Question

1. The standard recommendation for automobile oil changes is once every 5000 miles. A local mechanic is interested in determining whether people who drive more expensive cars are more likely to follow the recommendation. Independent random samples of 45 customers who drive luxury cars and 40 customers who drive compact lower-price cars were selected. The average distance driven between oil changes was 5187 miles for the luxury car owners and 5389 miles for the compact lower-price car owners. The sample standard deviations were 424 and 507 miles for the luxury and compact groups, respectively. Assume that the two population distributions of the distances between oil changes have the same standard deviation. You would like to test if the mean distance between oil changes is less for all luxury cars than that for all compact lower-price cars.

Let μ₁ denote the mean distance between oil changes for luxury cars, and μ₂ denote the mean distance between oil changes for compact lower-price cars. Suppose the test statistic for this case is -2. Calculate the p-value. Round your final answer to the nearest ten thousandth (e.g., 0.1234).

2. Using data from the U.S. Census Bureau and other source, 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. You would like to test whether the average credit card debt for such households was higher in 2014 than in 2013.

a. Let μ₁ denote the average credit card debt in 2014, and μ₂ denote the average credit card debt in 2013. Calculate the appropriate test statistic. Round your intermediate calculation and final answer to the nearest hundredth.

b. Let μ₁ denote the average credit card debt in 2014, and μ₂ denote the average credit card debt in 2013. Calculate the degree of freedom for this test.

c. Let μ₁ denote the average credit card debt in 2014, and μ₂ denote the average credit card debt in 2013. Suppose the test statistic is 1.32 and the degree of freedom is 1256. Calculate the p-value for this test. Round your answer to the nearest ten thousandth (e.g., 0.1234).

Answer 1