Question: Let X1, ...,Xn be a random sample from the N(,2) distribution with both parameters unknown. Find an unbiased test with a critical region of the

Let X1, ...,Xn be a random sample from the N(μ,σ2) distribution with both parameters unknown. Find an unbiased test with a critical region of the form “reject H0 if n i=1 (Xi − X)2/σ2 0 < C1 or n i=1 (Xi − X)2/σ2 0 > C2” to test the hypothesis H0 : σ = σ2 0 against the alternative H1 : σ2

= σ2 0. Use significance level α.

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