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.

Answer 1

a)

Hypothesis:

OR Difference in the mean rating between the two brands.

Where,

= Brand A - Brand B

Computational Table:

BRAND
EXPERT	A	B	Difference (D)	D2
C.C.	24	26	-2	4
S.E.	27	27	0	0
E.G.	19	22	-3	9
B.L.	24	27	-3	9
C.M.	22	25	-3	9
C.N.	26	27	-1	1
G.N.	27	26	1	1
R.M.	25	27	-2	4
P.V.	22	23	-1	1
Total			-14	38

Calculation:

Test statistic:

Degrees of Freedom = n-1 = 9-1 = 8

Critical value:

...............From t table

Conclusion:

| Test statistic | > Critical value, i.e. 3.28 > 2.3060, That is Reject Ho at 5% level of significance.

Therefore, there is difference in the mean rating between the two brands.

b) The assumption necessary about the population distribution to perform this test is that the distribution should be normally distributed.

C)

P-value: 0.0112 ...............From t table

d)

Critical value:

...............From t table

95% Confidence Interval:

Here, = 0, Does not lies in this Confidence Interval, So We conclude that Reject Ho.

Therefore, there is difference in the mean ratings between the two brands.