A bank wonders whether offering a higher cash back percent would increase the amount charged on its credit card. The bank makes this offer to randomly selected 85 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 increase in the amount charged for the sample is $312, and the sample standard deviation is $1327.

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

b. Is there significant evidence at the 1% level that the mean amount charged increases under the higher cash back offer? State 0 and and carry out a test. Sketch the distribution of test statistic when the null is true, and shade the area that corresponds to the p-value.