o w e r C r e t a c e o u s

2 . T h e K i n g o f E n g la n d f r o m 1 8 2 0 t o 1 8 3 0 w a sa . G e o r g e Ib . G e o r g e I Ic . G e o r g e I I I

d . G e o r g e I Ve . G e o r g e V

3 . T h e c h e m i c a l e l e m e n t w i t h t h e a t o m i c n u m b e r 7 7 i sa . I r i d i u mb . O s m i u mc . R h e n i u m

d . T h a l l i u me . R h o d iu m

4 . T h e K i n g o f S p a in f r o m 1 4 5 2 t o 1 5 1 6 w a sa . F e r d i n a n d I d . F e r d i n a n d IVb . F e r d i n a n d I I e . F e r d i n a n d Vc . F e r d i n a n d I I I

5 . T h e B a b y lo n i a n c u n e i f o r m n u m e r a l f o r 1 3 1 i sa . 9 I d .

b . e . c . C X X X I


6. The third largest planet in our solar system isa. Saturnb. Earthc. Jupiter

d. Uranuse. Neptune

7. The 11th president of the United States wasa. Fillmoreb. Polkc. Pierce

d. Tylere. Buchanan

8. The first two men on the moon were Armstrong and Aldrin. On that Apollo flight, who was the thirdcrew member?a. Shepardb. Schirrac. Grissom

d. Whitee. Collins

9. Who recorded the 1979 disco hit “Bad Girls?”a. Patti LaBelleb. Robert Flackc. Donna Summers

d. Gladys Knighte. none of the above

10. The real name of Lewis Carroll isa. Charles Lambb. Charles Brownc. Charles Doyle

d. Charles Dodgsone. Charles McCarthy


Triola, page 258:Given that the population of men has normally distributed weights, with a mean of173 lb. and a standard deviation of 30 lb., find the probability that if one man israndomly selected, his weight is greater than 180 lb.


Triola, page 362

The Jack Wilson Health Club claims in advertisements that “you will lose weight aftertwo days of the Jack Wilson diet and exercise program.” The Dade County Bureau ofConsumer Affairs conducts a test of that claim by randomly selecting 33 people whohave signed up for the program. It was found that the 33 people lost an average of .37lb., with a standard deviation of .98 lb. Use a .05 level of significance to test theadvertised claim.


Uniform

Normal

Skewed Right Skewed Left

Important Distributions


µ µ is pronounced ‘mu’ and denotes theis pronounced ‘mu’ and denotes the mean of mean of all valuesall values

Notation

x is pronounced ‘x-bar’ and denotes the mean of a set ofsample values

denotes the summation of a set of values

x is the variable usually used to represent the individual data values

n represents the number of data values in a sample

N represents the number of data values in a population

in a population


x =

Definitions MeanMean

the value obtained by adding the scores and the value obtained by adding the scores and dividing the total by the dividing the total by the number of scoresnumber of scores

n x

Sample

Nµ = xPopulation


DefinitionDefinitionStandard Normal DistributionStandard Normal Distribution

• a normal probability distribution that has a a normal probability distribution that has a

• mean of 0 mean of 0 and a and a standard deviation of 1standard deviation of 1

0 1 2 3-1-2-3 0 z = 1.58

Figure 5-5 Figure 5-6

•Area = 0.3413 •Area found in

•Table A-2

•0.4429

Score (z )


Figure 5-10 Figure 5-10 Interpreting Area CorrectlyInterpreting Area Correctly

"between x1 and x

2"

x2

Add

Use A = C – B

x1

x2

x1

A B

C

"less than x" "at most x" "no more than x" "not greater than x"

Subtract from 0.5

Add to 0.5

0.5x x

x x

"greater than x" "at least x" "more than x" "not less than x"

0.5

Add to 0.5

Subtract from 0.5


7-1 7-1 OverviewOverviewDefinitionDefinition

HypothesisHypothesis

in statistics, is a claim or statement in statistics, is a claim or statement about a property about a property of a populationof a population

Method of ReasoningMethod of ReasoningAnalyze a sample in an attempt to distinguish between results Analyze a sample in an attempt to distinguish between results

that can easily occur and results that are highly unlikely.that can easily occur and results that are highly unlikely.


Assessment


Mat 131 Students Survey – Velleman CDDuring this semester, I have asked you to use the Velleman CD. Sometimes I have usedVelleman to demonstrate different topics being discussed in class. Please give yourcandid opinion about this CD.

1. Is the Velleman CD helpful?Explain:

2. Were parts of Velleman(movies, testing, etc.) more helpful than others?Which? Why?

3. Should I use Velleman next semester?Explain:

4. If this course were given on-line (no face-to-face instruction – strictly computer)would you recommend that the students purchase the Velleman CD?

5. Were the powerpoint slides helpful? Explain:

6. Were the powerpoint handouts helpful? Explain:


RESULTS Mat 131 Students Survey – Velleman CD1. Is the Velleman CD helpful? Explain:

Yes 12So-So 5No 9

2. Were parts of Velleman(movies, testing, etc.) more helpful than others? Which? Why?

3. Should I use Velleman next semester? Explain:Yes 17Optional 2No 9

4. If this course were given on-line (no face-to-face instruction – strictly computer)would you recommend that the students purchase the Velleman CD?

Yes 23No 2

5. Were the powerpoint slides helpful? Explain:Yes 19So-So 3No 4

6. Were the powerpoint handouts helpful? Explain:


Velleman CD


Would I do it again? Would I do it again? Yes, for the students.Yes, for the students.

• Computer animations surpass chalk and Computer animations surpass chalk and talktalk

• Sound helped ESL studentsSound helped ESL students

• CD allows students to reviewCD allows students to review

• Access for students who missed classAccess for students who missed class


Would I do it again? Yes, for the teacher. Would I do it again? Yes, for the teacher. Would I recommend that you try it? Yes! Would I recommend that you try it? Yes!

• ImmediacyImmediacy

• Flexibility on two levelsFlexibility on two levels

• Computer AnimationsComputer Animations

• VisualizationVisualization

• Record of material presentedRecord of material presented

• Computer is another teaching toolComputer is another teaching tool


uestionsuestionsQQ??

integrating the computer and the calculator in the statistics classroom international conference on...

Documents

statistics cd

statistics ifall

descriptive statistics

graphing calculator

ti calculator

binomial distribution

selfcontained course

probability distribution