A bank wonders whether omitting the annual credit card fee for customers who charge at least $3,000 in a year would increase the amount charged on their credit card. The bank makes an offer to an SRS of 500 existing credit card customers. It then compares how much these customers charge this year with the amount they charges last year. The mean increase is $565, and the standard deviation is $267.

a. Is there significant evidence at the 1% level that the mean amount charged increases under the no-fee offer? State the null Ho and alternative hypothesis Ha and carry out a statistical test. (HINT: the hypothesis test evaluates if the average increase in charges is significantly larger than zero)

b.Give a 95% confidence interval for the mean amount of the increase

c.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.