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

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: ?Based on the results of the hypothesis test, it appears that there is a significant effect on the approval rating associated with the color of the logo.? Explain how you obtain your answer.

d) What is the critical value in the test for a significant interaction? Explain how you obtain your answer.

e) What is the value of the statistic used to test for an interaction? Explain how you obtain your answer.

f) True or False: ?Based on the results of the hypothesis test, it appears that there is a significant interaction.? Explain how you obtain your answer.

SHAPES Red Circle 54 44 Square 34 36 Diamond 46 48 COLORS Green 67 61 56 58 60 60 Blue 36 44 36 30 34 38 Yellow 45 41 21 25 31 33 Analysis of Variance Source df Colors Shapes Interaction Error Total SS 3 2711.17 2 579.00 6 MS F 903.72 72.30 289.50 23.16 2.00 150.33 25.06 12.50 12 150.00 23 3590.50 0.000 0.000 0.144