Question A:

The marketing manager of a company producing a new cereal aimed for children wants to examine the effect of thecolorandshapeof the box's logo on the approval rating of the cereal. He combined 3 colors and 2 shapes to produce a total of 6 designs. Each logo was presented to 3 different groups (a total of 18 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, and a partially completed 2-way ANOVA table is also provided below.

COLORSRedGreenBlue546736Circle446140SHAPES496444345636Square365733355830

Analysis of Variance

SourcedfSSMSF

Shapes392.00

Colors1897.00

Interaction49.00

Error

Total2460.00

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1) What is the sum of squares due toError?(10 points)

2) What are the degrees of freedom for the factorColorsand theError? (10 points)

3) How many treatment combinations are there in the experiment and how many replicates for each treatment combination? (10 points)

4) Perform the F- test on 'Shapes'. Is the factor 'Shapes' significant ( = 0.05)? Please show all the relevant calculations. (10 points)

5) Perform the F- test on 'Interaction'. Is'Interaction' significant (=0.05)? Please show all the relevant calculations.(10 points)