Textbook Problem

A stratified simple random sample is to be taken of a bank’s customers to learn about a variety of altitudinal and demographic issues. The stratification is to be based on savings account balances as of January 30, 2013. A frequency distribution showing the number of accounts in each stratum, together with the standard deviation of account balances by stratum, follows.

Stratum ($)	Accounts	Standard Deviation of Account Balances
0.00–1000.00	3000	80
1000.01–2000.00	600	150
2000.01–5000.00	250	220
5000.01–10,000.00	100	700
over 10,000.00	50	3000

1. a. Assuming the cost per unit sampled is approximately equal across strata, determine the total number of persons to include in the sample. Assume we want a bound on the error of estimate of the population mean for savings account balances of B = $20.
2. b. Use the Neyman allocation procedure to determine the number to be sampled for each stratum.