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.

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.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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 =
n
i=1(Xi − μ0)2/θ0.
Determine the null distribution of W and give, explicitly, the rejection rule for a
level α test.

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