A financial analyst is interested in estimating the average amount of a foreign loan by U.S. banks. The analyst believes that the amount of a loan may be different depending on the bank, or, more precisely, on the extent of the bank's involvement in foreign loans. The analyst obtains the following data on the percentage of profits of U.S. banks from loans to Mexico and proposes to use these data in the construction of stratum weights. The strata are the different banks: First Chicago, 33%; Manufacturers Hanover, 27%; Bankers Trust, 21%; Chemical Bank, 19%; Wells Fargo Bank, 19%; Citicorp, 16%; Mellon Bank, 16%; Chase Manhattan, 15%; Morgan Guarantee Trust, 9%.
a. Construct the stratum weights for proportional allocation.
b. Discuss two possible problems with this study.