A bank compares two proposals to increase the amount that it

A bank compares two proposals to increase the amount that its credit card customers charge on their cards. (The bank earns a percentage of the amount charges, paid by the stores that accept the card). Proposal A offers to eliminate the annual fee for customers who charge $3600 or more during the year. Proposal B offers a small percentage of the total amount charges as a cash rebate at the end of the year. The bank offers proposal A to an SRS of 25 customers, and it offers proposal B to an SRS of 30 customers (independently drawn). At the end of the year, the total amount charged by each customer is recorded. Here is a summary:

Group A: (n = 25) (Xbar = $3385) (s = $468)

Group B: (n = 30) ($3124) (s = 411)

a) Do the data show a significant difference between the mean amounts charged by customers offered the two plans? State H0 and Ha. Calculate the two-sample test statistic. Test the hypothesis at 0.05 significance level. [Use the approximate d.f.]

b) Your experience suggests that the two samples of customers share the same population standard deviation . Test your hypothesis under this new assumption, again at 0.05 significance level.

c) Construct the (approximate) 95% confidence intervals (CI) under a) and under b). Compare and comment on the pros and cons of the two procedures. [Note: a) has NO assumption on 1 and 2 , and b) assumes 1 =2 ]

Solution