Banks frequently compete by adding special services that distinguish them from rivals. These services can be expensive to provide. The bank hopes to retain customers who keep high balances in accounts that do not pay large interest rates. Typical customers at this bank keep an average balance of $3,500 in savings accounts that pay 2% interest annually. The bank loans this money to other customers at an average rate of 6%, earning 4% profit on the balance. A sample of 65 customers was offered a special personalized account. After three months, the average balance in savings for these customers was $5,000 (σ = $3,000). If the service costs the bank $50 per customer per year, is this going to be profitable to roll out on a larger scale?
(a) State the null and alternative hypotheses. Describe the parameters.
(b) Describe Type I and Type II errors in this context.
(c) What is necessary for the sample size to be adequate for using a t-test?
(d) Find the p-value of the test. Do the data supply enough evidence to reject the null hypothesis if a = 0.05? (Assume that the data meet the sample size condition.)