# Solved > SCENARIO 11-12 The marketing manager of a company:1754097 …

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 ? = 0.05 level of significance for all inferences.

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 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

199.Referring to Scenario 11-12, the mean square for the factor color is ________.

200.Referring to Scenario 11-12, the mean square for the factor shape is ________.

201.Referring to Scenario 11-12, the mean square for the interaction of color and shape is ________.

202.-12, the mean square for error is ________.

203.Referring to Scenario 11-12, the critical value of the test for significant differences between colors is ________.

204.Referring to Scenario 11-12, the value of the statistic used to test for significant differences between colors is ________.

205.True or False:  Referring to Scenario 11-12, 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.

206.Referring to Scenario 11-12, the critical value in the test for significant differences between shapes is ________.

207.Referring to Scenario 11-12, the value of the statistic used to test for significant differences between shapes is ________.

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