Stats Solutions

Solution: Nine experts rated four brands of Colombian coffee in a taste-testing experiment. A rating on a 7-point scale (1 = extremely unpleasing, 7 =

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 in file COFFEE give the ratings for four brands of coffee.

  1. 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 H 0 .
    		\[{{\mu }_{1}}={{\mu }_{2}}={{\mu }_{3}}\]
    2. State H 1 . 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 H 0 and why. Reject Ho (because p < 0.05)
    7. State the decision in terms of the problem. Not all three population means are equal
  2. If appropriate, determine which brands differ.
  3. 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 H 0 .
\[\sigma _{1}^{2}=\sigma _{2}^{2}=\sigma _{3}^{2}\]
2. State H 1 . 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 H 0 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.

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