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

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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 COLORS\text {COLORS}
 SHAPES  Red  Green  Blue  Yellow  Circle 5467364544614441 Square 3456362136583025 Diamond 4660343148603833\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}


Analysis of Variance\text {Analysis of Variance}
 Source df SS  MS Fp Colors 32711.17903.7272.300.000 Shapes 2579.00289.5023.160.000 Interaction 6 150.3325.062.000.144 Error 12150.0012.50 Total 233590.50\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, based on the results of the hypothesis test, it appears
that there is a significant effect associated with the shape of the logo.


Definitions:

Preceding August

Indicates a time period or events that occurred before the month of August.

Payment Stream

A series of payments made or received over time, usually as part of a financial agreement such as a mortgage or annuity.

Economically Equivalent

Having the same financial value when considering various factors like time, risk, and opportunity cost.

Invested Rate

The rate of return on an investment, reflecting the annual income earned on the investment expressed as a percentage of its original cost.

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