Only need part b An experiment was performed to compare the

Only need part b.

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 = 33 specimens, the sample average toughness was X = 62.1 for the high-purity steel, where for n = 36 specimens of commercial Y = 56.4 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 thart both toughness distributions are normal.

Solution

Given m=33, n=36, xbar=62.1,ybar=56.4, ₁=1.4 & ₂=1.1. Ho:1-2=5 against H1:1-2>5( this is right tail test), then Ztab at 0.001 level of significance of right tail test is 3.8. Zcal=(xbar-ybar)/[[(1²/m)+(2²/n)]]=(62.1-56.4)/[[(1.96/33)+(1.21/36)]]=5.7/0.305=18.6885, so we reject null hypothesis, i.e., H1:1-2>5. Therefore, the data suggests that the fracture toughness of high-purity steel exceeds that of commercial-purity steel more than 5. (b):=1-alpha=1-0.001=0.999. Ho:1-2=6 , against H1:1-2 not= 6( two tailed test) , then the table value of Z at 99.9% i.e.,=0.4995 is 3.27. Then Zcal=6/0.305=19.6721>Ztab, so we reject Ho, i.e., H1:1-2 not= 6.