Question 7.87

7.87 Credit card fees.

The bank in Exercise 7.30 (page 377) tested a new idea on a sample of 125 customers. Suppose that the bank wanted to be quite certain of detecting a mean increase of in the credit card amount charged, at the significance level. Perhaps a sample of only customers would accomplish this. Find the approximate power of the test with for the alternative as follows:

  1. What is the critical value for the one-sided test with and ?
  2. Write the criterion for rejecting in terms of the statistic. Then take and state the rejection criterion in terms of
  3. Assume that (the given alternative) and that The approximate power is the probability of the event you found in part (b), calculated under these assumptions. Find the power. Would you recommend that the bank do a test on 60 customers, or should more customers be included?

7.87

(a) . (b) Reject when , or when . (c) 0.5398. This power is not sufficient, we should recommend that the bank use more customers to increase power.