HW9Sol - are the same 3 Finding the signed ranks we see...

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Homework 9 – solution 1. For the given r max , we can compute the P-value as follows. P = 2 Pr( R + r max ) = 2 1 2 15 15 X i = r max ˆ 15 i ! . So for the value of r max from 8 to 15 (and thus for r min from 7 to 0) we obtain the following P-values Now, looking for the first value of r max (or r min ) such r max 8 9 10 11 12 13 14 15 r min 7 6 5 4 3 2 1 0 P 1 0.61 0.30 0.12 0.035 0.007 0.001 0.00006 that the P-value drop below α , we obtain the critical values for the various significance levels. α 0.01 0.02 0.05 0.10 0.25 r * max α 13 13 12 12 11 r * min α 2 2 3 3 4 2. Computing the differences x 2 i - x 1 i we see that r min = r + = 3 r * min 0 . 05 , and therefore we have to reject the hypothesis that the two means
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Unformatted text preview: are the same. 3. Finding the signed ranks, we see that w + = 13 + 14 + 15 = 42 and w-= 1 + 2 + ... + 12 = 78. We see that w min = w + > w min0 . 05 = 25 and we cannot reject the hypothesis that the two means are the same. We see that this result contradicts the result of the sign test for the same significance level. Since the signed rank test is generally better, we would be better off going with this result. 1...
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