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hw1ans - Stat 500 HW 1 Solution 1 Design-based p-values and...

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Stat 500: HW 1, Solution 1. Design-based p-values and confidence intervals (a) Use the randomization data (lab1bigex1.txt) to compute the p-value. For the one-sided test of H o difference = 0, there are 11 values larger than 4.49, so p = (11+1)/(500+1) = 0.024 or 2.4%. For the one-sided test of H o ratio = 1, there are 11 values larger than 3.84, so p = (11+1)/(500+1) = 0.024. (b) For the two-sided test of H o difference = 0, there are 10 values less than -4.49 and 11 larger than 4.49, so p = (21+1)/(500+1) = 0.044 or 4.4%. For the two-sided test of H o ratio =1, there are 10 values less than 0.2604 and 11 values more than 3.84, so p = (21+1)/(500+1) = 0.044. (c) Use the bootstrap data (lab1bigex2.txt) to get the confidence interval. Endpoints of the 95% confidence interval are given by the 0.025*500 =12.5, rounded to 13’th sorted value, and the 0.975*500 = 487.5, rounded to 488’th sorted value. 95% confidence interval for the difference is (0.440, 10.257). 95% confidence interval for the ratio is (1.226, 9.495). Note: Notice that these 13’th and 488’th observations values are symmetrical from the ends of the sorted list. The 13’th largest is skip the first 12 and take the 13’th.
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