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    Likelihood Tests

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    Let X1, X2, ...., Xn be a random sample from a N(µ0, σ ^2= Ө) distribution, where 0 < Ө < Infinity and µ0 is known. Show that the likelihood ratio test of H0: Ө = Ө0 versus H1: Ө Not = Ө0 can be based upon the statistic W= the sum from i=1 to n (Xi - µ0)^2/ &#1257;0. Determine the null distribution of W and give, explicitly, the rejection rule for a level α test.

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