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hw6.sol

# hw6.sol - AMS 7 Biostatistics Week 7 Homework Solutions...

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AMS 7, Biostatistics Week 7 Homework Solutions Chapter 7 (Glover & Mitchell) 1. Big decrease in phosphate levels due to new laws? First determine if the variances are equal: H 0 : σ 2 2 = σ 2 1 , and H a : σ 2 1 6 = σ 2 1 . The F -statistic s 2 2 /s 2 1 = 2 . 7. Using the F - distribution with v 1 = 11 and v 2 = 9 degrees of freedom gives the critical value F 0 . 975 = 3 . 96 leading the conclusion that there is not enough evidence to reject H 0 . So, treat the variances as equal ( σ 2 2 = σ 2 1 ) when testing the two-sample hypothesis for the means: H 0 : μ 1 μ 2 , and H 0 : μ 1 > μ 2 . Calculate s 2 p = 1238 . 4 and test statistic t = 9 . 78, and use a t -distribution with 20 degrees of freedom and obtain a critical value of t 0 . 95 = 1 . 725 and thus reject H 0 . 3. Paired data for antibiotic effects. Subtract the amoxicillin column from the penicillin column and get ( n d = 6) differences d = 6 , - 10 , 4 , 5 , - 7 , - 2 and calculate ¯ X d = - 2 , ¯ s 2 d = 4 . 12. Test H 0 = μ d = 0 against H a : μ d 6 = 0 using a two-sided t -test on 5 degrees of freedom. The critical values are ± t o = ± 2 .
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