Let X1,X2 be iid uniform(θ,θ + 1). For testing H0: θ = 0 versus H1: θ > 0, we have two competing tests:

(a) Find the value of C so that Ï•2 has the same size as Ï•i.
(b) Calculate the power function of each test. Draw a well-labeled graph of each power function.
(c) Prove or disprove: Ï•2 is a more powerful test than Ï• i.
(d) Show how to get a test that has the same size but is more powerful than Ï•2.

(X1) :Reject Ho if Xi > .95, (X, X2) : Reject Ho ifx, + X2 > C.