Using data from the U.S. Census Bureau and other sources, www.nerdwallet.com estimated that considering only the households with credit card debts, the average credit card debt for U.S. households was $15,523 in 2014 and $15,242 in 2013. Suppose that these estimates were based on random samples of 600 households with credit card debts in 2014 and 700 households with credit card debts in 2013. Suppose that the sample standard deviations for these two samples were $3870 and $3764, respectively. Assume that the standard deviations for the two populations are unknown and unequal.
a. Let μ1 and μ2 be the average credit card debts for all such households for the years 2014 and 2013, 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 card debt for such households was higher in 2014 than in 2013? Use both the p-value and the critical-value approaches to make this test.