# Likelihood Tests

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Let X1, X2, ...., Xn be a random sample from a N(Âµ0, Ïƒ ^2= Ó¨) distribution, where 0 < Ó¨ < Infinity and Âµ0 is known. Show that the likelihood ratio test of H0: Ó¨ = Ó¨0 versus H1: Ó¨ Not = Ó¨0 can be based upon the statistic W= the sum from i=1 to n (Xi - Âµ0)^2/ ө0. Determine the null distribution of W and give, explicitly, the rejection rule for a level Î± test.

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#### Solution Summary

Likelihood test is performed in the solution.

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