Problem 6 (20pts) Two different hardening processes - (1) saltwater quenching and (2) oil quenching - are used on samples of a particular type of metal alloy. The results are shown as below. Assume that hardness is normally distributed. (a) Test the hypothesis that the mean hardness for the saltwater quenching process equals the mean hardness for the oil quenching process. Use a = 0.05 and assume equal variances. (b) Assuming that the variances o and o are equal, construct a 95% confidence interval on the difference in mean hardness. (c) Construct a 95% confidence interval on the ratio o /02. Does the assumption made earlier of equal variances seem reasonable? (Only required for IEM5103 students) (d) Does the assumption of normality seem appropriate for these data? Why? (Only required for IEM5103 students)