Let X1,X2, . . . , Xn be a random sample from a N(μ0, σ2 = θ) distribution,where 0 < θ < ∞and μ0 is known. Show that the likelihood ratio test of H0 : θ = θ0versus H1 : θ = θ0 can be based upon the statistic W =ni=1(Xi − μ0)2/θ0.Determine the null distribution of W and give, explicitly, the rejection rule for alevel α test.

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