Suppose that a researcher is interested in estimating the mean systolic blood pressure of executives of major corporations. He plans to use the blood pressures of a random sample of executives of major corporations to estimate the population mean. Assuming that the standard deviation of the population of systolic blood pressures of executives of major corporations is 27 mm Hg, what is the minimum sample size needed for the researcher to be 95% confident that his estimate is within 6 mm Hg of the population mean?
Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).
This problem shows how to find the sample size necessary to estimate a population mean with a sample mean. The confidence level, a bound on the margin of error, and an estimate of the population standard deviation are given. Using this information, we find the necessary sample size.