For the test described in Exercise 6 3 5, obtain the distribution of the test statistic under general alternatives If computational facilities are available, sketch this power curve for the case when 0 1, n 10, 0, and 0 05 Exercise 6 3 5 Let X 1 ,X 2 , , X n be a random sample from a N( 0 , 2 ) distribution, where 0 and 0 is known Show that the likelihood ratio test of H 0 0 versus H 1 0 can be based upon the statistic W n i 1 (X i 0) 2 0 Determine the null distribution of W and give, explicitly, the rejection rule for a level test

Question: For the test described in Exercise 6.3.5, obtain the distribution of the test statistic under general alternatives. If computational facilities are available, sketch this power

For the test described in Exercise 6.3.5, obtain the distribution of the test statistic under general alternatives. If computational facilities are available, sketch this power curve for the case when θ₀ = 1, n = 10, μ = 0, and α = 0.05.

Exercise 6.3.5

Let X₁,X₂, . . . , X_n 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 = Σⁿ_i=1(X_i − μ0)²/θ₀. Determine the null distribution of W and give, explicitly, the rejection rule for a level α test.

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