Let X1, ..., Xn ∼ Uniform(0, θ) and let Y = max{X1, ..., Xn}. We want to test H0 : θ = 1/2 versus H1 : θ > 1/2. The Wald test is not appropriate since Y does not converge to a Normal. Suppose we decide to test this hypothesis by rejecting H0 when Y > c.(a) Find the power function.(b) What choice of c will make the size of the test .05?(c) In a sample of size n = 20 with Y=0.48 what is the p-value? What conclusion about H0 would you make?(d) In a sample of size n = 20 with Y=0.52 what is the p-value? What conclusion about H0 would you make?
