SCENARIO 11-12
The marketing manager of a company producing a new cereal aimed for children wants to examine the effect of the color and shape of the box's logo on the approval rating of the cereal. He combined 4 colors and 3 shapes to produce a total of 12 designs. Each logo was presented to 2 different groups (a total of 24 groups) and the approval rating for each was recorded and is shown below. The manager analyzed these data using the α = 0.05 level of significance for all inferences.

-Referring to Scenario 11-11,what degrees of freedom should be used to determine the critical value of the F ratio against which to test for interaction between the two factors?
A)numerator df = 1,denominator df = 159
B)numerator df = 3,denominator df = 159
C)numerator df = 1,denominator df = 152
D)numerator df = 3,denominator df = 152

Question

SCENARIO 11-12
The marketing manager of a company producing a new cereal aimed for children wants to examine the effect of the color and shape of the box's logo on the approval rating of the cereal. He combined 4 colors and 3 shapes to produce a total of 12 designs. Each logo was presented to 2 different groups (a total of 24 groups) and the approval rating for each was recorded and is shown below. The manager analyzed these data using the α = 0.05 level of significance for all inferences.

-Referring to Scenario 11-11,what degrees of freedom should be used to determine the critical value of the F ratio against which to test for interaction between the two factors?
A)numerator df = 1,denominator df = 159 
B)numerator df = 3,denominator df = 159 
C)numerator df = 1,denominator df = 152 
D)numerator df = 3,denominator df = 152

Quizplus · Accepted Answer

To determine the critical value of the F ratio for interaction, we need to use the degrees of freedom for the interaction term, which is the product of the degrees of freedom for the two main effects (dfA and dfB). In this case, dfA = 3 and dfB = 4, so the interaction df = 3 x 4 = 12. Therefore, the numerator df is 3 (the number of main effects) and the denominator df is 152 (the error df). The critical value at α = 0.05 for df = 3, 152 is 3.00, which is the value we would compare to the calculated F ratio to determine if there is significant interaction.

SCENARIO 11-12 The Marketing Manager of a Company Producing a New Cereal