A small corporation makes insulation shields for electrical wires using three different types of machines. The corporation wants to evaluate the variation in the inside diameter dimensions of the shields produced by the machines. A quality engineer at the corporation randomly ­selects shields produced by each of the machines and records the inside diameter of each shield (in millimeters). She wants to determine whether the means and standard deviations of the three machines differ.

a. Conduct a test for the homogeneity of the population variances. Use α = .05.
b. Would it be appropriate to proceed with an analysis of variance based on the results of this test? Explain.
c. If the variances of the diameters are different, suggest a transformation that may alleviate their differences, and then conduct an analysis of variance to determine whether the mean diameters differ. Use α = .05.
d. Compare the results of your analysis in part (c) to an analysis of variance on the original diameters.
e. How could the engineer have designed her experiment differently if she knew that the variances of machine B and machine C were so much larger than that of machine A?

Shield Machine A Machine B Machine C 181 2.4 2.7 7.5 8.7 56.8 29.7 18.7 16.5 63.7 18.9 107.2 19.7 93.4 21.6 8.3 5.8 10