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Chapter 12: Q8BSC (page 566)

Pancake Experiment Listed below are ratings of pancakes made by experts (based on data from Minitab). Different pancakes were made with and without a supplement and with different amounts of whey. The results from two-way analysis of variance are shown. Use the displayed results and a 0.05 significance level. What do you conclude?

Whey


0%

10%

20%

30%

No Supplement

4.4

4.5

4.3

4.6

4.5

4.8

4.5

4.8

4.8

4.6

4.7

5.1

Supplement

3.3

3.2

3.1

3.8

3.7

3.6

5.0

5.3

4.8

5.4

5.6

5.3

Short Answer

Expert verified

It can be concluded that there is a significant interaction effect between the presence of a supplement and the amount of whey on the ratings of the pancakes.

Step by step solution

01

Given information

The ANOVA table is provided for the data given on the ratings of pancakes under two factors: the presence of a supplement and the amount of whey.

02

Set up the statistical hypothesis for two-way analysis of variance

For the given two-way analysis of variance, the following hypotheses are set up in the case of interaction effect:

Null Hypothesis: There is no interaction between the factors: the presence of a supplement and the amount of whey.

Alternative Hypothesis: There is an interaction between the factors: the presence of a supplement and the amount of whey.

03

Interpret the results

The ANOVA output shows that the p-value corresponding to the F statistic value (under interaction) of 41.38 is equal to 0.000.

As the p-value is less than 0.05, the null hypothesis is rejected.

It can be concluded that there is an interaction between the factors: the presence of a supplement and the amount of whey.

Since the interaction effect is significant, the individual effects of the presence of a supplement and the amount of whey need not be tested.

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