A Conidence Interval for a Population Proportion A Confidenc

A Conidence Interval for a Population Proportion A Confidence Interval for a Population Proportion Let p denote the proportion of \"successes\" in a population, where success identifies an individual or object that has a specified property. A random sample of n individuals is to be selected, and X is the number of successes in the sample Provided that n is small compared to the population size, X can be regarded as a binomial rv with E(X)- np and oxVnp(1 -p). Furthermore, if n is large (np 2 10 and n10), X has approximately a normal distribution The natural estimator of p isp - X/n, the sample fraction of successes. Since p is just X multiplied by a constant 1/n, p also has approximately a nomal distribution. As shown in Section 7, I, E(p)=p (unbiasedness) and Op-V/p(1-p)/n. The standard deviation involves the unknown parameter p. Standardizing p by subtracting p and dividing by then implies that Proceeding as suggested in the subsection \"Deriving a Confidence Interval\" (Section 8.1), the confidence limits result from replacing each

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