(g) [2 marks] Show that there exists no UMP test when the alternative hypothesis is replaced with H1: θ ≠ 1.
(h) [2 marks] Extend the above result to the more general situation where X1, ..., Xn ~ iid Gamma(2, θ). Show that the UMP test for testing H0: θ = 1 against H1: θ > 1 exists and has the critical region of the form Cα = {x: x̄ < bα}, where x̄ = n^-1 ∑i=1 to n xi.
(i) [2 marks] Compute the value of bα, when n = 10 and α = 0.05.
(Hint: What is the distribution of ∑i=1 to n Xi under H0?)