Question

2. Nine experts rated two brands of Colombian 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 following data contain the ratings accumulated over all four characteristics:

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

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

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

3. c) Construct and interpret a 95% confidence interval estimate of the difference in the mean ratings between the two brands.

Answer 1

using minitab>stat>basic stat>two sample t

we have

Two-Sample T-Test and CI: A, B

Two-sample T for A vs B

N Mean StDev SE Mean
A 9 24.00 2.65 0.88
B 9 25.56 1.88 0.63

Difference = μ (A) - μ (B)
Estimate for difference: -1.56
95% CI for difference: (-3.85, 0.74)
T-Test of difference = 0 (vs ≠): T-Value = -1.44 P-Value = 0.170 DF = 16
Both use Pooled StDev = 2.2943

a )  At the 0.05 level of significance,since p value of t = 0.170>0.05 so we cannot conclude that there is  a difference in the mean ratings between the two brands.

Ans b ) the assumptions are, samples should be independent

population from which samples are drawn should be normal.

and samples drom the bopulation should be drawn randomly

Ans c ) 95% confidence interval is (-3.85, 0.74) .we are 95% confident that the difference in the mean ratings between the two brands lies in between (-3.85, 0.74)