Find the distribution of the test statistic when the null, Ask an Expert

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Suppose that X1, X2, ..., Xn are iid with a beta (nu,1) distribution and Y1, Y2, ..., Ym are iid beta (theta, 1) distribution. Assume Xs and Ys are independent.

1) FInd a likelihood ratio test of Ho: theta = nu vs. Ha: theta different from nu

2) Show that the test in part A can be based on the statistic

T = (sum of log(Xi))/((sum of log(Xi))+(sum of log(Yi)))

3) Find the distribution of the test statistic when the null hypothesis is true, and then show how to get a test size alpha= 0.10

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Statistics and Probability, Statistics

Category:- Statistics and Probability
Reference No.:- M9379878

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