Answered: d. Construct a 95% confidence interval…

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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Statistic Problem: Question d) please.

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. Click the icon to view the data table. a. At the 0.05 level of significance, is there evidence of a difference in the mean ratings between the two brands? Let u, be the mean rating for brand A and µ, be the mean rating for brand B. Determine the null and alternative hypotheses for this test. A. Ho: HD #0 (where Hp = H1 H2) H1: HD = 0 B. Ho: HD = 0 (where Hp = H1 - H2) H1: HD #0 D. Ho: Hp 20 (where Hp = H1 - H2) C. Ho: HD S0 (where µp = H1 - H2) H1: HD > 0 H1: HD <0 The test statistic is tsTAT Data Table = - 3.25 . (Type an integer or a decimal. Round to two decimal places as needed.) The critical value(s) is(are) - 2.31,2.31. (Type integers or decimals. Round to two decimal places as needed. Use a comma to separate answers as needed.) Expert C.C. Brand A Brand B Since the test statistic does not fall between the critical value(s), reject Ho. There is sufficient evidence to conclude that the mean ratings are different between the two brands. 24 26 S.E. 23 23 E.G 17 19 b. What assumption is necessary about the population distribution in order to perform this test? B.I. С.М. 22 25 22 25 A. It must be assumed that the distribution of the differences between the measurements is skewed. C.N. 25 26 G.N. 26 25 B. It must be assumed that the distribution of the differences between the measurements is approximately normal. R.M. 24 25 C. It must be assumed that the distribution of the differences between the measurements is approximately uniform. P.V. 23 25 c. Determine the p-value in (a) and interpret its meaning. Print Done The test statistic gives a p-value of 0.012. (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 failing to reject the null hypothesis when it is actually false. B. 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. 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. Construct a 95% confidence interval estimate of the difference in the mean ratings between the two brands. Recall that u, = µ, - µ2, where u, is the mean rating for brand A and u, is the mean rating for brand B. The 95% confidence interval estimate is SHDS (Type integers or decimals. Round to two decimal places as needed.)

X Try again.
Both of your answers are incorrect. Use technology to find a confidence interval
estimate for the mean difference. The formula for the confidence interval is shown
below, where o is the population mean difference, D is the sample mean
difference, Sp is the sample standard deviation of the difference, n is the number
of pairs of data, and t,12 is the critical value of the t distribution with an area of
a /2 in the upper tail and n - 1 degrees of freedom.
SD
SD
SHDSD+ta/2-
D-ta/2"

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