hw3-solution.pdf

# Where the interval correspond to the confidence

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. where the interval correspond to the confidence limits in (17.7) with = . 05. What does this plot suggest about the e ect of color on the response rate? Is your conclusion in accord with the test result in Problem 16.8e? b. Estimate the mean response rate for blue questionnaires: use a 90 percent confidence interval. c. Test whether or not D = μ 3 - μ 2 = 0: use = . 10. State the alternatives, decision rule, and conclusion. In Iight of the result for the ANOVA test in Problem 16.8e, is your conclusion surprising? Explain. Solution: 2

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a. ¯ Y 1 . = 29 . 4, ¯ Y 2 . = 29 . 6 and ¯ Y 3 . = 28 are the heights of the three bars. Since s ( ¯ Y 1 . ) = s ( ¯ Y 2 . ) = s ( ¯ Y 3 . ) = p MS E / 5 = 1 . 3928, t (1 - / 2; n T - I ) = t ( . 975; 12) = 2 . 179, the half length of the three confidence intervals is 1 . 3928 2 . 179 = 3 . 035. b. Since ¯ Y 1 . = 29 . 4, s ( ¯ Y 1 . ) = 1 . 3928 and t (1 - / 2; n T - I ) = t ( . 95; 12) = 1 . 782, the 90 percent confidence interval of μ 1 is: ¯ Y 1 . ± s ( ¯ Y 1 . ) t (1 - / 2; n T - I ) = 29 . 4 ± 1 . 3928(1 . 782) = [26 . 92 , 31 . 88] . c. H 0 : D = 0 , H a : D , 0 . ˆ D = ¯ Y 3 . - ¯ Y 2 . = 28 - 29 . 6 = - 1 . 6 , s ( ˆ D ) = p MS E (1 / 5 + 1 / 5) = 1 . 970 , ) t = ˆ D s ( ˆ D ) = - 0 . 812 . The decision rule is: If | t | > t (1 - / 2; n T - I ) = t ( . 95; 12), reject H 0 . Since t ( . 95; 12) = 1 . 782, we should not reject H 0 . This conclusion is in accord with the test result in Problem 16.8e. 17.10 Refer to Rehabilitation therapy Problem 16.9. a. Prepare a line plot of the estimated factor level means ¯ Y i . . What does this plot suggest about the e ect of prior physical fitness on the mean time required in therapy? 3
b. Estimate with a 99 percent confidence interval the mean number of days required in therapy for persons of average physical fitness. c. Obtain confidence intervals for D 1 = μ 2 - μ 3 and D 2 = μ 1 - μ 2 : use the Bonferroni procedure with a 95 percent family confidence coe ffi cient. Interpret your results. d. Would the Tukey procedure have been more e ffi cient to use in part (c)? Explain. e. If the researcher also wished to estimate D 3 = μ 1 - μ 3 still with a 95 percent family confidence coe ffi cient, would the B multiple in part (c) need to be modified? Would this also be the case if the Tukey procedure had been employed?

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• Spring '13
• Statistics, Student's t-distribution, Credible interval

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