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In: Statistics and Probability

In intaglio printing, a design or figure is carved beneath the surface of hard metal or...

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

159.018, 163.903

153.871, 167.802

165.096, 160.818

157.184, 167.433

154.496, 163.538

160.920, 164.525

164.917, 171.230

169.091, 174.964

175.276, 166.311

Treated

158.239, 150.223

138. 216, 155. 620

168.006, 151.233

149.654, 150.653

145.456, 151.204

168.178, 150.689

154.321, 161.657

162.763, 157.016

161.020, 156.670

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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Expert Solution

orchestra answered 2 years ago
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