1. This table summarizes results from a survey of more than 30,000 North American households that ask, “What kind of Internet connection do you use at home?”

Type

2003

(%)

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2007

(%)

Cable

16

33

DSL

8

33

Satellite

0

1

Wireless

0

2

Dial-up

68

26

(a) Prepare a chart that shows the shares in both years as well as identifies the technologies that are growing or fading

(b) Does this table prove that fewer households were using dial-up in 2007 than in 2003?

2.

A survey of the competition between two new handheld games produced the

following data. A magazine in Japan surveyed 1,000 of its readers; 140 reported owning a Sony PSP and 250 reported that they owned a Nintendo DS. In addition, the two groups reported owning the following number of games. (Because systems like PSP can be used to play a certain type of DVD, it is possible that someone might have one and not own any games!)

Number of games

Sony PSP

(%)

Nintendo DS

(%)

0

2

2

1

27

16

2

25

20

3

14

19

4

8

12

5

10

8

>5

14

23

(a) Is a pie chart of either column appropriate?

(b) In order to show a bar chart of the number of owners rather than percentages, what must be done to the table first?

(c) Use a single chart to compare the number of games owned by these respondents.

Are percentages or counts more natural for this comparison?

(d) What is the median number of games bought by an owner of the Sony? Of the Nintendo?

(e) How do you interpret the differences in game ownership between those who own a PSP and those who own a DS?

3.

The attached excel (car.xls) gives the rated highway gasoline mileage (in miles per gallon) for 233 cars sold in the United States during 2003 and 2004. (a) Produce a histogram of these data. Describe and interpret the histogram. (b) Compare the histogram to the boxplot. What does the histogram tell you that the boxplot does not, and vice versa?

(c) Find the mean and standard deviation of the rated mileages. How are these related to the histogram, if at all?

(d) Find the coefficient of variation and briefly interpret its value. (e) Identify any unusual values (outliers). Do you think that these are coding errors?

(f)

4.

How does a car that gets 20 miles per gallon stack up against the models? Is it typical or does it get relatively low or high mileage?

To gauge the reactions of possible customers, the manufacturer of a new type of cellular telephone displayed the product at a kiosk in a busy shopping mall. The following table summarizes the results for the customers who stopped to look at the phone:

Male

Female

Favorable

36

18

Ambivalent

42

7

Unfavorable

29

9

(a) Is the reaction to the new phone associated with the sex of the customer? How strong is the association?

(b) How should the company use the information from this study when marketing its new product?

(c) Can you think of an underlying lurking variable that might complicate the relationship shown here? Justify your answer.

5. A study reported in The New England Journal of Medicine revealed surprisingly large differences in rates of lung cancer among smokers of different races. For each group, the study reported a rate among smokers per 100,000. Race

Male

Female

Black

264

161

White

158

134

Japanese-American

121

50

Latino

79

47

(a) What is the probability that a black male smoker develops lung cancer? (b)What is the probability that at least one of four Japanese-American women who smoke develops cancer? Do you need any assumptions for this calculation? (c)If the four women were from the same family, would you question any assumptions used in answering the previous item?

6. A fast-food chain randomly attaches coupons for prizes to the packages used to serve French fries. Most of the coupons say “Play again”, but a few

are winners. 75% of the coupons pay nothing, with the rest evenly divided between “Win a free order of fries” and “Win a free sundae”.

(a) If each member of a family of 3 orders fries with her or his meal, what is the probability that someone in the family is a winner?

(b) What is the probability that one member of the family gets a free order of fries and another gets the sundae? The third wins nothing.

(c) The fries normally cost $1 and the sundae $2. What are the chances of the family wining $5 or more in prizes?

7.

A company buys components from two suppliers. One produces components that are of higher quality than the other. The high-quality supplier, call it Supplier A, has a defect rate of 2%. The low-quality supplier, Supplier B, has a defect rate of 10% but offers lower prices. This company buys in equal volume from both suppliers, with half of the orders going to each supplier.

(a) What is the probability that a component to be installed is defective? (b) If a defective component is found, what is the probability it came from Supplier A?

8.

A company conducted a survey of its employees to determine their attitude toward a buyout of the company’s stock. Each of the company’s 1040 employees was asked whether they favored the buyout and whether they planned to retire within the next 15 years. The number of employees falling in the four buyout-retirement categories is shown in the following table.

Suppose an employee is selected at random from the company.

(a) What is the probability that the employee favors a buyout? (b) What is the probability that the employee will retire within the next 15 years? (c) What is the probability that the employee favors the buyout given that he or she plans to retire within the next 15 years?

(d) Is an employee’s attitude toward the buyout independent of his or her retirement plans?