Refer to Exercise 10.32. As mentioned in that exercise, according to the credit rating agency Equifax, credit limits on newly issued credit cards increased between January 2011 and May 2011. Suppose that random samples of 400 new credit cards issued in January 2011 and 500 new credit cards issued in May 2011 had average credit limits of $2635 and $2887, respectively. Suppose that the sample standard deviations for these two samples were $365 and $412, respectively. Now assume that the population standard deviations for the two populations are unknown and not equal.
a. Let µ1 and µ2 be the average credit limits on all credit cards issued in January 2011 and in May 2011, respectively. What is the point estimate of µ1 – µ2?
b. Construct a 98% confidence interval for µ1 – µ2.
c. Using a 1% significance level, can you conclude that the average credit limit for all new credit cards issued in January 2011 was lower than the corresponding average for all credit cards issued in May 2011? Use both the p-value and the critical-value approaches to make this test.