Question

Nine experts rated two brands of 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 accompanying data table contains the ratings accumulated over all four characteristics. Complete parts (a) through (d) below 囲Click the icon to view the data table a. At the 0.10 level of significance, is there evidence of a difference in the mean ratings between the two brands? Let μ1 be the mean rating for brand A and μ2 be the mean rating for brand B. Determine the null and alternative hypotheses for this test. The test statistic is tSTAT (Type an integer or a decimal. Round to two decimal places as needed.) The critical value(s) is(are) Type integers or decimals. Round to two decimal places as needed. Use a comma to separate answers as needed.) Since the test statistic the critical value(s) VHo. There is ▼ evidence to conclude that the mean ratings are different between the two brands b. What assumption is necessary about the population distribution in order to perform this test? O A. It must be assumed that the distribution of the differences between the measurements is approximately uniform. O B. It must be assumed that the distribution of the differences between the measurements is approximately normal. O C. It must be assumed that the distribution of the differences between the measurements is skewed. c. Determine the p-value in (a) and interpret its meaning The test statistic gives a p-value of (Type an integer or a decimal. Round to three decimal places as needed.) Interpret the meaning of the p-value in (a). Choose the correct answer below. ○ A The p-value is he probability o obtaining a sample mean difference ess extreme than O B. The p-value is the probability of failing to reject the null hypothesis when it is actually false. is one f he population mean ratin s et bands are he same O c The p value is the probability of obtaining a sample mean difference at least as extreme as this one if the population mean ratings or the two brands are the same. d. Construct a 90% confidence interval estimate of the difference in the mean ratings between the two brands. Recall thatụD-μι-u2' where μ1 is the mean rating for brand A and H2 is the mean rating for brand B. The 90% confidence interval estimate is LSpD s ». (Type integers or decimals. Round to two decimal places as needed.) i Data Table Expert Brand A Brand B C.C S.E E.G 25 25 27 25 19 24 С.М C.N G.N R.Μ 19 26 26 24 27 25 25 P.V. 24 Print Done

Answer 1

EXCEL (Mega Stat) output: Hypothesis Test: Paired Observations 0.000 hypothesized value 22.889 mean Brand A 24.222 mean Brand B 1.333 mean difference (Brand A Brand B) 1.225 std. dev 0.408 std. error 8 df 3.27 t 0114 p-value (two-tailed) -2092 confidence interval 90% lower -0574 confidence interval 90% upper 0.759 margin of error The test statistic isr-3.27

The critical values are -1.86,1.86 Since the test statistic less than the critical value(s), reject Ho. There is sufficient evidence to conclude that the mean ratings are different between the two brands *13 B. It must be assumed that the distribution of the differneces between the measurements is 3 appriximately nomal. The test statistic gives a p-value of 0.011 C. The p-value is the probability of obtaining a sample mean difference at least as extreme as this one if the population mean ratings for the two brands are the same.

(d) The 90% confidence interval estamte is-2.09 μ, s-057