# hw3+++.pdf - Statistics 106 Homework 3 Solution Due Oct 17...

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Statistics 106 Homework 3 Solution Due : Oct. 17, 2016, In Class 17.1 A student, asked to give a class demonstration of the use of a confidence interval for comparing two treatment means, proposed to construct a 99 percent confidence interval for the pairwise comparison D = μ 5 - μ 3 , where there are a total of five factor levels. The student selected this particular comparison because the estimated treatment means ¯ Y 5 . and ¯ Y 3 . are the largest and smallest, respectively, and stated: “This confidence interval is particularly useful. If it does not contain zero, it indicates, with significance level α = . 01, that the factor level means are not equal.” a. Explain why the student’s assertion is not correct. b. How should the confidence interval be constructed so that the assertion can be made with significance level α = . 01? Solution: a. One can only get the largest pairwise comparison by considering the family of all pairwise compar- isons. The student tried to construct a single confidence interval of the largest pairwise comparison using the t distribution. This action does not maintain the family-wise confidence coe ffi cient at 99% since each additional pairwise comparison conducted (whether reported or not) increases the risk of a type I error. The student made a comparison that was suggested by the data (finding the largest dif- ference between treatment sample means) such that the correct confidence interval should be wider and includes a multiplier that accounts for all pairwise comparisons being inferred from the sampled data (see part b). b. The Tukey’s procedure with family-wise confidence coe ffi cient .99 should be used, since the Tukey’s procedure considers all pairwise comparisons simultaneously through the studentized-range distri- bution, denoted by q . 17.2 A trainee examined a set of experimental data to find comparisons that ”look promising” and calculated a family of Bonferroni confidence intervals for these comparisons with a 90 percent family confidence coe ffi cient. Upon being informed that the Bonferroni procedure is not applicable in this case because the comparisons had been suggested by the data, the trainee stated: ”This makes no di ff erence. I would use the same formulas for the point estimates and the estimated standard errors even if the comparisons were not suggested by the data.” Respond. Solution: 1 This study resource was shared via CourseHero.com