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 Γ(α = 3, β = θ) distribution, where 0 < θ < ∞.
(a) Show that the likelihood ratio test of H0 : θ = θ0 versus H1 : θ ≠ θ0 is based upon the statistic W = Σn i=1 Xi. Obtain the null distribution of 2W /θ0.
(b) For θ0 = 3 and n = 5, find c1 and c2 so that the test that rejects H0 when W ≤ c1 or W ≥ c2 has significance level 0.05.

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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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