SCENARIO 11-9
the Marketing Manager of a Company Producing a New

SCENARIO 11-9
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 α = 0.05 level of significance for all inferences. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text {COLORS}$
$\begin{array}{r||cccc}\text { SHAPES } & \text { Red } & \text { Green } & \text { Blue } & \text { Yellow } \\\hline \text { Circle } & 54 & 67 & 36 & 45 \\& 44 & 61 & 44 & 41 \\\text { Square } & 34 & 56 & 36 & 21 \\& 36 & 58 & 30 & 25 \\\text { Diamond } & 46 & 60 & 34 & 31 \\& 48 & 60 & 38 & 33\end{array}$


$\text {Analysis of Variance}$
$\begin{array}{lrrrrc}\text { Source } & d f & {\text { SS }} & {\text { MS }} & {F} & p \\\hline \text { Colors } & 3 & 2711.17 & 903.72 & 72.30 & 0.000 \\\text { Shapes } & 2 & 579.00 & 289.50 & 23.16 & 0.000 \\\text { Interaction 6 } & 150.33 & 25.06 & 2.00 & 0.144 \\\text { Error } & 12 & 150.00 & 12.50 & & \\\text { Total } & 23 & 3590.50 & & &\end{array}$

-Referring to Scenario 11-9, the critical value of the test for significant differences between
colors is ________.