Question

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.
(a) Is there significant evidence at the 1% level that the
mean amount charged increases under the no-fee offer?
State H0 and Ha and carry out a t test.
(b) Give a 95% confidence interval for the mean amount
of the increase.
(c) 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
t procedures is justified in this case even though the
population distribution is not Normal. Explain why.
(d) 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.

Answer 1