An experiment was performed to compare the fracture toughness ofhigh-purity 18 Ni maraging steel with commercial-purity steel ofthe same type. For m = 34 specimens, the sample averagetoughness was x = 63.4 for the high-purity steel, whereasfor n = 37 specimens of commercial steel y =57.8. Because the high-purity steel is more expensive, its use fora certain application can be justified only if its fracturetoughness exceeds that of commercial-purity steel by more than 5.Suppose that both toughness distributions are normal.
(a) Assuming that σ1 = 1.2 andσ2 = 1.1, test the relevant hypotheses usingα = 0.001. (Use μ1 −μ2, where μ1 is the averagetoughness for high-purity steel and μ2 is theaverage toughness for commercial steel.)
Calculate the test statistic and determine theP-value. (Round your test statistic to two decimal placesand your P-value to four decimal places.)
(b) Compute β for the test conducted in part(a) when μ1 − μ2 = 6.(Round your answer to four decimal places.)
β =
You may need to use the appropriate table in the Appendix of Tablesto answer this question.
