A manufacturing company produces steel housings for electrical equipment. The main component part of the housing is a steel trough that is made out of a 14-gauge steel coil. It is produced using a 250-ton progressive punch press with a wipe-down operation that puts two 90-degree forms in the flat steel to make the trough. The distance from one side of the form to the other is critical because of weatherproofing in outdoor applications. The company requires that the width of the trough be between 8.31 inches and 8.61 inches.
The file Trough contains the widths of the troughs, in inches, for a sample of n = 49:

a. At the 0.05 level of significance, is there evidence that the mean width of the troughs is different from 8.46 inches?
b. What assumption about the population distribution is needed in order to conduct the t test in (a)?
c. Evaluate the assumption made in (b).
d. Do you think that the assumption needed in order to con¬duct the t test in (a) is valid? Explain.