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 = 65.3 for the high-purity steel, whereas for n = 39 specimens of commercial steel y = 59.9. 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 ?1 = 1.2 and ?2 = 1.0, test the relevant hypotheses using ? = 0.001. (Use ?1 ? ?2, where ?1 is the average toughness for high-purity steel and ?2 is the average toughness for commercial steel.)
State the relevant hypotheses.

H0: ?1 ? ?2 = 5
Ha: ?1 ? ?2 > 5H0: ?1 ? ?2 = 5
Ha: ?1 ? ?2 ? 5 H0: ?1 ? ?2 = 5
Ha: ?1 ? ?2 < 5H0: ?1 ? ?2 = 5
Ha: ?1 ? ?2 ? 5

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z =
P-value =

State the conclusion in the problem context.

Reject H0. The data suggests that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5.Fail to reject H0. The data does not suggest that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5. Reject H0. The data does not suggest that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5.Fail to reject H0. The data suggests that the fracture toughness of high-purity steel exceeds that of commercial-purity steel by more than 5.

(b) Compute ? for the test conducted in part (a) when ?1 ? ?2 = 6. (Round your answer to four decimal places.)
? =