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Assume that we have two independent samples from two populations: n subjects from population A and n subjects from populations B. To test if the population A has a larger location parameter than that of population B, we can use (a) the Wilcox ranksum test or (b) the permutation test on sample means difference. What are the smallest values of n for each test so that, at α=0.01 level, the test can reject the null hypothesis of equal population mean? Show your calculation. (Not asking the likelihood of rejecting the null hypothesis, just the existence of a single data set that allows rejecting the null hypothesis. For example, when n=1, no such data set exists. Even if you got the following data set: one from A with value 1billion and one from B with value zero. The two tests still can not reject the null hypothesis for this data set, at α=0.01 level.)
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