# Question

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 < 0.9?

(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 < 0.9?

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