Nondestructive evaluation is a method that is used to describe the properties of components or materials without causing any permanent physical change to the units. It includes the determination of properties of materials and the classification of flaws by size, shape, type, and location. This method is most effective for detecting surface flaws and characterizing surface properties of electrically conductive materials. Data were collected that classified each component as having a flaw or not, based on manual inspection and operator judgment, and the data also reported the size of the crack in the material. Do the components classified as unflawed have a smaller mean crack size than components classified as flawed? The results in terms of crack size (in inches) are stored in Crack. (Data extracted from B. D. Olin and W. Q. Meeker, "Applications of Statistical Methods to Nondestructive Evaluation," Technometrics, 38, 1996, p. 101.)
a. Assuming that the population variances are equal, is there evidence that the mean crack size is smaller for the unflawed specimens than for the flawed specimens? (Use α = 0.05.)
b. Repeat (a), assuming that the population variances are not equal.
c. Compare the results of (a) and (b).