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

question 139

True/False

TABLE 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.
$\begin{array}{l}\text { \quad\quad\quad\quad\quad\quad\quad\quad COLORS }\\\begin{array}{lllll}\text { SHAPES } & \text { Red } & \text { Green } & \text { Blue } & \text { Yellow } \\\hline \text { Circle } & 54 & 67 & 36 & 45 \\& 44 & 61 & 44 & 41 \\\text { Square } & 34 & 56 & 36 & 21 \\& 36 & 58 & 30 & 25 \\\text { Diamond } & 46 & 60 & 34 & 31 \\& 48 & 60 & 38 & 33\end{array}\end{array}$

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


-Referring to Table 11-9, based on the results of the hypothesis test, it appears that there is a significant interaction.

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Definitions:

Lewis Structure

A graphical representation of the distribution of electrons in molecules, showing how the atoms are bonded together and the pairs of electrons not involved in bonding.

Boron Trifluoride

A pungent, toxic gas that forms white fumes in moist air and is used in various chemical reactions as a catalyst.

Octet

The state of an atom achieved when it has a full valence shell of eight electrons, making it stable and less reactive.

Methyl Chloride

A colorless, flammable gas used as a refrigerant, solvent, and in organic synthesis.