Suppose that X1, ...,Xn is a random sample from the U[0,] distribution. (i) Hypothesis H0 : 0 is to be tested against the

Suppose that X1, ...,Xn is a random sample from the U[0,θ] distribution.

(i) Hypothesis H0 : θ ≤ θ0 is to be tested against the alternative H1 : θ>θ0. Argue that the UMP test rejects H0 if Xn:n >

c. Find c for θ0 = 5,n = 10, and α = 0.05.

(ii) If the hypothesis H0 : θ ≥ θ0 is tested against H1 : θ<θ0, show that the UMP test rejects H0 if Xn:n <

c. Find c if θ0 = 5,n = 10, and α = 0.05.