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A management consultant wants to determine whether the age and gender of a restaurant’s wait staff...

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 is produced.

ANOVA
Source of Variation SS df MS F p-value
Sample 0.04278 1 0.04278 16.595 0.000
Columns 0.01793 2 0.00897 3.479 0.038
Interaction 0.00561 2 0.00281 1.089 0.344
Within 0.1392 54 0.00258
Total 0.20552 59

a. Can you conclude that there is interaction between age and gender at the 1% significance level?


  • Yes, since the p-value associated with interaction is less than significance level.

  • Yes, since the p-value associated with interaction is greater than significance level.

  • No, since the p-value associated with interaction is less than significance level.

  • No, since the p-value associated with interaction is greater than significance level.


b-1. Are you able to conduct tests based on the main effects?


  • Yes, since the interaction between the two factors is not significant.

  • Yes, since the interaction between the two factors is significant.

  • No, the interaction between the two factors is not significant.

  • No, the interaction between the two factors is significant.


b-2. If yes, conduct these tests at the 1% significance level. (You may select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer. Any boxes left with a question mark will be automatically graded as incorrect.)


  • We can conclude the mean tips differ by age.unchecked
  • We cannot conclude the mean tips differ by age.unanswered
  • We can conclude the mean tips differ by gender.unanswered
  • We cannot conclude the mean tips differ by gender.
Math   Statistics-And-Probability   
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