Suppose a random sample of 137 households in Detroit was selected to determine the average annual household spending on food at home for Detroit residents. The sample results are contained in the file Detroit Eats.
a. Using the sample standard deviation as an estimate for the population standard deviation, calculate the sample size required to estimate the true population mean to within ± $25 with 95% confidence. How many additional samples must be taken?
b. Using the sample standard deviation as an estimate for the population standard deviation, calculate the sample size required to estimate the true population mean to within ± $25 with 90% confidence. How many additional samples must be taken?