Question: The accounts of a firm have been classified into 56 large accounts, 956 medium-sized accounts, and 16,246 small accounts. Each account has a book value (which is provided to you) representing the amount of money that is supposed to be in the account. Each account also has an audit value (which requires time and effort to track down) representing the amount of money that is really in the account. You are working with the auditors in preparing financial statements. The group has decided to examine all 56 large accounts, 15% of the medium-sized accounts, and 2% of the small accounts. The total error (book value minus audit value) was found to be $15,018.00 for the large accounts, $1,165.00 for the sampled medium-sized accounts, and $792.00 for the sampled small accounts. The standard deviations of the errors were $968.62, $7.12, and $5.14, respectively. (Hint: Do not confuse the error, which is measured for each account, with the standard error of an average.)
a. Find the sample average error per account in each of the three strata (groups) of accounts.
b. Combine these three averages to find the stratified sampling average estimate of the population mean error per account.
c. Find the standard error of your estimate in part b both with and without use of the finite-population correction factor. Why are the answers so different in this case?
d. Interpret the (corrected) standard error value in terms of the (unknown) population mean error per account.