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...

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. 

b) Your experience suggests that the two samples of customers share the same population standard deviation σ. 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 σ1 and σ2 , and b) assumes σ1 =σ2 ]