Question

Nine experts rated two brands of Colombian coffee in a taste-testing experiment. A rating on a 7-point scale ( 1=1= 1 equals extremely unpleasing, 7=7= 7 equals extremely pleasing) is given for each of four characteristics: taste, aroma, richness, and acidity. The following data stored in Coffee contain the ratings accumulated over all four characteristics:

	BRAND
EXPERT	A	B
C.C.	24	26
S.E.	27	27
E.G.	19	22
B.L.	24	27
C.M.	22	25
C.N.	26	27
G.N.	27	26
R.M.	25	27
P.V.	22	23

• a. At the 0.05 level of significance, is there evidence of a difference in the mean ratings between the two brands?

• b. What assumption is necessary about the population distribution in order to perform this test?

• c. Determine the p-value in (a) and interpret its meaning.

• d. Construct and interpret a 95% confidence interval estimate of the difference in the mean ratings between the two brands.

SHOW EXCEL FUNCTIONS USED TO ANSWER.

Answer 1

a) Let us denote

d = Brand A rating - Brand B rating

To test whether there is a difference in the mean ratings between the two brands, i.e. to test

against

Now,

The value of test statistic t = -3.27715

and P-value = 0.1112

Since P-value < 0.05, so we reject H₀ at 0.05 level of significance and we can conclude that there is evidence of a difference in the mean ratings between the two brands.

b) Assumptions - Brand A ratings and Brand B ratings follow normal distributions.

c) P-value = 0.0112

Interpretation of p-value - The probability that value of test statistic will be as extreme as observed value of test statistic when null hypothesis is true equals the p-value.

d)