Question: Refer to Exercise. It was mentioned that the average credit limit on 200 credit cards issued during 2008 was $4710 with a standard deviation of $485, and the mean and standard deviation for 200 credit cards issued during the first 4 months of 2009 were $4602 and $447, respectively. Suppose that the standard deviations for the two populations are not equal.
a. Construct a 95% confidence interval for the difference in the mean credit limits for all new credit cards issued in 2008 and during the first 4 months of 2009.
b. Using the 2.5% significance level, can you conclude that the average credit limit for all new credit cards issued in 2008 is higher than the corresponding average for the first 4 months of 2009?
c. Suppose that the standard deviations for the two samples were $590 and $257, respectively. Redo parts a and b. Discuss any changes in the results.
Exercise: According to the credit rating firm Equifax, credit limits on newly issued credit cards decreased between 2008 and the period of January to April 2009 (USA TODAY, July 7, 2009). Suppose that random samples of 200 credit cards issued in 2008 and 200 credit cards issued during the first 4 months of 2009 had average credit limits of $4710 and $4602, respectively, which are comparable to the values given in the article. Although no information about standard deviations was provided, suppose that the sample standard deviations for the 2008 and 2009 samples were $485 and $447, respectively, and that the assumption that the population standard deviations are equal for the two time periods is reasonable.
a. Construct a 95% confidence interval for the difference in the mean credit limits for all new credit cards issued in 2008 and during the first 4 months of 2009.
b. Using the 2.5% significance level, can you conclude that the average credit limit for all new credit cards issued in 2008 was higher than the corresponding average for the first 4 months of 2009?