Matrix Metals is concerned that the variation in the diameters (measured in millimeters) of the metal wafers produced by two of its metal stamping machines is different for the two machines. You take a random sample of 8 wafers from machine A and 8 wafers from machine B. The diameters in the machine A sample have a variance of 1.6. The diameters in the machine B sample have a variance of 2.8. Assume that both populations represented here have a normal distribution.
a. Test the hypothesis that the variances of the two populations are equal. Use a significance level of 2%.
b. Test the null hypothesis that the Machine B population variance is no greater than the Machine A population variance, against an alternative hypothesis that the Machine B population variance is greater than the Machine A population variance. Use a significance level of 5% for this one tailed test.