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section11_problem4

section11_problem4 - b The rejection region is of the form...

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OR 2700, Spring’09 Section 11 Section 11 Apr 13 and 14, 2009. Problem (Devore 8.47 modified) Let μ denote the mean reaction time to a certain stimulus. For a large-sample test of H 0 : μ = 5 find the P-values associated with each of the various alterna- tives if the observed value for the test statistic Z is 1 . 42. Also indicate whether the null hypothesis will be rejected at 5% level. a. H a : μ < 5 b. H a : μ > 5 c. H a : μ = 5 Solution a. The rejection region is of the form Z c for some c . Hence the P-value is P ( X 1 . 42) where X is a standard normal distribution. Thus P-value equals Φ(1 . 42) = 0 . 9222. Since this is larger than 0 . 05, the null hypothesis is not rejected at 5% level.
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Unformatted text preview: b. The rejection region is of the form Z ≥ c for some c . Hence the P-value is P ( X ≥ 1 . 42) where X is a standard normal distribution. Thus P-value equals 1-Φ(1 . 42) = 0 . 0778. Since this is larger than 0 . 05, the null hypothesis is not rejected at 5% level. c. The rejection region is of the form | Z | ≥ c for some c . Hence the P-value is P ( | X | ≥ 1 . 42) where X is a standard normal distribution. Thus P-value equals 2(1-Φ(1 . 42)) = 0 . 1556. Since this is larger than 0 . 05, the null hypothesis is not rejected at 5% level. 1...
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