Test 1CAP StatisticsName:

Part 1: Multiple Choice. Circle the letter corresponding to the best answer.

1. At the beginning of the school year, a high-school teacher asks every student in her classes to fill out a survey that asks for their age, gender, the number of years they have lived at their current address, their favorite school subject, and whether they plan to go to college after high school. Which of the following best describes the variables that are being measured?

(a) four quantitative variables

(b) five quantitative variables

(c) two categorical variables and two quantitative variables

(d) two categorical variables and three quantitative variables

(e) three categorical variables and two quantitative variables

2. The graph below shows how mothers of young children respond to the question, “How many times a week do you choose fast food as a dining option for your family?”

60

30

Percentage of responses

48

The Practice of Statistics, 4/e- Chapter 1

© 2011 BFW Publishers

© 2011 BFW Publishers

The Practice of Statistics, 4/e- Chapter 1

40

Never1 – 3

times

What’s wrong with this method of presenting information?

4 or more times

(a) This kind of data should always be presented in a pie chart.

(b) The vertical axis should be “number of responses,” not “percentage of responses.”

(c) The horizontal axis should be divided into more than three categories.

(d) Using proportionally-sized hamburgers exaggerates differences between responses.

(e) We don’t know if the mothers who responded were thinking about dinner, or both lunch and dinner.

3. The median age of five people in a meeting is 30 years. One of the people, whose age is 50 years, leaves the room. The median age of the remaining four people in the room is

(a) 40 years.

(b) 30 years.

(c) 25 years.

(d) less than 30 years.

(e) Cannot be determined from the information given.

4. Below is a pie chart of how a randomly selected group of people described the cost of their heath insurance.

Which of the following bar graphs is equivalent to the pie chart?

(a) (b)

40

30

20

10

0

Low costFairly pricedExpensiveDon't know

60

50

40

30

20

10

0

Low costFairly pricedExpensiveDon't know

(c)(d)

60

50

40

30

20

10

0

Low costFairly pricedExpensiveDon't know

40

30

20

10

0

Low costFairly pricedExpensiveDon't know

(e)

40

30

20

10

0

Low costFairly pricedExpensiveDon't know

5. A researcher reports that the participants in his study lost a mean of 10.4 pounds after two months on his new diet. A friend of yours comments that she tried the diet for two months and lost no weight, so clearly the report was a fraud. Which of the following statements is correct?

(a) Your friend must not have followed the diet correctly, since she did not lose weight.

(b) Since your friend did not lose weight, the report must not be correct.

(c) The report gives only the mean. This does not imply that all participants in the study lost

10.4 pounds or even that all lost weight. Your friend’s experience does not necessarily contradict the study results.

(d) In order for the study to be correct, we must now add your friend’s results to those of the study and recompute the new average.

(e) Your friend is an outlier.

6. The following is a histogram showing the actual frequency of the closing prices of a particular stock on the New York Stock Exchange

over a 50-day period. The class that contains the third quartile is

(a) 10–20

Frequency

(b) 20–30

(c) 30–40

(d) 40–50

(e) 50–60

Closing Price

7. For the data in the previous problem, which measures of center and spread would be most appropriate to use?

(a) Mean and standard deviation

(b) Mean and interquartile range

(c) Mean and range

(d) Median and interquartile range

(e) Median and standard deviation

8. According to the U.S. Bureau of Labor Statistics, the monthly percentage change in the number of jobs in a certain state for the twelve months of 2007 had a mean of 0.08% and a standard deviation of 1.70%. From this information we can conclude that

(a) The largest monthly change was 1.78%

(b) The distribution of monthly changes is strongly skewed to the right.

(c) Most of the monthly changes were negative.

(d) The magnitude of the monthly deviations from the mean change averaged about 1.70%.

(e) A mistake has been made. It makes no sense for the standard deviation to be greater than the mean.

9. The weights of the male and female students in a class are summarized in the following boxplots:

Which of the following is NOT correct?

(a) About 50% of the male students have weights between 150 and 185 pounds.

(b) About 25% of female students have weights above 130 pounds.

(c) The median weight of male students is about 162 pounds.

(d) The mean weight of female students is about 120 pounds.

(e) The male students have less variability than the female students.

10. When testing water for chemical impurities, results are often reported as bdl, that is, below detection limit. The following are the measurements of the amount of lead in a series of water samples taken from inner-city households (in parts per million):

5, 7, 12, bdl, 10, 8, bdl, 20, 6

Which of the following statements can we be sure is true?

(a) The mean lead level in the water is about 10 ppm.

(b) The mean lead level in the water is about 9 ppm.

(c) The median lead level in the water is 7 ppm.

(d) The median lead level in the water is 8 ppm.

(e) Neither the mean nor the median can be computed because some values are unknown.

Part 2: Free Response

Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.

The states differ greatly in the kinds of severe weather that afflict them. The histogram below shows the distribution of average annual property damage caused by tornadoes over the period from 1950 to 1999 in the 50 United States. (To adjust for the changing buying power of the dollar over time, all damages were restated in 1999 dollars.)

25

20

15

10

5

0

0102030405060708090

Average annual tornado damage, $millions

Number of states

11. Describe the important features of this distribution. What does this tell you about how the economic burden of tornados is distributed among the states?

12. When asked for summary statistics, MINITAB produced the following output:

VariableNMeanSE MeanStDevMinimumQ1MedianQ3Maximum Damage50 22.393.6025.450.002.2312.6641.6388.60

Give the five-number summary, and explain why you can see from these five numbers that the distribution is strongly skewed to the right.

13. The histogram suggests that there may be outliers. Use the 1.5 x IQR rule of thumb to show that no values in this distribution meet this criterion for outliers.

Below are the lengths, in minutes, of the 25 most popular movies, as voted on by visitors to a web site devoted to movies.

142

195

201

139

106

175

96

121

130

109

200

133

102

178

165

161

124

146

115

118

154

14. Make a stemplot of these data.

152

207

112

136

15. The mean of this distribution is 144.7 and the median is 139. Explain why you could have predicted that the mean would be higher than the median by looking at the stemplot.

16. The longest movie on the list, at 207 minutes, is Akira Kurosawa’s classic The Seven Samurai. Suppose its place on the list was replaced by Andy Warhol’s Sleep, which is 321 minutes of a man sleeping. Without performing any calculations, indicate whether each of the following measures of center and spread would increase, decrease, or remain the same.

· mean

· median

· standard deviation

· interquartile range

17. The two-way table below shows the relationship between means of transportation to work and gender for a simple random sample of 250 working adults in the United States.

Drive alone

Car Pool

Public transportation

Male

113

16

6

Female

85

23

7

Discuss the relationship between gender and means of transportation to work for the working adults in this sample. Provide appropriate marginal and conditional distributions to support your answer. You may choose whatever methods you want to present those distributions.

18. Below are dotplots of three different distributions, A, B, and C. Which one has the largest standard deviation? Justify your answer.

A

B

C

Extra problem on optional material (text pp30-32)

A study of the relationship between health and smoking asked a sample of 260 people two questions: “Do you smoke cigarettes?” and “Have you visited or stayed in a hospital as a result of illness in the past two years?” The results are in the table below:

Hospital

No Hospital

Smoker

37

93

Non-smoker

45

85

The researchers were initially astonished by this unexpected result: 34.6% of the non-smokers had visited a hospital, but only 38.55% of the smokers had visited a hospital. The mystery was resolved when one of the researchers made a new table that divided the subjects of the study up into five age groups

Smoker

Non-Smoker

Hospital

No Hospital

Hospital

No Hospital

Under 30 years

4

40

1

20

31-45 years

8

30

3

18

Age Group

46-60 years

7

14

6

20

61-75 years

8

8

13

22

Over 75 years

10

1

22

5

Total37934585

Within each age group, a higher percentage of smokers had visited a hospital. Explain this apparent contradiction.

Extra problem on optional material (text pp30-32)

A company decided to expand, so it opened a new factory with 455 available jobs. The following tables summarize the hiring decisions made by the company.

Workers MaleFemale

Managers MaleFemale

Applied

400100

Applied

200200

Hired

30085

Hired

3040

(a) Calculate the percent of male and female workers that were hired. Then do likewise for male and female managers.

(b) Use the tables above to create a two-way table that shows the relationship between gender and hiring decision (that is, combine the results for workers and managers).

(c) Calculate the percent of male and female applicants that were hired.

(d) Explain your findings in (a) and (c).