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5. We have two independent samples of n observations X1, X2, .. . , Xn and Yı, Y2,.. . , Yn We want to test the hvpothesis H 0 : μΧ-My versus the alternative H1 : μΧ * My (a) First, assume that the null hypothesis Ho is true and find the MLE for μ-Ac-My (b) Then plug this estimate into the log likelihood along with the MLEs μχ-x and My-- to calculate the LRT statistic (c) Is this likelihood ratio test equivalent to the test that rejects the null hypothesis when (x-ỹ) 2 〉 c? Justify your answer

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