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...

For a level test with significance ...

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

Question:

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.