Question: Will they charge more? In Exercise, you carried out the calculations for a confidence interval based on a bank's experiment in changing the rules for its credit cards. You ought to ask some questions about this study.
(a) The distribution of the amount charged is skewed to the right, but outliers are prevented by the credit limit that the bank enforces on each card. Why can we use a confidence interval based on a Normal sampling distribution for the sample mean x¯?
(b) The bank's experiment was not comparative. The increase in amount charged over last year may be explained by lurking variables rather than by the rule change. What are some plausible reasons why charges might go up? Outline the design of a comparative randomized experiment to answer the bank's question
Exercise: Will they charge more? A bank wonders whether omitting the annual credit card fee for customers who charge at least $2500 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 $346, and the standard deviation is $112. Give a 99% confidence interval for the mean amount charges would have increased if this benefit had been extended to all such customers.