A retailer that sells audio and video equipment accumulated 10,451 sales invoices during the previous year. The total of the sales amounts listed on these invoices (that is, the total sales claimed by the company) is $ 6,384,675. In order to estimate the true total sales for last year, an independent auditor randomly selects 350 of the invoices and determines the actual sales amounts by contacting the purchasers. The mean and the standard deviation of the 350 sampled sales amounts are $ 532 and $ 168, respectively.
a. Find point estimates of and 95 percent confidence intervals for (1) m, the true mean sales amount per invoice for the 10,451 invoices, and (2) , the true total sales amount for last year.
b. What does the interval for say about the company’s claim that the true total sales were $ 6,384,675? Explain.