untreated versus treated by light polishing; 10.1...

10.14 In intaglio printing, a design or figure is carved beneath the surface of hard metal or stone. Suppose that an experiment is
designed to compare differences in mean surface hardness of steel plates used in intaglio printing (measured in indentation numbers) based on two different surface conditions — untreated versus treated by light polishing with emery paper. In the experiment 40 steel plates are randomly assigned, 20 that are untreated and 20 that are treated. The results of the experiment in intaglio are as follows:
Untreated: 164.368, 159.018, 153.871, 165.096, 157.184, 154.496, 160.920, 164.917, 169.091, 175.276, 177.135, 163.903, 167.802, 160.818, 167.433, 163.538, 164.525, 171.230, 174.964, 166.311
Treated: 158.239, 138.216, 168.006, 149.654, 145.456, 168.178, 154.321, 162.763, 161.020, 167.706, 150.226, 155.620, 151.233, 158.653, 151.204, 150.869, 161.657, 157.016, 156.670, 147.920
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 plates (Use level of significance = 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.

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