Suppose that X1, . . . , Xn form a random sample from a density function, f (x|θ), for which T is a sufficient statistic for θ. Show that the likelihood ratio test of H0: θ = θ0 versus HA: θ = θ1 is a function of T . Explain how, if the distribution of T is known under H0, the rejection region of the test may be chosen so that the test has the level α.
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