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sec_9_1_and_9_2_sol

# sec_9_1_and_9_2_sol - APPM 4/5570 Solutions to Problems...

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APPM 4/5570 Solutions to Problems from Section 9.1 and 9.2 3. Test statistic Z = X - Y - 5000 r S 2 1 n 1 + S 2 2 n 2 = 42 , 500 - 40 , 400 - 5000 q 2200 2 45 + 1900 2 45 ≈ - 6 . 69 The rejection region is the upper tail area under the z -curve above the value 2 . 33. Conclusion: The test statistic is definitely not in there or even close! We fail to reject H 0 in favor of H a at 0 . 01 level of significance or at any almost other level! The data does not at all suggest that the premium brand has a true average tread life that is at least 5 , 000 more than that for the economy brand. The P-value for this problem is approximately 1 . 000. 7. Let μ 1 be the true mean boredom proneness rating for males and let μ 2 be the true mean boredom proneness rating for females. Hypotheses: H 0 : μ 1 - μ 2 = 0 H a : μ 1 - μ 2 > 0 Test Statistic: Z = X - Y - 5000 r S 2 1 n 1 + S 2 2 n 2 = 10 . 40 - 9 . 26 - 0 q 4 . 83 2 97 + 4 . 68 2 148 1 . 83 Rejection Region: The rejection region is the upper tail area under the z -curve above the value 1 . 645.

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