Homework SourseThe marketing manager of a company producing a new cereal ai
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 ? = 0.05 level of significance for all inferences.
COLORS
COLORS
SHAPES
Red
Green
Blue
Yellow
Circle
54
67
36
45
44
61
44
41
Square
34
56
36
21
36
58
30
25
Diamond
46
60
34
31
48
60
38
33
Analysis of Variance
Source df SS MS F p
Colors 3 2711.17 903.72 72.30 0.000
Shapes 2 579.00 289.50 23.16 0.000
Interaction 6 150.33 25.06 2.00 0.144
Error 12 150.00 12.50
Total 23 3590.50
a) What is the critical value of the test for significant differences between colors? Explain how you obtain your answer.
b) What is the value of the statistic used to test for significant differences between colors? Explain how you obtain your answer.
c) True or False:
| COLORS | ||||
| SHAPES | Red | Green | Blue | Yellow |
| Circle | 54 | 67 | 36 | 45 |
| 44 | 61 | 44 | 41 | |
| Square | 34 | 56 | 36 | 21 |
| 36 | 58 | 30 | 25 | |
| Diamond | 46 | 60 | 34 | 31 |
| 48 | 60 | 38 | 33 |
Solution
Analysis of Variance
Source df SS MS F p
Colors 3 2711.17 903.72 72.30 0.000
Shapes 2 579.00 289.50 23.16 0.000
Interaction 6 150.33 25.06 2.00 0.144
Error 12 150.00 12.50
Total 23 3590.50
Degrees of freedom for colors = 3, 12
Upper tail F distribution with DF 3,12 at 5% level of significance = 3.49
Test value F=903.72/12.5=72.3
