A bank wonders if omitting the annual credit card fee for customers who charge at least $2400 in a year will increase the amount charged on its credit cards. The bank makes this offer to an SRS of 200 of its credit card customers. It then compares how much these customers charge this year with the amount that they charged last year. The mean increase in the sample is $332, and the standard deviation is $108.

a. Construct and interpret a 99% confidence interval for the true mean increase.

b. Based on the interval from (a), can you conclude that dropping the annual fee would cause an increase in the average amount spent by this bank’s credit card customers? Why or why not?