A sample of 45 customers who drive luxury cars showed that their average distance driven between oil changes was 3187 miles with a sample standard deviation of 42.40 miles. Another sample of 40 customers who drive compact lower-price cars resulted in an average distance of 3214 miles with a standard deviation of 50.70 miles. Suppose that the standard deviations for the two populations are not equal. (a) Construct a 95% confidence interval for the difference in the mean distance between oil changes for all luxury cars and all compact lower-price cars. (b) Using the 1% significance level, can you conclude that the mean distance between oil changes is lower for all luxury cars than for all compact lower-price cars?