In a data analysis study conducted by personnel at the Statistics Consulting Center at Virginia Tech, two different materials, alloy A and alloy B, were compared in terms of breaking strength. Alloy B is more expensive, but it should certainly be adopted if it can be shown to be stronger than alloy A. The consistency of performance of the two alloys should also be taken into account. Random samples of beams made from each alloy were selected, and strength was measured in units of 0.001-inch deflection as a fixed force was applied at both ends of the beam. (The smaller measured value would suggest a stronger alloy.) Twenty specimens were used for each of the two alloys. The data are given in the following table: Alloy A: 88 79 84 89 81 83 82 79 86 85 Alloy B: 82 85 87 80 85 87 80 78 83 81 75 77 86 84 80 78 83 76 80 81 81 78 78 82 80 76 85 79 77 78 (a) Construct a quantile-quantile plot for each sample. Is it reasonable to assume that the two samples each came from a normal population? (b) Conduct a hypothesis test to compare the variances of the two samples. Use a = 0.05. (c) Is alloy B stronger than alloy A? Conduct a hypothesis test to answer this question. Use a 0.01.