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
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
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
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