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...

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 xA = 49.5, xB = 45.5; xA — xB = 4. The manufacturers of alloy A are convinced that this evidence shows conclusively that µA > µB and strongly supports their alloy. Manufacturers of alloy B claim that the experiment could easily have given xA – xB – 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 | µA = µB).

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