13.4.6 Suppose that XI,. . . , X, is a random sample from the U[O, 81 distribution.

(i) Hypothesis HO : 8 5 80 is to be tested against the alternative H I : 8 > 80.

Argue that the UMP test rejects HO if X,:, >

c. Find c for 80 = 5 ; n = 10, and Q = 0.05. (ii) If the hypothesis HO : 6 2 00 is tested against H I : 8 < 00, show that the UMP test rejects HO if X,:, <

c. Find c if 80 = 5 , n = 10, and Q = 0.05.