Quiz 11: Analysis of Variance

Instruction 11-10 The marketing manager of a company producing a new cereal aimed for children wants to examine the effect of the colour and shape of the box's logo on the approval rating of the cereal.He combined four colours and three shapes to produce a total of 12 designs.Each logo was presented to two different groups (a total of 24 groups)and the approval rating for each was recorded and is shown below.The manager analysed these data using the α = 0.05 level of significance for all inferences. $\begin{array}{l}\text { COLOURS }\\\begin{array} { | r | | c | c | c | c | } \hline \text { SHAPES } & \text { Red } & \text { Green } & \text { Blue } & \text { Yellow } \\\hline \hline \text { Circle } & 54 & 67 & 36 & 45 \\\hline & 44 & 61 & 44 & 41 \\\hline \text { Square } & 34 & 56 & 36 & 21 \\\hline & 36 & 58 & 30 & 25 \\\hline \text { Diamond } & 46 & 60 & 34 & 31 \\\hline & 48 & 60 & 38 & 33 \\\hline\end{array}\end{array}$ $\begin{array}{l}\text { Analysis of Variance }\\\begin{array} { l r r r r c } \hline \text { Source } & d f & { \text { SS } } & { \text { MS } } & { F } & p \\\hline \text { Colours } & 3 & 2711.17 & 903.72 & 72.30 & 0.000 \\\text { Shapes } & 2 & 579.00 & 289.50 & 23.16 & 0.000 \\\text { Interaction } & 6 & 150.33 & 25.06 & 2.00 & 0.144 \\\text { Error } & 12 & 150.00 & 12.50 & & \\\text { Total } & 23 & 3590.50 & & & \\\hline\end{array}\end{array}$ -Referring to Instruction 11-10,the value of the statistic used to test for an interaction is ________.