A company’s manager is considering simplification of a travel voucher form. In order to assess the costs associated with erroneous travel vouchers, the manager must estimate the total number of such vouchers that were filled out incorrectly in the last month. In a random sample of 100 vouchers drawn without replacement from the 1,323 travel vouchers submitted in the last month, 31 vouchers were filled out incorrectly.
a. Find point estimates of and 95 percent confidence intervals for (1) p, the true proportion of travel vouchers that were filled out incorrectly in the last month and (2) τ, the total number of vouchers filled out incorrectly in the last month.
b. If it costs the company $ 10 to correct an erroneous travel voucher, find a reasonable estimate of the minimum cost of correcting all of last month’s erroneous travel vouchers. Would it be worthwhile to spend $ 5,000 to design a simplified travel voucher that could be used for at least a year?