Question: 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 in Table 4E.2. Assume that hardness is normally distributed.

1. 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.
   TABLE 4 E . 2
   Hardness Data for Exercise 4.19
   Saltwater Quench Oil Quench
   145 152
   150 150
   153 147
   148 155
   141 140
   152 146
   146 158
   154 152
   139 151
   148 143
2. Assuming that the variances \(\sigma _{1}^{2}\) and \(\sigma _{2}^{2}\) oil are equal, construct a 95% confidence interval on the difference in mean hardness.
3. Construct a 95% confidence interval on the ratio \(\sigma _{1}^{2}\) / \(\sigma _{2}^{2}\). Does the assumption made earlier of equal variances seem reasonable?
4. Does the assumption of normality seem appropriate for these data?

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