2. b) [15] The standard recommendation for automobile oil changes is once every 5,000 kilometres (km). 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 25 customers who drive luxuryr cars and 30 customers who drive lower-price compact cars were selected. The results from the samples follow. Assume that the population distributions of the distances between oil changes have the same standard deviations for the two populations. Compact Sample size Sample mean (km) 5200 5100 samlestd km -m [5] Construct a 99% condence interval for the difference in the mean distances between oil changes for all luxury cars and all lower-price compact cars. [7] Using a 1% signicance level, can you conclude that the mean distance between oil changes is less for all luxury cars than that for all lower-price compact cars? Use a critical value approach. c) [3] Suppose that the assumption of equal population variances is not valid. Redo the decision rule for part b. Does this change your conclusions