n 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 are as follows: Untreated

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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 are as follows:

Untreated

Treated

164.368          177.135

158.239          150.223

159.018          163.903

138.216          155.620

153.871          167.802

168.006          151.233

165.096          160.818

149.654          158.653

157.184          167.433

145.456          151.204

154.496          163.538

168.178          150.689

160.920          164.525

154.321          161.657

164.917          171.230

162.763          157.016

169.091          174.964

161.020          156.670

175.276          166.311

167.706          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 steel plates? (Use α = 0.05.) (Include: null and alternate hypotheses, value of test statistic, decision rule, conclusion in a complete sentence that includes why in terms of the decision rule.)

(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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