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. E Click the icon to view the data table. Expert С.С. Brand A Brand B a. At the 0.05 level of significance, is there evidence of a difference in the mean ratings between the two brands? 24 26 Let u, be the mean rating for brand A and uz be the mean rating for brand B. Determine the null and alternative hypotheses for this test. S.E. 23 23 E.G B.I. 17 19 O A. Ho: Ho #0 (where Ho "P -P2) H: HD =0 O B. Ho: Ho =0 (where Ho = , -P2) H,: Ho #0 22 25 OC. Ho: Ho s0 (where Ho "H1 -P2) С.М. 22 25 O D. Ho: Ho 20 (where Ho "H4 - P2) H: Hp <0 H: Ho >0 C.N. 25 26 G.N. 26 25 The test statistic is tSTAT = R.M. 24 25 (Type an integer or a decimal. Round to two decimal places as needed.) P.V. 23 25 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.) does not fall between reject sufficient Since the test statistic or the critical value(s), or Ho. There is or evidence to conclude that the mean ratings are different between the two brands. falls between do not reject insufficient b. What assumption is necessary about the population distribution in order to perform this test? A. It must be assumed that the distribution of the differences between the measurements is approximately uniform. B. It must be assumed that the distribution of the differences between the measurements is approximately normal. 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 the probability of obtaining a sample mean difference less extreme than this one if the population mean ratings for the two brands are the same. B. 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. C. The p-value is the probability of failing to reject the null hypothesis when it is actually false.

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. E Click the icon to view the data table. Expert С.С. Brand A Brand B a. At the 0.05 level of significance, is there evidence of a difference in the mean ratings between the two brands? 24 26 Let u, be the mean rating for brand A and uz be the mean rating for brand B. Determine the null and alternative hypotheses for this test. S.E. 23 23 E.G B.I. 17 19 O A. Ho: Ho #0 (where Ho "P -P2) H: HD =0 O B. Ho: Ho =0 (where Ho = , -P2) H,: Ho #0 22 25 OC. Ho: Ho s0 (where Ho "H1 -P2) С.М. 22 25 O D. Ho: Ho 20 (where Ho "H4 - P2) H: Hp <0 H: Ho >0 C.N. 25 26 G.N. 26 25 The test statistic is tSTAT = R.M. 24 25 (Type an integer or a decimal. Round to two decimal places as needed.) P.V. 23 25 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.) does not fall between reject sufficient Since the test statistic or the critical value(s), or Ho. There is or evidence to conclude that the mean ratings are different between the two brands. falls between do not reject insufficient b. What assumption is necessary about the population distribution in order to perform this test? A. It must be assumed that the distribution of the differences between the measurements is approximately uniform. B. It must be assumed that the distribution of the differences between the measurements is approximately normal. 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 the probability of obtaining a sample mean difference less extreme than this one if the population mean ratings for the two brands are the same. B. 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. C. The p-value is the probability of failing to reject the null hypothesis when it is actually false.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Transcribed Image Text: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. E Click the icon to view the data table. Expert Brand A Brand B a. At the 0.05 level of significance, is there evidence of a difference in the mean ratings between the two brands? C.C. 24 26 Let u, 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. S.E. 23 23 E.G 17 19 O A. Ho: Hp #0 (where Hp = H1 - 42) H1: Ho =0 O B. Ho: Ho = 0 (where Hp = H1 - 42) H1: HD *0 В. 22 25 OC. Ho: Ho S0 (where Hp = H1 - 42) O D. Ho: Ho 20 (where Hp =H1 - H2) С.М. 22 25 H1: Ho >0 H4: Hp <0 C.N. 25 26 G.N. 26 25 The test statistic is tSTAT = R.M. 24 25 (Type an integer or a decimal. Round to two decimal places as needed.) P.V. 23 25 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.) reject or do not reject does not fall between sufficient Since the test statistic the critical value(s), Họ. There is evidence to conclude that the mean ratings are different between the two brands. or or falls between insufficient b. What assumption is necessary about the population distribution in order to perform this test? A. It must be assumed that the distribution of the differences between the measurements is approximately uniform. B. It must be assumed that the distribution of the differences between the measurements is approximately normal. 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 the probability of obtaining a sample mean difference less extreme than this one if the population mean ratings for the two brands are the same. B. 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. C. The p-value is the probability of failing to reject the null hypothesis when it is actually false. d. Construct a 99% confidence interval estimate of the difference in the mean ratings between the two brands. Recall that HD = H1 - 42, where uj is the mean rating for brand A and µ2 is the mean rating for brand B. The 99% confidence interval estimate is_ SHDS (Type integers or decimals. Round to two decimal places as needed.)

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