An experiment was performed to compare the fracture toughness of high-purity 18 Ni maraging steel with commercial-purity steel of the same type (Corrosion Science, 1971: 723–736). For specimens, the sample average toughness was for the high-purity steel, whereas for specimens of commercial steel

. Because the high-purity steel is more expensive, its use for a certain application can be justified only if its fracture toughness exceeds that of commercial-purity steel by more than 5.

Suppose that both toughness distributions are normal.

a. Assuming that and , test the relevant hypotheses using .

b. Compute b for the test conducted in part

(a) when

.