An accounting firm works for a number of clients in the banking, insurance, and brokerage industries: N1 = 50 banks, N2 = 38 insurance companies, and N3 = 35 brokerage firms. A marketing research firm has been hired to survey the accounting firm's clients in these three industries. The survey will ask a variety of questions about both the clients' businesses and their satisfaction with services provided by the accounting firm. Suppose an approximate 95% confidence interval is requested for the mean number of employees for the 123 clients with a bound on the error of estimation of B = 30.
a. Suppose a pilot study finds s1 = 80, s2 = 150, and s3 = 45. Choose a total sample size, and explain how the sample size should be allocated to the three strata.
b. Suppose the pilot test is called into question and a decision is made to assume the stratum standard deviations are all equal to 100 in choosing the sample size. Choose a total sample size, and determine how many elements should be sampled in each stratum.