In a study of store checkout scanners, 1234 items were checked and 20 of them were found to be overcharges (based on data from "UPC Scanner Pricing Systems: Are They Accurate?" by Goodstein, Journal of Marketing, Vol. 58).
a. Using the sample data, construct a 95% confidence interval for the proportion of all such scanned items that are overcharges.
b. Use the sample data as a pilot study and find the sample size necessary to estimate the proportion of scanned items that are overcharges. Assume that you want 99% confidence that the estimate is in error by no more than 0.005.