sol.hw9.stat3011

sol.hw9.stat3011 - Homework 9 Solutions Yicheng Kang...

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Unformatted text preview: Homework 9 Solutions Yicheng Kang November 18, 2010 Problem 9.21 9.21.a The variable has two categories: (1)garlic being more effective; (2)placebo being more effective. And the parameter is the proportion of the population indicating that garlic is more effective. Lets denote it by p . 9.21.b H : p = 1 2 , H a : p 6 = 1 2 . Check large sample size assumption:37 15 , 29 15. 9.21.c z = 37 / (37 + 29)- 1 / 2 p . 5 2 / (37 + 29) = 0 . 984732 9.21.d &amp;gt; 2*(1-pnorm(0.984732)) [1] 0.3247557 1 Thus the p-value is 0.32. If given significance level 0.05, we fail to reject the null hypothesis that there is no real difference between garlic and placebo. Problem 9.32 9.32.a Variable: the number of hours workers work per week. Parameter: mean . 9.32.b H : = 40 H a : 6 = 40 9.32.c t = 37 . 8- 40 13 . 3 / 197 =- 2 . 321690 . 9.32.d &amp;gt; 2*(1-pt(2.321690,196)) [1] 0.02127725 The P-value is 0.02. Thus we may reject the null hypothesis and conclude that the population mean work week for this age group differs from 40 hours. Problem 9.40 After changing 20.9 to 2.9, the test statistic changes from 2.21 to 1.98, and the P-value changes from 0.04 t 0.06. The test statistic is less extreme, and the P-value is no longer smaller than 0.05. We can no longer reject the null hypothesis. The conclusion does depend on the single observation of 20.9....
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sol.hw9.stat3011 - Homework 9 Solutions Yicheng Kang...

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