Construct a dot plot for the CTQ. Construct dot plots to study the CTQ for the different levels of X1 and X2. Construct main effects plots and interaction plots for the following data set. Answer: The

Question

Exhibit

Options

• AThere is a significant interaction between X1 and X2 that will affect the CTQ. The interaction is seen in the crossed lines.

• A
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Explanation

Option A is correct because when interaction plots show crossed or non-parallel lines, it indicates that the effect of one factor (X1) on the CTQ depends on the level of the other factor (X2) - this is the definition of a significant interaction effect. Parallel lines in an interaction plot would indicate no interaction, but crossing lines confirm that X1 and X2 do not act independently on the response variable.

Since only one choice is presented here, there are no distractors to evaluate - this question tests whether you can correctly read and interpret interaction plots rather than distinguish between competing claims.

Memory tip: Think of the phrase "crossing lines = crossing effects" - when the lines in an interaction plot cross, the factors are "crossing" each other's influence, meaning you cannot interpret X1's effect without knowing the level of X2. Non-parallel = interaction present; parallel = no interaction.

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