When one is attempting to determine the required sample size for estimating a population mean, and the information on the population standard deviation is not available, it may be feasible to take a small preliminary sample and use the sample standard deviation to estimate the required sample size, n. Suppose that we want to estimate µ, the mean commuting distance for students at a community college, to a margin of error within 1 mile with a confidence level of 95%. A random sample of 20 students yields a standard deviation of 4.1 miles. Use this value of the sample standard deviation, s, to estimate the required sample size, n. Assume that the corresponding population has a normal distribution.
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