Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The executives hire a statistical consultant and ask her to determine the mean shopping time of customers at the supermarkets. The consultant will collect a random sample of shopping times at the supermarkets and use the mean of these shopping times to estimate the population mean. Assuming that the standard deviation of the population of shopping times at the supermarkets is 26 minutes, what is the minimum sample size she must collect in order for her to be 95% confident that her estimate is within 4 minutes 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).
Calculate the sample size necessary for the sample mean to estimate ...
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.