Solutions Statistics

Nine experts rated four brands of Colombian coffee in a taste-testing experiment. A rating on a 7-po

Question: Nine experts rated four 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 the four characteristics: taste, aroma, richness, and acidity. The data for COFFEE BELOW gives the ratings for four brands of coffee.

	A	B	C	D
1	24	26	25	22
2	27	27	26	24
3	19	22	20	16
4	24	27	25	23
5	22	25	22	21
6	26	27	24	24
7	27	26	22	23
8	25	27	24	21
9	22	23	20	19

a. At the .05 level of significance, is there evidence of a difference in the mean ratings for the four brands of coffee?

Complete the following:
1. State H₀.	\[{{\mu }_{1}}={{\mu }_{2}}={{\mu }_{3}}={{\mu }_{4}}\]
2. State H₁.	Not all the means are equal
3. State the value of α.	0.05
4. State the value of the test statistic.	4.79
5. State the p-value.	0.007223
6. State the decision in terms of H₀ and why.	Reject Ho (because p < 0.05)
7. State the decision in terms of the problem.	Not all three population means are equal

b. If appropriate, determine which brands differ.

Only B and D.

c. One assumption of ANOVA is that the variances of the populations are equal. At the .05 level of significance, is there evidence of a difference in the variation in the ratings of the four brands of coffee?

Complete the following:
1. State H₀.	\[\sigma _{1}^{2}=\sigma _{2}^{2}=\sigma _{3}^{2}=\sigma _{4}^{2}\]
2. State H₁.	Not all the variances are equal
3. State the value of α.	0.05
4. State the value of the test statistic.	0.288
5. State the p-value.	0.834
6. State the decision in terms of H₀ and why.	Fail to reject Ho (p > 0.05)
7. State the decision in terms of the problem.	There is not enough evidence to claim that the variances are not all equal.