hw1 - Stat120C Homework 1 (due Thursday April 10, 2008)...

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Stat120C Homework 1 (due Thursday April 10, 2008) Instructor: Zhaoxia Yu TA: Vinh Nyugen Note : Where appropriate, all relevant software code and output should be also handed in. Problem 1. (11.10 of Rice) Verify that the two-sample t test at level α of H 0 : μ X = μ Y versus H A : μ X 6 = μ Y rejects if and only if the confidence interval for μ X - μ Y does not contain zero. Problem 2. (11.14 of Rice) Suppose that X 1 , · · · ,X n are i.i.d. N ( μ,σ 2 ). To test the null hypothesis H 0 : μ = μ 0 , the t-test is often used: t = ¯ X - μ 0 s ¯ X Under H 0 , t follows a t distribution with n - 1 df. Show that the likelihood ratio test of this H 0 is equivalent to the t test. Problem 3. (11.36 of Rice) Lin, sutton, and Qurashi (1979) compared microbiological and hydroxylamine methods for the analysis of ampicillin dosages. In one series of experiments, pairs of tablets were analyzed by the two methods. The data in the following table give the percentages of claimed amount of ampicillin found by the two methods in several pairs of tablets. What are
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hw1 - Stat120C Homework 1 (due Thursday April 10, 2008)...

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