HW6-Solutions

# HW6-Solutions - STAT 101 Agresti Homework 6 Solutions...

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STAT 101 - Agresti Homework 6 Solutions 10/25/10 Chapter 7 7.26. df = 29 – 1 = 28. The one-sided P -value is between 0.005 and 0.01 (software indicates P = 0.006), and the two-sided P -value is between 0.01 and 0.02 (software indicates P = 0.012). There is strong evidence that those who are not children of alcoholics have a higher population mean well-being than those who are children of alcoholics. 7.27. The estimated standard error is 49.4 12 14.3 = , and the test statistic is t = 70.1/14.3 = 4.9 with df = 11, which has P < 0.01. 7.28. (a) We should treat these as dependent samples, since the same subjects are used in each sample. (b) We are 95% confidence that the mean number of times students went to movies was between 7.6 below and 15.6 above the mean number of times students went to sporting events. (c) t = 4.0/5.112 = 0.78. P = 0.454. It appears that there is no significant difference between the mean number of times students went to movies and the mean number of times students went to sporting events. 7.31. (a) (i) 40 – 20 = 20 (ii) 20; The difference between the means is equal to the mean difference. (b) s = 5.0; 5 3 2.887 se = = . (c) The 95% confidence interval is ( 29 20 4.303 2.887 7.6 to 32.4 ± = . We are 95% confident that the mean difference between patients receiving therapy B and patients receiving therapy A is between 7.6 and 32.4. (d) t = 20/2.887 = 6.93; df = 3 – 1 = 2; 0.02 < P < 0.05 ( P = 0.0202). There appears to be a difference between the mean scores for patients receiving therapy B and those receiving therapy A. 7.41. (a) The following is a bar chart:

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Summary statistics for political ideology: (b) Software gives us the following for a hypothesis test: Hypothesis test results: μ 1 : mean of Dem μ 2 : mean of Rep H 0 : μ 1 - μ 2 = 0 H A : μ 1 - μ 2 0 (allowing unequal population variances) Software gives us the following for a confidence interval: 95% confidence interval results: μ 1 : mean of Dem μ 2 : mean of Rep (allowing unequal population variances) The hypothesis test tells us that there is strong evidence that the population mean political ideology differs for students identifying with the Democratic party and with the Republican party. We would reject the null hypothesis of equal population means at the usual significance levels such as 0.05. The confidence interval tells us that we are 95% confident that the population mean political ideology for students identifying with the Democratic party is between 2.3 and 4.0 below (i.e., more liberal) than the population mean political ideology for students identifying with the Republican party. Chapter 8

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HW6-Solutions - STAT 101 Agresti Homework 6 Solutions...

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