Section_12 - Anna Lee Jery Stedinger Fall 2006 CEE 304...

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Anna Lee & Jery Stedinger Fall 2006 CEE 304 – Section 12 Handout Solutions Nonparametric Statistical Tests Example: Q1: Wind speed The appropriate hypotheses are: H o : μ d = 0 H a : μ d 0 α = 5% n = 11, 67 . 0 = d , s d = 1.12 (a) Wilcoxon Sign Rank Test: S + = Sum of ranks of positive differences = 15 S = [n(n + 1)/2] – S + = 51 Find rejection region and p-value using Table A.13. Reject H o if S + 55 or S + [n(n + 1)/2] – 55 = 11 with actual significance level α = 2(0.027) = 0.054 What do we conclude for this data set? We observed S + = 15, so we fail to reject H o . p-value = 2*P[S + 51] = 2(0.064) = 0.13 (b) For sign test, use the attached page of pmf of binomial distribution with n = 11 instead of n = 10 as was indicated in the original test question. Sign Test: S = # of positive differences = 3 Under H o : S ~ Bin(n = 11, p = 0.5) Want rejection region with α = 5% Could restrict α 0.05, and choose rejection region S 1 or S 10, with an actual significance level of 0.01. But no such restriction was required in this problem.
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