I will flip a coin three times and let X stand for the

Chapter 9, Problem 1

(choose chapter or problem)

I will flip a coin three times and let X stand for the number of times that the coin comes up heads. Let stand for the probability that the coin comes up heads on a single flip, and assume that the flips are independent given . I wish to test the null hypothesis H0 : = 1/2 against the alternative hypothesis H1 : = 3/4. Find the test that minimizes () + (), the sum of the type I and type II error probabilities, and find the two error probabilities for the test.

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