In Section 8.9, we gave a sample size formula for confidence interval estimation of a mean. If the confidence level is 95%, then because the z-multiple is about 2, this formula is essentially

n = 4σ2 / B2

However, this formula is based on the assumption that the sample size n will be small relative to the population size N. If this is not the case, the appropriate formula turns out to be

Now suppose you want to find a 95% confidence interval for a population mean. Based on preliminary (or historical) data, you believe that the population standard deviation is approximately 15. You want the confidence interval to have length 4. That is, you want the confidence interval to be of the form x̄ +. What sample size is required if N = 400? If N = 800? If N = 10,000? If N = 100,000,000? How would you summarize these findings in words?

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