The standard recommendation for automobile oil changes is onceevery 5000 miles. A local mechanic is interested in determiningwhether people who drive more expensive cars are more likely tofollow the recommendation. Independent random samples of 45customers who drive luxury cars and 40 customers who drive compactlower-price cars were selected. The average distance driven betweenoil changes was 5187 miles for the luxury car owners and 5389 milesfor the compact lower-price car owners. The sample standarddeviations were 424 and 507 miles for the luxury and compactgroups, respectively. Assume that the two population distributionsof the distances between oil changes have the same standarddeviation. You would like to test if the mean distance between oilchanges is less for all luxury cars than that for all compactlower-price cars.
Let μ1 denote the mean distance between oil changesfor luxury cars, and μ2 denote the mean distance betweenoil changes for compact lower-price cars. Suppose the teststatistic for this case is -2. Calculate the p-value. Round yourfinal answer to the nearest ten thousandth (e.g.,0.1234).
