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A reporter took a simple random sample of 725 voters in a region that has a population of 12,457. He recorded that 338 of the persons polled favored Issue 1 on the ballot. Construct a 95% confidence interval for the proportion that favor the issue and then discuss what the reporter can and cannot say in his report. If you were the editor of a newspaper reporting on the results, what questions would you have of the reporter before you printed his story?

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This solution is comprised of an explanation of how to construct a 95% confidence interval within the context of close approximation.

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Our sample probability of favoring Issue 1 is p = 338/725 = 0.466, and our sample size is n = 725. Standard error for a poll is calculated as S.E. = Sqrt[p(1-p) / n], and the 95% confidence interval for the true proportion of the population favoring Issue 1 is the mean plus or minus 1.96 x S.E. (1.96 is a constant determined by the normal distribution; it's ...

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