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 maximum rating for any one coffee brand by one expert = 7 points times 4 characteristics = 28.) The data table at the bottom of the page contains the ratings accumulated over all four characteristics. (You can copy this data table directly into Excel, so no need to copy.) Complete parts (a) through (d) below. Part 1 a. At the 0.01 level of significance, is there evidence of a difference in the mean ratings between the two brands? b. Compute the difference of the sample means c. Compute the test statistic. (Type an integer or a decimal. Round to two decimal places to the right of the decimal point as needed.) e. Statistical conclusions by comparing the tSTAT with the critical values. Since the test statistic . . . A. falls within the range of critical values, B. does not fall within the range of critical values, C. always falls within the range of critical values, D. is irrelevant for a paired t test, then . . . A. do not reject H0 B. H0 should be re-written. C. H0 should be rejected. D. both H0 and H1 should be accepted. A. There is insufficient (not enough) statistical evidence to conclude that the mean ratings are statistically different between the two brands. B. Since both H0 and H1 are to be accepted, no decision can be made. C. After re-writing H0 , run the analysis once again. D.There is sufficient evidence to conclude that the mean ratings are statistically different between the two brands. f. 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 normal. B.It must be assumed that the distribution of the differences between the measurements is skewed. C.It must be assumed that the distribution of the differences between the measurements is approximately uniform. g.Determine the p-value. (Type an integer or a decimal. Round to three decimal places to the right of the decimal point as needed.) A.p-value = T.DIST.2T(ABS(-3.16),8) = 0.013 B.p-value = T.DIST.2T(ABS(-2.98),8) = 0.018 C.p-value = T.DIST(-2.85,8,1) = 0.011 D.p-value = T.DIST(-0.72,8,1) = h.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 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 obtaining a sample mean difference less extreme than this one if the population mean ratings for the two brands are the same. i. Construct a 99% confidence interval estimate of the difference in the mean ratings between the two brands. Recall that μD=μ1−μ2,where μ1 is the mean rating for brand A and μ2 is the mean rating for brand B. The 99% confidence interval estimate is .... (Type integers or decimals. Round to two decimal places to the right of the decimal point as needed.) A. −2.42 ≤ μD ≤ +0.19 , found using −1.111 ± CONFIDENCE.T.(0.01,1.054,8) B. −1.12 ≤ μD ≤ −1.11 , found using −1.111 ± CONFIDENCE.T.(0.99,1.054,9) C. −0.19 ≤ μD ≤ +2.30 , found using +1.054 ± CONFIDENCE.T.(0.01,1.111,9) D. −2.29 ≤ μD ≤ +0.07 , found using −1.111 ± CONFIDENCE.T.(0.01,1.054,9) Expert Initials Brand A Rating Brand B Rating C.C. 25 27 S.E. 27 27 E.G. 19 21 B.I. 22 24 C.M. 19 21 C.N. 24 25 G.N. 26 25 R.M. 22 23 P.V. 22 23

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 maximum rating for any one coffee brand by one expert = 7 points times 4 characteristics = 28.) The data table at the bottom of the page contains the ratings accumulated over all four characteristics. (You can copy this data table directly into Excel, so no need to copy.) Complete parts (a) through (d) below. Part 1 a. At the 0.01 level of significance, is there evidence of a difference in the mean ratings between the two brands? b. Compute the difference of the sample means c. Compute the test statistic. (Type an integer or a decimal. Round to two decimal places to the right of the decimal point as needed.) e. Statistical conclusions by comparing the tSTAT with the critical values. Since the test statistic . . . A. falls within the range of critical values, B. does not fall within the range of critical values, C. always falls within the range of critical values, D. is irrelevant for a paired t test, then . . . A. do not reject H0 B. H0 should be re-written. C. H0 should be rejected. D. both H0 and H1 should be accepted. A. There is insufficient (not enough) statistical evidence to conclude that the mean ratings are statistically different between the two brands. B. Since both H0 and H1 are to be accepted, no decision can be made. C. After re-writing H0 , run the analysis once again. D.There is sufficient evidence to conclude that the mean ratings are statistically different between the two brands. f. 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 normal. B.It must be assumed that the distribution of the differences between the measurements is skewed. C.It must be assumed that the distribution of the differences between the measurements is approximately uniform. g.Determine the p-value. (Type an integer or a decimal. Round to three decimal places to the right of the decimal point as needed.) A.p-value = T.DIST.2T(ABS(-3.16),8) = 0.013 B.p-value = T.DIST.2T(ABS(-2.98),8) = 0.018 C.p-value = T.DIST(-2.85,8,1) = 0.011 D.p-value = T.DIST(-0.72,8,1) = h.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 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 obtaining a sample mean difference less extreme than this one if the population mean ratings for the two brands are the same. i. Construct a 99% confidence interval estimate of the difference in the mean ratings between the two brands. Recall that μD=μ1−μ2,where μ1 is the mean rating for brand A and μ2 is the mean rating for brand B. The 99% confidence interval estimate is .... (Type integers or decimals. Round to two decimal places to the right of the decimal point as needed.) A. −2.42 ≤ μD ≤ +0.19 , found using −1.111 ± CONFIDENCE.T.(0.01,1.054,8) B. −1.12 ≤ μD ≤ −1.11 , found using −1.111 ± CONFIDENCE.T.(0.99,1.054,9) C. −0.19 ≤ μD ≤ +2.30 , found using +1.054 ± CONFIDENCE.T.(0.01,1.111,9) D. −2.29 ≤ μD ≤ +0.07 , found using −1.111 ± CONFIDENCE.T.(0.01,1.054,9) Expert Initials Brand A Rating Brand B Rating C.C. 25 27 S.E. 27 27 E.G. 19 21 B.I. 22 24 C.M. 19 21 C.N. 24 25 G.N. 26 25 R.M. 22 23 P.V. 22 23

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Part 1 a. At the 0.01 level of significance, is there evidence of a difference in the mean ratings between the two brands?

b. Compute the difference of the sample means

c. Compute the test statistic. (Type an integer or a decimal. Round to two decimal places to the right of the decimal point as needed.)

e. Statistical conclusions by comparing the tSTAT with the critical values. Since the test statistic . . .

A. falls within the range of critical values,

B. does not fall within the range of critical values,

C. always falls within the range of critical values,

D. is irrelevant for a paired t test,

then . . .

A. do not reject H0

B. H0 should be re-written.

C. H0 should be rejected.

D. both H0 and H1 should be accepted.

A. There is insufficient (not enough) statistical evidence to conclude that the mean ratings are statistically different between the two brands.

B. Since both H0 and H1 are to be accepted, no decision can be made.

C. After re-writing H0 , run the analysis once again.

D.There is sufficient evidence to conclude that the mean ratings are statistically different between the two brands.

f. 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 normal.

B.It must be assumed that the distribution of the differences between the measurements is skewed.

C.It must be assumed that the distribution of the differences between the measurements is approximately uniform.

g.Determine the p-value. (Type an integer or a decimal. Round to three decimal places to the right of the decimal point as needed.)

A.p-value = T.DIST.2T(ABS(-3.16),8) = 0.013

B.p-value = T.DIST.2T(ABS(-2.98),8) = 0.018

C.p-value = T.DIST(-2.85,8,1) = 0.011

D.p-value = T.DIST(-0.72,8,1) =

h.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 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 obtaining a sample mean difference less extreme than this one if the population mean ratings for the two brands are the same.

i. Construct a 99% confidence interval estimate of the difference in the mean ratings between the two brands. Recall that μD=μ1−μ2,where μ1 is the mean rating for brand A and μ2
is the mean rating for brand B.

The 99% confidence interval estimate is ....

(Type integers or decimals. Round to two decimal places to the right of the decimal point as needed.)

−2.42 ≤ μD ≤ +0.19

, found using

−1.111 ±

CONFIDENCE.T.(0.01,1.054,8)

−1.12 ≤ μD ≤ −1.11

, found using

−1.111 ±

CONFIDENCE.T.(0.99,1.054,9)

−0.19 ≤ μD ≤ +2.30

, found using