Homework 6

Chapter 12

18.Consider the following hypothesis test. . The following data are from matched samples taken from two populations.

Population
Element / 1 / 2
1 / 21 / 20
2 / 28 / 26
3 / 18 / 18
4 / 20 / 20
5 / 26 / 24
  1. Compute the difference value for each element.
  2. Compute .
  3. Compute the standard deviation .
  4. Test the hypothesis using . What is your conclusion?

19. The following data are from matched samples taken from two populations.

Population
Element / 1 / 2
1 / 11 / 8
2 / 7 / 8
3 / 9 / 6
4 / 12 / 7
5 / 13 / 10
6 / 15 / 15
7 / 15 / 14
  1. Compute the difference value for each element.
  2. Compute .
  3. Compute the standard deviation .
  4. What is the point estimate of the difference between the two population means?
  5. Provide a 95% confidence interval for the difference between the two population means.

25.The 1997 price/earnings ratios and estimated 1998 price/earnings ratios for a sample of 12 stocks are shown here (Kiplinger’s Personal Finance Magazine, November 1997).

Stock / 1997 P/E Ratio / Est. 1998 P/E Ratio
Coca-Cola / 40 / 32
Walt Disney / 33 / 23
Du Pont / 24 / 16
Eastman Kodak / 21 / 13
General Electric / 30 / 23
General Mills / 25 / 19
IBM / 19 / 14
Merck / 29 / 21
McDonald’s / 20 / 17
Motorola / 35 / 20
Philip Morris / 17 / 13
Xerox / 20 / 17
  1. Use and test for any change in the population mean price/earnings ratios for the two-year period.
  2. Provide a 95% confidence interval for the change in the population mean price/earnings ratios for the two-year period. What is your conclusion?

27. Four observations were selected from each of three populations. The data obtained follow.

Observation / Sample 1 / Sample 2 / Sample 3
1 / 165 / 174 / 169
2 / 149 / 164 / 154
3 / 156 / 180 / 161
4 / 142 / 158 / 148
Sample mean / 153 / 169 / 158
Sample variance / 96.67 / 97.33 / 82.00
  1. Compute the between-treatments estimate of .
  2. Compute the within-treatments estimate of .
  3. At the level of significance, can we reject the null hypothesis that the three population means are equal? Explain.
  4. Set up the ANOVA table for this problem.

28. A random sample of 16 observations was selected from each of four populations. A proportion of the ANOVA table follows.

Source of Variation / Sum of Squares / Degrees of Freedom / Mean Square / F
Treatments / 400
Error
Total / 1500
  1. Provide the missing entries for the ANOVA table.
  2. At the level of significance, can we reject the null hypothesis that the means of the four populations are equal?

30. Managers at all levels of an organization need adequate information to perform their respective tasks. One study investigated the effect the source has on the dissemination of information. In this particular study the sources of information were a superior, a peer, and a subordinate. In each case, a measure of dissemination was obtained, with higher values indicating greater dissemination of information. Using and the following data, test whether the source of information significantly affects dissemination. What is your conclusion, and what does it suggest about the use and dissemination of information?

Superior / Peer / Subordinate
8 / 6 / 6
5 / 6 / 5
4 / 7 / 7
6 / 5 / 4
6 / 3 / 3
7 / 4 / 5
5 / 7 / 7
5 / 6 / 5

Chapter 13

2. Consider the following hypothesis test: . The following results are for two independent samples taken from the two populations.

Sample 1 / Sample 2
  1. Using , what is your hypothesis-testing conclusion?
  2. What is the p-value?

6.Fortune enlisted Yankelovich Partners to poll 600 adults on their ideas about marriage, divorce, and the contribution of the corporate wife to her executive husband (Fortune, February 2, 1998). In response to the statement, “In a divorce in a long-term marriage where the husband works outside the home and the wife is not employed for pay, the wife should be entitled to half the assets accumulated during the marriage,” 279 of 300 women agreed and 255 of 300 men agreed.

a. What are the sample proportions for the two populations, women and men?

b. Test the hypothesis using . What is your conclusion?

c. Provide a 95% confidence interval for the difference between the population proportions.

8. (Data set: Survey)A survey firm conducts door-to-door surveys on a variety of issues. Some individuals cooperate with the interviewer and complete the interview questionnaire, and others do not. A recent survey of 200 men and 300 women resulted in the data set Survey. A response of Yes means that the respondent completed the questionnaire.

a. Using , test the hypothesis that the response rate is the same for both men and women.

b. Compute a 95% confidence interval for the difference between the proportions of men and women who completed the questionnaire.

11. Test the following hypotheses using the goodness of fit test.

.

A sample of size 200 yielded 60 in category A, 120 in category B, and 20 in category C.

16. Negative appeals have been recognized as an effective method of persuasion in advertising. A study in The Journal of Advertising (Summer 1997) reported the results of a content analysis of guilt advertisements in 24 magazines. The number of ads with guilt appeals that appeared in selected types follow.

Magazine Type / Number of Ads with Guilt Appeals
News and opinion / 20
General editorial / 15
Family-oriented / 30
Business/financial / 22
Female-oriented / 16
African-American / 12

Use test to determine any differences in the proportion of ads with guilt appeals among the six types of magazines.

19. Shown is a contingency table with observed frequencies for a sample of 200. Test for independence of the row and column variables by using the test with .

Column Variable
A / B / C
Row Variable / P / 20 / 44 / 50
Q / 30 / 26 / 30

23. Starting positions for business and engineering graduates are classified by industry as shown in the following table.

Industry
Degree Major / Oil / Chemical / Electrical / Computer
Business / 30 / 15 / 15 / 40
Engineering / 30 / 30 / 20 / 20

Use and test for independence of degree major and industry type.

27. A sport preference poll yielded the following data for men and women:

Favorite Sport
Sex / Baseball / Basketball / Football
Men / 19 / 15 / 24
Women / 16 / 18 / 16

Use and test for the same sport preferences by men and women. What is your conclusion?

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