New Service Introduction: Banks frequently compete by adding special services that distinguish them from rivals. These services can be expensive to provide. A bank hopes to retain customers that 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 a 4% spread (profit) on the balance. A sample of 65 customers was offered a special "personalized" account. After 3 months, the average balance in savings for these customers was $5,000 (sample SD = $3,000).
A. If the service costs the bank an incremental $50 per customer per year, is this going to be profitable to roll out on a larger scale? State the null and alternative hypotheses. (Note: Think carefully about what hypotheses will help you answer whether the new service will be profitable or not).
B. Describe Type I and Type II errors in this context.
C. Do the data reject the null hypothesis if alpha =0.05? Find the p-value of the test. What is your recommendation to the bank?