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.

Analysis of Variance

Requirements:

a) What is the sum of squares due to interaction?

b) How many degrees of freedom does 'Error' have?

c) How many treatment combinations are there in the experiment?

d) Perform the F-test on 'Shapes.' Is the factor 'Shapes' significant?

e) Perform the F-test on 'Interaction.' Is the factor 'Interaction' significant?

SHAPES Circle Square Diamond COLORS Red 54 44 34 36 46 48 Green 67 61 56 58 60 60 Blue 36 44 36 30 34 38 Yellow 45 41 21 25 31 33 Source Colors df 3 Shapes 2 Interaction 6 Error Total SS MS 2711.17 903.72 579.00 150.00 3590.50 F 72.30 Fcr