Question: Say X1, . . ., Xm ~ N(ux, 07 ), and Y1, . .., Ym~ N(uy, o' ); all of the random variables are all

Say X1, . . ., Xm ~ N(ux, 07 ), and Y1, . .., Ym~ N(uy, o' ); all of the random variables are all independent. The parameters o' and of are known, whereas ux and my are unknown. We are going to test the equality of the means of two Normal populations: Ho : ux = my versus H1 : ux # MY. We now design a test based on the statistic W = Xn - Ym. (1) What is the sampling distribution of W? (2) Consider the hypothesis test with the rejection region R = {W| > k}. Which value of k achieves a pre-specified significance level of a? Express the result in terms of the known parameters of, ov, m, n, and a

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