Let X 1 , , X n be iid n( , 1), and let 0 be a specified value of . (a)

Let X₁, …, X_n be iid n(θ, 1), and let θ₀ be a specified value of θ.

(a) Find the UMP, size α, test of H₀ : θ ≥ θ₀ versus H₁ : θ < θ₀.

(b) Show that there does not exist a UMP, size α, test of H₀ : θ = θ₀ versus H₁ : θ ≠ θ₀.