An experiment was performed to compare the fracture toughness of high-purity steel with commercial purity steel. Because the high purity steel is more expensive, its use for a certain application can be justified only if its mean fracture toughness exceeds that of the commercial purity steel by more than 5. Suppose both toughness distributions are normal with equal variances.

(a)Formulate the hypotheses.

(b)A random sample of 15 high-purity steel yielded an average of 65.9 and a standard deviation of 1.5. Whereas, a random sample of 20 commercial purity steel yielded an average of 59.8 and a standard deviation of 1.2. Calculate the value of the test statistic for the hypotheses in part (a), state the degrees of freedom and approximate the p-value

(c)Would you reject H0or fail to reject H0at 1% level of significance?

(d)Is the use of high purity steel justified? Explain