A report in 2004 by the U.S. National Center for Health Statistics provided an estimate of 20.4% for the percentage of Americans over the age of 18 who were currently smokers. The sample size was 30,000. Assuming that this sample has the characteristics of a random sample, a 99.9% confidence interval for the proportion of the population who were smokers is (0.20, 0.21). When the sample size is extremely large, explain why even confidence intervals with large confidence levels are narrow.
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