Let X1, X2, . . . , Xn be a random sample of Bernoulli trials b(1, p).
(a) Show that a best critical region for testing H0: p = 0.9 against H1: p = 0.8 can be based on the statistic

c) What is the approximate value of β = P[ Y > n(0.85); p = 0.8 ] for the test given in part (b)?
(d) Is the test of part (b) a uniformly most powerful test when the alternative hypothesis is H1: p

Y _ 1-1 Xi, which is b(n, p). (b) If C {(X1,X2, ,xn): lxi n(0.85)) and = < Y = _iXi, find the value of n such that = P[Y < n(0.85); p = 0.9] 0.10.