Suppose an experiment was conducted to compare the fracturetoughness of high-purity steel of some type with commercial-puritysteel of the same type. For 9 high-purity specimens, the samplemean toughness and sample standard deviation of toughness (in somescale) were 1.82 and 0.6, respectively, whereas for 9commercial-purity specimens, the sample mean and sample standarddeviations were 2.43 and 0.82, respectively. Assume the data forboth the high- and commercial-purity steels are normallydistributed. Does this data suggest that the true mean toughnessfor the population of commercial-purity steel exceeds that ofhigh-purity steel? To answer this question, state and test theappropriate hypotheses using a significance level of 0.05.
