1. Consider the following results for independent samples taken from two populations.

1. What is the point estimate of the difference between the two population proportions?
2. Develop a \(90 \%\) confidence interval for the difference between the two population proportions.
3. Develop a \(95 \%\) confidence interval for the difference between the two population proportions.

3. A BusinessWeek/Harris survey asked senior executives at large corporations their opinions about the economic outlook for the future. One question was "Do you think that there will be an increase in the number of full-time employees at your company over the next 12 months?" In the current survey, 220 of 400 executives answered yes, while in a previous year's survey, 192 of 400 executives had answered yes. Provide a \(95 \%\) confidence interval estimate for the difference between the proportions at the two points in time. What is your interpretation of the interval estimate?

7. In a test of the quality of two television commercials, each commercial was shown in a separate test area six times over a one-week period. The following week a telephone survey was conducted to identify individuals who had seen the commercials. Those individuals were asked to state the primary message in the commercials. The following results were recorded.

1. Use \(\alpha=.05\) and test the hypothesis that there is no difference in the recall proportions for the two commercials.
2. Compute a \(95 \%\) confidence interval for the difference between the recall proportions for the two populations.

9. A 2003 New York Times/CBS News poll sampled 523 adults who were planning a vacation during the next six months and found that 141 were expecting to travel by airplane (New York Times News Service, March 2, 2003). A similar survey question in a May 1993 New York Times/CBS News poll found that of 477 adults who were planning a vacation in the next six months, 81 were expecting to travel by airplane.

1. State the hypotheses that can be used to determine whether a significant change occurred in the population proportion planning to travel by airplane over the 10-year period.
2. What is the sample proportion expecting to travel by airplane in 2003 ? In 1993?
3. Use \(\alpha=.01\) and test for a significant difference. What is your conclusion?
4. Discuss reasons that might provide an explanation for this conclusion.

12. Suppose we have a multinomial population with four categories: A, B, C, and D. The null hypothesis is that the proportion of items is the same in every category. The null hypothesis is

A sample of size 300 yielded the following results.

\(\mathrm{A}: 85 \quad \mathrm{~B}: 95 \quad \mathrm{C}: 50 \quad \mathrm{D}: 70\)

Use \(\alpha=.05\) to determine whether \(H_{0}\) should be rejected. What is the \(p\) -value?

15. Where do women most often buy casual clothing? Data from the U.S. Shopper Database provided the following percentages for women shopping at each of the various outlets (The Wall Street Journal, January 28, 2004)

The other category included outlets such as Target, Kmart, and Sears as well as numerous smaller specialty outlets. No individual outlet in this group accounted for more than \(5 \%\) of the women shoppers. A recent survey using a sample of 140 women shoppers in Atlanta, Georgia, found 42 Wal-Mart, 20 traditional department store, 8 J.C. Penney, 10 Kohl's, 21 mail order, and 39 other outlet shoppers. Does this sample suggest that women shoppers in Atlanta differ from the shopping preferences expressed in the U.S. Shopper Database? What is the \(p\) -value? Use \(\alpha=.05\). What is your conclusion?

17. The Wall Street Journal's Shareholder Scoreboard tracks the performance of 1000 major U.S. companies (The Wall Street Journal, March 10,2003 ). The performance of each company is rated based on the annual total return, including stock price changes and the reinvestment of dividends. Ratings are assigned by dividing all 1000 companies into five groups from \(A\) (top \(20 \%\) ), B (next \(20 \%\) ), to \(\mathrm{E}\) (bottom \(20 \%\) ). Shown here are the one-year ratings for a sample of 60 of the largest companies. Do the largest companies differ in performance from the performance of the 1000 companies in the Shareholder Scoreboard? Use \(\alpha=.05\).

23. With double-digit annual percentage increases in the cost of health insurance, more and more workers are likely to lack health insurance coverage (USA Today, January 23, 2004). The following sample data provide a comparison of workers with and without health insurance coverage for small, medium, and large companies. For the purposes of this study, small companies are companies that have fewer than 100 employees. Medium companies have 100 to 999 employees, and large companies have 1000 or more employees. Sample data are reported for 50 employees of small companies, 75 employees of medium companies, and 100 employees of large companies.

1. Conduct a test of independence to determine whether employee health insurance coverage is independent of the size of the company. Use \(\alpha=.05\). What is the \(p\) -value, and what is your conclusion?
2. The USA Today article indicated employees of small companies are more likely to lack health insurance coverage. Use percentages based on the preceding data to support this conclusion.

25. Negative appeal is recognized as an effective method of persuasion in advertising. A study in The Journal of Advertising reported the results of a content analysis of guilt and fear advertisements in 24 magazines. The number of ads with guilt and fear appeals that appeared in selected magazine types follows.

Use the chi-square test of independence with a .01 level of significance to analyze the data, What is your conclusion?

27. The National Sleep Foundation used a survey to determine whether hours of sleeping per night are independent of age (Newsweek, January 19,2004 ). The following show the hours of sleep on weeknights for a sample of individuals age 49 and younger and for a sample of individuals age 50 and older.

1. Conduct a test of independence to determine whether the hours of sleep on weeknights are independent of age. Use \(\alpha=.05\). What is the \(p\) -value, and what is your conclusion?
2. What is your estimate of the percentage of people who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 or more hours on weeknights?

M&M WORKSHEET:

Purpose In this assignment, you will use the Chi Squared test of Goodness of Fit to see if M&M‘s really do have the percentages of color that are published by Mars. Action Items 1. Purchase a package of M&M’s that is at least 4 ounces. 2. Download the M and M Worksheet. 3. Using e-mail, chat rooms, or the telephone, discuss your worksheet responses with your team, appoint a team leader to lead the discussion. Submission Instructions One team member should post the results of the worksheet to the bulletin board as a reply to the topic "M and M Posting. "

Price: $29.57

Solution: The downloadable solution consists of 13 pages, 1657 words and 11 charts.
Deliverable: Word Document