National Discount Has 260 Retail Outlets Throughout the United States $\sigma$

Essay

National Discount has 260 retail outlets throughout the United States. National evaluates each potential location for a new retail outlet in part on the mean annual income of the households in the marketing area of the new location. National develops an interval estimate of the mean annual income in a potential marketing area after taking a random sample of households.For a marketing area being studied, a sample of 36 households was taken and the sample mean income was $21,100.39. Based on past experience, National Discount assumes a known value of $\sigma$ = $4500 for the population income standard deviation.
a. Develop a 95% confidence interval for the mean annual income of households in this marketing area.
b. Suppose that National's management team wants a 95% confidence interval estimate of the population mean with a margin of error of E = $500. How large a sample size is needed?