There are two hypotheses about the probability of heads
Chapter , Problem 22(choose chapter or problem)
There are two hypotheses about the probability of heads for a given coin: 0 = 0.5 (hypothesis Ho ) and 0 = 0.6 (hypothesis HI ) . Let X be the number of heads obtained in n tosses, where n is large enough so that normal approximations are appropriate. We test Ho against HI by rejecting Ho if X is greater than some suitably chosen threshold kn. (a) What should be the value of kn so that the probability of false rejection is less than or equal to 0.05? (b) What is the smallest value of n for which both probabilities of false rejection and false acceptance can be made less than or equal to 0.05? (c) For the value of n found in part (b), what would be the probability of false acceptance if we were to use a LRT with the same probability of false rejection?
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