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 differences in the mean charges for doctors among the four primary specialty areas?
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 differences in the mean charges for doctors among the four primary specialty areas?
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

The numerator degrees of freedom is equal to the number of groups minus 1, and the denominator degrees of freedom is equal to the total sample size minus the number of groups. In this case, there are four groups, so the numerator degrees of freedom is 3. The total sample size is 160, so the denominator degrees of freedom is 152.

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