Finite populations allow you to use the confidence interval for a population mean μ to produce a confidence interval of the population total. To estimate the population total, multiply the lower and upper confidence limits of the estimate of μ by the population size N. So the confidence interval estimator of the total is
(N*{x - tα/2s/sqrt(n)}, N*{x + tα/2s/sqrt(n)})
Pepsi wants to use this technique to determine if they should bid for an exclusivity agreement with NCSU. Such an agreement would bind NCSU to sell Pepsi soft drink products exclusively on campus.
To determine if an exclusivity agreement would be profitable, Pepsi must estimate the total number of 12 ounce cans (or their equivalent) that NCSU students would buy per week. NCSU's Office of Registration and Records informs Pepsi that N = 28,000 different students are on campus at least once during a typical week. Pepsi randomly samples 500 NCSU students and asks them to record the number of 12 ounce cans of soda (or their equivalent) that they purchase on campus over the next 7 days. The results are in this Excel file cans of soda per week.
Question. Use the data in the file to calculate a 95% confidence interval for the total number of 12 ounce cans of soda that NCSU students will purchase on campus in a week.
lower limit of 95% confidence interval
upper limit of 95% confidence interval.