Suppose that Y has a binomial distribution based on n
Chapter 9, Problem 36E(choose chapter or problem)
Suppose that Y has a binomial distribution based on n trials and success probability p. Then \(\hat{p}_{n}=Y / n\) is an unbiased estimator of p. Use Theorem 9.3 to prove that the distribution of \(\left(\hat{p}_{n}-p\right) / \sqrt{\hat{p}_{n} \hat{q}_{n} / n}\) converges to a standard normal distribution. [Hint: Write Y as we did in Section 7.5.]
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