An experiment was performed to compare the fracture toughness of high-purity 18 Ni maraging steel with commercial-purity steel of the same type. For m = 34 specimens, the sample average toughness was x = 65.2 for the high-purity steel, whereas for n = 36 specimens of commercial steel y = 59.7. 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.

Assuming that Ï1 = 1.2 and Ï2 = 1.1, test the relevant hypotheses using α = 0.001. (Use μ1 â μ2, where μ1 is the average toughness for high-purity steel and μ2 is the average toughness for commercial steel.)