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Determine constants using the Central Limit Theorem

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8.1.9 Let X1,X2...,Xn be iid with pfm f(x;p)=p^x*(1-p)^(1-x), x=0,1, zero elsewhere. C={(x1,...,xn): Sum from 1 to n xi <=c} is the best critical region for testing H0: p=1/2 against p=1/3. Use the Central Limit Theorem to find n and c so that approximately P(Sum from 1 to n Xi <=c; H0) = 0.10 and P(sum from 1 to n Xi<=c; H1)=0.80

The answer is: n=about 39 and c=15.

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The solution contains detailed explanation of how to determine constants by using the Central Limit Theorem.