17.15 The program director for Aarhus School of Business, Denmark, is analyzing the marks obtained by students from three different modules—Business Economics, and Political Science. For Business, he sampled 58 students’ results from the total of 472, 66 out of 687 for Economics, and 57 out of 461 for Political Science.

He estimated the standard deviations for each module from the previous results to be 34, 56, and 21, respectively.

Determine the total sample size under both proportional allocation and optimal allocation when a 95% confidence interval for the overall population mean extended to 20 points for both side of the sample estimate.