a. Calculate the means

b. The MINITAB ANOVA printout is shown here. Test for interaction at the α = 0.05 level of significance.

Analysis of variance for response.

**Solution: **(a) We get

Level 1: _{}

Level 2: _{}

Level 3: _{}

A: _{}

B: _{}

(b) We need to test for the significance of the interaction AB at the 0.05 level of significance. The F-statistics is equal to 1.48678, as we can see in the table above. The critical F value, at the 0.05 significance level, and 2, 6 degrees of freedom is equal to 5.1433. *This means that we fail to reject the null hypothesis of no interaction between the variables.*

c. Do the results warrant tests of the two factor mean effects?

**Solution: **Since from part b) we can assume that there's no interaction between the factors A and B, now we test for the significance of the main effects.

- Factor A: The F-statistics is equal to 0.11851. The critical F-value for
_{}and 1, 6 degrees of freedom is 5.9874. This means that we fail to reject the null hypothesis of lack of significance of factor A

- Factor B: The F-statistics is equal to 0.55391. The critical F-value for
_{}and 2, 6 degrees of freedom is 5.1433. This means that we fail to reject the null hypothesis of lack of significance of factor B

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