Question 16.20 :

A manufacturer of small appliances employs a market research firm to estimate retail sales of its products by gathering information from a sample of retail stores. This month an SRS of 75 stores in the Midwest sales region finds that these stores sold an average of 24 of the manufacturer’s hand mixers, with standard deviation 11.

1. Give a 95% confidence interval for the mean number of mixers sold by all stores in the region.
2. The distribution of sales is strongly right-skewed because there are many smaller

stores and a few very large stores. The use of t in (a) is reasonably safe despite this violation of the Normality assumption. Why?

Question 16.24 :

The data show that many people paid $20 per month for Internet access, presumably because major providers such as AOL charged this amount. Do the data give good reason to think that the mean cost for all Internet users differs from $20 per month?

20 40 22 22 21 21 20 10 20 20

20 13 18 50 20 18 15 8 22 25

22 10 20 22 22 21 15 23 30 12

9 20 40 22 29 19 15 20 20 20

20 15 19 21 14 22 21 35 20 22

Question 16.30 :

Here is the data on the annual returns (percent) for the Vanguard International Growth Fund and its benchmark index, the Morgan Stanley EAFE index. Doe the fund significantly outperform its benchmark?

1. Explain clearly why the matched pairs t test is the proper choice to answer this question.
2. Make a stemplot of the differences (fund-EAFE) for the 20 years. There is no reason to doubt the approximate Normality of the differences. (More detailed study shows that the differences follow a Normal distribution quite closely.)
3. Carry out the test and state your conclusion about the fund’s performance.

Question 17.20 :

Is there a statistically significant difference between the standard deviations of blood polyphenol level change in the red and white groups?

Question 17.24 :

"The phenomenon of road rage has been frequently discussed but infrequently examined." So begins a report based on interviews with randomly selected drivers. The respondents’ answers to interview question produced scores on an "angry/threatening driving scale" with values between 0 and 19. Here are summaries of the scores:

Group n \[\overline{x}\] s

Male 596 1.78 2.79

Female 769 0.97 1.84

1. We suspect that men are more susceptible to road rage than women. Carry out a test of the hypothesis (State hypotheses, find the test statistic and P value, and state your conclusion)
2. The subjects were selected using random-digit dialing. The large sample sizes make the Normality condition unnecessary. There is one aspect of the data production that might reduce the validity of the data. What is it?

Question 18.28:

Have efforts to promote equality for women gone far enough in the United States? A poll on this issue by the cable network MSNBC contacted 1019 adults. A newspaper article about the poll said, "Results have a margin of sampling error of plus or minus 3 percentage points."

1. Overall, 54% of the sample (550 of 1019 people) answered "Yes" Find a 95% confidence interval for the proportion in the adult population who would say "Yes" if asked. Is the report’s claim about the margin of error roughly right? (Assume that the sample is an SRS.)
2. The news article said the 65% of men, but only 43% of women think that efforts to promote equality have gone far enough. Explain why we do not have enough information to give confidence intervals for men and women separately.
3. Would a 95% confidence interval for women alone have a margin of error less that 0.03, about equal to 0.03, or greater than 0.03? Why? You see that the news article’s statement about the margin of error for poll results is a bit misleading.

Question 18.30:

The National AIDS Behavioral Surveys interviewed a sample of adults in cities where AIDS is most common. This sample included 803 heterosexuals who reported having more than one sexual partner in the past year. We can consider this an SRS size 803 from the population of all heterosexuals in high-risk cities who have multiple partners. The people risk infection with the AIDS virus. Yet 304 of the respondents said they never use condoms. Is this strong evidence that more than one-third of this population never use condoms?

Question 19.20:

North Carolina State University looked at the factors that affect the success of students in a required chemical engineering course. Students must get a C or better in the course in order to continue as chemical engineering majors. There were 65 students from urban or suburban backgrounds, and 52 of these students succeeded. Another 55 students were from rural or small-town backgrounds; 30 of these students succeeded in the course.

1. Is there good evidence that the proportion of students who succeed is different for urban/suburban versus rural/small-town backgrounds? State hypotheses, give the P-value of a test, and state your conclusion.
2. Give a 90% confidence interval for the size of the difference.

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