In each of the parts below, first decide whether or not to use the pooled estimator of variance. Assume that the populations are normal.

(a) The following are the Brinell hardness values obtained for samples of two magnesium alloys before testing:

Use the 0.05 level of significance to test the null hypothesis \(\mu_{1}-\mu_{2}=0\) against the alternative hypothesis \(\mu_{1}-\mu_{2}

(b) To compare two kinds of bumper guards, 6 of each kind, were mounted on a certain kind, of compact car. Then each car was run into a concrete wall at 5 miles per hour, and the following are the costs of the repairs (in dollars):

Use the 0.01 level of significance to test whether the difference between the two sample means is significant.

Transcribed Image Text:

Alloy 1: 66.3 63.5 64.9 61.8 64.3 64.7 65.1 64.5 68.4 63.2 Alloy 2: 71.3 60.4 62.6 63.9 68.8 70.1 64.8 68.9 65.8 66.2