06exHTs_p1-5

# 06exHTs_p1-5 - ISOM111 Business Statistics(Fall 2010...

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ISOM111 Business Statistics (Fall 2010) Tutorial Exercise 6 Solution for Exercise for Testing Hypotheses 1. Let X be the time to recovery for the new therapy and μ be the mean time to recovery for the new therapy. (a) We want to test H 0 : μ 15 H a : μ< 15 Note: where μ 0 =15 (b) With α =0 . 05 , the critical value = z α = z 0 . 05 = 1 . 645 We reject H 0 if z obs < 1 . 645 Note: Give the rejection region is the same as State the decision rule because the rejection region is the range of Z obs which you will reject the null hypothesis. (c) z obs = X 15 σ/ n = 12 15 3 / 70 = 8 . 37 < 1 . 645 so we reject H 0 at α =0 . 05 . We conclude that there is evidence to show that the new therapy is more e f ective than the standard therapy at 5% signi f cance level. 1

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2. Let X be the weight of a bag of cement and μ be the mean weight per bag of cement. X N X N ( μ, 1 10 ) (a) H 0 : μ 94 vs H a : μ< 94 With α =0 . 01 , the critical value = Z α = Z 0 . 01 = 2 . 33 We reject H 0 if z obs < 2 . 33 X =93 . 75 z obs = X 94 σ/ n = 93 . 75 94 1 / 10 = 0 . 79 6 < 2 . 33 and we do not reject H 0 at α =0 . 01 . There is no su
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06exHTs_p1-5 - ISOM111 Business Statistics(Fall 2010...

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