1)A bank wonders whether omitting the annual credit card fee for customers who charge at least $2500 in a year will alter the amount charged on its credit cards. The bank makes this offer to 60 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 difference in spending in the sample is $24, and the standard deviation is $110. Is there significant evidence at the 5% level that the mean amount charged differed under the no-fee offer? Use a t-critical of 2.00. (10 pts)

a.What are the null hypothesis (H_o) and alternative hypothesis (H_a)? (1 pt)

b.Calculate the appropriate test statistic for this test. Show your work. (3 pts)

c.Sketch the null distribution and indicate where your t-statistic falls in it. (1.5 pts)

d.What is your answer to the bank's question? Include statistics in your answer. (1.25 pts)

e.Calculate the 95% confidence interval for this test. Interpret the confidence interval. Does the interpretation of this interval support what you concluded in d? What evidence does the confidence interval provide with regards to the null hypothesis?(3.25 pts)