Question

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 charged, paid by the stores that accept the card). Proposal A offers to eliminate the annual fee for customers who charge $2,400 or more during the year. Proposal B offers a small percent of the total amount charged as a cash rebate at the end of the year. The bank offers each proposal to an SRS of 150 of its existing credit card customers. At the end of the year, the total amount charged by each customer is recorded. Here are the summary statistics:

Group n x s
A 150 $1,987 $392
B 150 $2,056 $413
A) Do the data show a significant difference between the mean amounts charged by customers offered the two plans?
B) The distributions of amounts charged are skewed to the right, but outliers are prevented by the limits that the bank imposes on credit balances. Do you think that skewness threatens the validity of the test? Explain.

Answer 1

a) There is no significant difference between the mean amounts charged

b) The skewness threatens the validity of the test

Explanation:

Given data:

Group n x s

A 150 $1,987 $392

B 150 $2,056 $413

n1 = n2 = 150

x1 = 1987

x2 = 2056

s1 = 392

s2 = 413

∝ = 0.05

Attached below is the detailed solution