Nine experts rated two brands of Colombian coffee in a taste-testing experiment. A rating on a 7-point scale (1 = extremely unpleasing, 7 = extremely pleasing) is given for each of four characteristics: taste, aroma, richness, and acidity. The following data represents the ratings accumulated over all four characteristics: Brand Expert A B C.C. 24 26 S.E. 27 27 E.G. 19 22 B.L. 24 27 C.M. 22 25 C.N. 26 27 G.N. 27 26 R.M. 25 27 P.V. 22 23 (a) At the 0.05 level of significance, is there evidence of a difference in the mean ratings between the two brands? (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) What assumption is necessary about the population distribution in order to perform this test? (c) Determine the p-value in (a) and interpret its meaning. (d) Construct and interpret a 95% confidence interval estimate of the difference in the mean rating between the two brands.
Nine experts rated two brands of Colombian coffee in a taste-testing experiment. A rating on a 7-point scale (1 = extremely unpleasing, 7 = extremely pleasing) is given for each of four characteristics: taste, aroma, richness, and acidity. The following data represents the ratings accumulated over all four characteristics:
Brand
Expert A B
C.C. 24 26
S.E. 27 27
E.G. 19 22
B.L. 24 27
C.M. 22 25
C.N. 26 27
G.N. 27 26
R.M. 25 27
P.V. 22 23
(a) At the 0.05 level of significance, is there evidence of a difference in the mean ratings between the two brands? (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) What assumption is necessary about the population distribution in order to perform this test?
(c) Determine the p-value in (a) and interpret its meaning.
(d) Construct and interpret a 95% confidence
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