Two alloys A and B are being used to manufacture a certain steel product. An experiment needs to be designed to compare the two in terms of maximum load capacity in tons. This is the maximum that can be tolerated without breaking. It is known that the two standard deviations in load capacity are equal at 5 tons each. An experiment is conducted in which 30 specimens of each alloy (A and B) are tested and the results gave x_A = 49.5, x_B = 45.5; x_A — x_B = 4. The manufacturers of alloy A are convinced that this evidence shows conclusively that μ_A > μ_B and strongly supports their alloy. Manufacturers of alloy B claim that the experiment could easily have given x_A – x_B – 4 even if the two population means arc: equal. In other words, "tilings are inconclusive!"

(a) Make an argument that manufacturers of alloy B are wrong. Do it by computing P(XA - XB > 4 | μ_A = μ_B).

(b) Do you think these data strongly support alloy A!