Let Y be the number of successes in a binomial experiment with n trials and probability of success p. Assuming that n is large, use the sample proportion of successes p̂ = Y/n to form a confidence interval for p with confidence coefficient (1 - α). Start with the pivotal statistic

 and use the fact (proof omitted) that for large n, Z is approximately a standard normal random variable.]

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p - p Z =