According to the information given in Exercise 10.25, 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 a 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?
c. Suppose that the sample standard deviations were 28.9 and 61.4 miles, respectively. Redo parts a and b. Discuss any changes in the results.