Let X 1 ,X 2 , . . . , X n be a random sample from

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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 = θ0 versus H1 : θ ≠ θ0 can be based upon the statistic W = Σni=1(Xi − μ0)20. Determine the null distribution of W and give, explicitly, the rejection rule for a level α test.

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Introduction To Mathematical Statistics

ISBN: 9780321794710

7th Edition

Authors: Robert V., Joseph W. McKean, Allen T. Craig

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