# hw12sol - Solutions to Homework 12 Problem 10.5 a The point...

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Unformatted text preview: Solutions to Homework 12 Problem 10.5 a. The point estimate is ¯ x 1- ¯ x 2 = 135 . 67- 68 . 64 = 67 . 03 . b. The margin of error is MOE = z α/ 2 s σ 2 1 n 1 + σ 2 2 n 2 = 2 . 576 s 35 2 40 + 20 2 30 = 17 . 08 . c. The 99% confidence interval is (¯ x 1- ¯ x 2 ) ± MOE = 67 . 03 ± 17 . 08 = (49 . 95 , 84 . 11) . Problem 10.8 a. The test statistic is z = (¯ x 1- ¯ x 2 )- D r σ 2 1 n 1 + σ 2 2 n 2 = (9 . 95- 69 . 56)- q 2 . 5 2 112 + 2 . 5 2 84 = 1 . 08 . b. The p-value is 2 P ( Z > 1 . 08) = 2(0 . 1401) = 0 . 2802 . c. Since the p-value is greater than α = 0 . 01, we do not reject H and conclude that it is possible that Palmer and Woods have the same mean score. Problem 10.17 a. The hypotheses are H : μ 1- μ 2 ≤ H a : μ 1- μ 2 > b. The test statistic is t = (¯ x 1- ¯ x 2 )- D r s 2 1 n 1 + s 2 2 n 2 = (6 . 82- 6 . 25)- q . 64 2 16 + . 75 2 10 = 1 . 99 . 1 c. To compute the p-value, we first need to compute the degrees of freedom....
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hw12sol - Solutions to Homework 12 Problem 10.5 a The point...

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