hw22soluf08

hw22soluf08 - Assignment 2 Answer Keys 1 Because the two...

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Unformatted text preview: Assignment 2 Answer Keys 1. Because the two samples are paired, the paired t-test based on the differences of the two samples should be used. The differences are d 1 d 2 d 3 d 4 d 5 d 6 d 7 d 8 d 9 . 125 . 159 . 259 . 277 . 135 . 224 . 328 . 451 . 507 a). H : μ 1 = μ 2 vs H 1 : μ 1 6 = μ 2 or equivalently H : μ d = 0 vs H 1 : μ d 6 = 0 Based on d 1 , . . . , d 9 , ¯ d = 0 . 274, s d = 0 . 135. The observed t-statistic is t = ¯ d s d / √ n = 6 . 08 . Because t . 025 , 8 = 2 . 306 and t > t . 025 , 8 , we reject H . b) P- value = P ( t ≥ t or t ≤ - t | H ) = 0 . 0003 c) The 95% confidence interval for μ d is ( ¯ d- t α/ 2 ,n- 1 s d / √ n, ¯ d + t α/ 2 ,n- 1 s d / √ n ) = (0 . 274- 2 . 306 × . 135 / √ 9 , . 274 + 2 . 306 × . 135 / √ 9) = (0 . 170 , . 378) d) e): QQplots are omitted. The paired t test only needs to assume that the differences form a sample drawn from a normal distribution. The QQ plot of the diffrences does not suggest any significant departure from the normality assumption. f) Blocking was used. Blockingany significant departure from the normality assumption....
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hw22soluf08 - Assignment 2 Answer Keys 1 Because the two...

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