An article in the Journal of Materials Engineering (1989, Vol. 11, No. 4, pp. 275–282) reported the results of an experiment to determine failure mechanisms for plasma sprayed thermal barrier coatings. The failure stress for one particular coating (NiCrAlZr) under two different test conditions is as follows:
Failure stress (X 106 Pa) after nine 1-hour cycles: 19.8, 18.5, 17.6, 16.7, 16.7, 14.8, 15.4, 14.1, 13.6
Failure stress (X 106 Pa) after six 1-hour cycles: 14.9, 12.7, 11.9, 11.4, 10.1, 7.9
(a) What assumptions are needed to construct confidence intervals for the difference in mean failure stress under the two different test conditions? Use normal probability plots of the data to check these assumptions.
(b) Find a 99% confidence interval on the difference in mean failure stress under the two different test conditions.
(c) Using the confidence interval constructed in part (b), does the evidence support the claim that the first test conditions yield higher results, on the average, than the second? Explain your answer.