The table gives data for a 2 2 factorial experiment, with four replications per treatment. a. The accompanying graph was generated by MINITAB. Verify

The table gives data for a 2 × 2 factorial experiment, with four replications per treatment.

a. The accompanying graph was generated by MINITAB. Verify that the four points that connect the two lines are the means of the four observations within each factor level combination. What does the graph tell you about the interaction between factors A and B?
MINITAB interaction plot for Exercise 11.49

b. Use the MINITAB output to test for a significant interaction between A and B. Does this confirm your conclusions in part a?
MINITAB output for Exercise 11.49

c. Considering your results in part b, how can you explain the fact that neither of the main effects is significant?
d. If a significant interaction is found, is it necessary to test for significant main effect differences? Explain.
e. Write a short paragraph summarizing the results of this experiment.

Levels of Factor A Levels of Factor B 1 2.1, 2.7, 3.7, 3.2, 2.4, 2.5 3.0, 3.5 3.1, 3.6, 2.9, 2.7 3.4, 3.9 2.2, 2.5 Interaction Plot (data means) for Response 3 50 3.25 E 3.00 250 Factor B Two-way ANOVA: Response versus Factor A, Factor B DF Source Factor A Factor B Interaction 1 Error Total MS 0.0000 0.0900 3.4225 1.0850 4.5975 0.00000 0.09000 3.42250 37.85 0.000 0.09042 0.00 1.000 1.00 0.338 15