Question: Suppose that X1, . . . , Xn form a random sample from the Bernoulli distribution with unknown parameter p, and suppose that it is

Suppose that X1, . . . , Xn form a random sample from the Bernoulli distribution with unknown parameter p, and suppose that it is desired to test the following hypotheses:
H0: p ≤ 1/2 ,
H1: p > 1/2.
Show that if the sample size is n = 20, then there exists a nonrandomized UMP test of these hypotheses at the level of significance α0 = 0.0577 and at the level of significance α0 = 0.0207.

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