Question 7.30

7.30 Credit card fees.

A bank wonders whether omitting the annual credit card fee for customers who charge at least $5000 in a year would increase the amount charged on its credit card. The bank makes this offer to an SRS of 125 of its existing credit card customers. It then compares how much these customers charge this year with the amount that they charged last year. The mean is $685, and the standard deviation is $1128.

  1. Is there significant evidence at the 1% level that the mean amount charged increases under the no-fee offer? State and and carry out a test.
  2. Give a 95% confidence interval for the mean amount of the increase.
  3. The distributions of the amount charged are skewed to the right, but outliers are prevented by the credit limit that the bank enforces on each card. Use of the procedures is justified in this case even though the population distribution is not Normal. Explain why.
  4. A critic points out that the customers would probably have charged more this year than last even without the new offer because the economy is more prosperous and interest rates are lower. Briefly describe the design of an experiment to study the effect of the no-fee offer that would avoid this criticism.