(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.
Test H0: 1 2 = 0 vs. H1: 1 2 0. Reject H0 if |t0|>t/2, n1+n2-2.
(b) Assuming that the variances 12 and 22 are equal, construct a 95% confidence interval on the difference in mean hardness.
(c) Construct a 95% confidence interval on the ratio 12 / 22. Does the assumption made earlier of equal variances seem reasonable?
(d) Does the assumption of normality seem appropriate for these data?