In intaglio printing, a design or figure is carved beneath the surface of hard metal or stone. The business objective of an intaglio printing company is to determine whether there are differences in the mean surface hardness of steel plates, based on two different surface conditions-untreated and treated by lightly polishing with emery paper. An experiment is designed in which 40 steel plates are randomly assigned-20 plates are untreated and 20 plates are treated. The results of the experiment, stored in Intaglio. are as follows:

a. Assuming that the population variances from both conditions are equal, is there evidence of a difference in the mean surface hardness between untreated and treated steel plates? (Use a = 0.05.)
b. Determine the p-value in (a) and interpret its meaning.
c. In addition to equal variances, what other assumption is necessary in (a)?
d. Construct and interpret a 95% confidence interval estimate of the difference between the population means from treated and untreated steel plates.