A management consultant wants to determine whether the age and gender of a restaurant's wait staff influence the size of the tip the customer leaves. Three age brackets (factor A in columns: young, middle-age, older) and gender (factor B in rows: male, female) are used to construct a two way ANOVA experiment with interaction. For each combination, the percentage of the total bill left as a tip for 10 wait staff is examined. The following ANOVA table with α = 0.01 is produced.

a. Can you conclude that there is interaction between age and gender at the 1% significance level?
b. Are you able to conduct tests based on the main effects? If yes, conduct these tests at the 1% significance level. If no, explain.

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Source of Variation Sample 0.04278 10.04278 16.5951 0.00015 7.129 Columns 0.01793 20.008973.47884 0.03792 5.021 Interaction 0.00561 2 0.002811.08872 0.34392 5.021 Within 0.1392 54 0.00258 SS df MS F p-value F crit Total 0.20552 59