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 oftour characteristics: taste, aroma, richness, and acidity. The accompanying data table contains the ratings accumulated over all four characteristics. Complete parts (a) through (d) below. 3 Click the icon to view the data table. a. At the 0.10 level of signicance, is there evidence of a difference in the mean ratings between the two brands? Let M be the mean rating for brand A and p2 be the mean rating for brand B. Determine the null and alternative hypotheses for this test. O A- Ho: PD 20(where PD =P1 'l'z) O 5- Ho: PDS\" (where Po =l'1 'Pz) H1:pD0 O 5- Ho: PD #0(where Po =l'1'l'2) O D- Ho: PD=(Whefe l'o =l'1'l'2) H1:|,|D=O H1:pDU The test statistic = (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 V the critical value(s), V H0. There is V 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? 0 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. 0 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. 0 A. The p-value is the probability of obtaining a sample mean difference at least as extreme as this one it the population mean ratings for the two brands are the same. 0 B- The pvalue is the probability of obtaining a sample mean difference less extreme than this one if the population mean ratings tor the two brands are the same. 0 C. The p-value is the probability of failing to reject the null hypothesis when it is actually false. \f