In: Statistics and Probability
Suppose an experiment was conducted to compare the fracture toughness of high-purity steel of some type with commercial-purity steel of the same type. For 9 high-purity specimens, the sample mean toughness and sample standard deviation of toughness (in some scale) were 1.82 and 0.6, respectively, whereas for 9 commercial-purity specimens, the sample mean and sample standard deviations were 2.43 and 0.82, respectively. Assume the data for both the high- and commercial-purity steels are normally distributed. Does this data suggest that the true mean toughness for the population of commercial-purity steel exceeds that of high-purity steel? To answer this question, state and test the appropriate hypotheses using a significance level of 0.05.