Data Was Collected from CEOs of Companies Within Both the Low-Tech

Data was collected from CEOs of companies within both the low-tech industry and the consumer products industry. The following printout compares the mean return-to-pay ratios between CEOs in the low-tech industry with CEOs in the consumer products industry. HYPOTHESIS: MEAN X = MEAN Y SAMPLES SELECTED FROM RETURN
$\begin{array} { l l l } \text { industry } 1 & \text { (low tech) } & \text { (NUMBER } = 15 \text { ) } \\ \text { industry } 3 & \text { (consumer products) } & \text { (NUMBER } = 15 \text { ) } \end{array}$
$$\begin{array} { l } X = \text { industry1 } \\Y = \text { industry } 3\end{array}$$
$$\begin{array}{l}\text { SAMPLE MEAN OF X \( =157.286 \) }\\\text { SAMPLE VARIANCE OF \( X=1563.45 \) }\\\text { SAMPLE SIZE OF X \( =14 \) }\\\text { SAMPLE MEAN OF \( Y=217.583 \) }\\\text { SAMPLE VARIANCE OF \( Y=1601.54 \) }\\\text { SAMPLE SIZE OF Y \( =12 \) }\\\\\text { MEAN X - MEAN } Y=-60.2976 \\t=-4.23468 \\\mathrm{P}-\mathrm{VALUE}=\quad 0.000290753 \\\text { P-VALUE } / 2=0.000145377 \\\text { SD. } \mathrm{ERROR}=14.239 \\\end{array}$$ Using the printout, which of the following assumptions is not necessary for the test to be valid?

A) The population means are equal.
B) Both populations have approximately normal distributions.
C) The population variances are equal.
D) The samples were randomly and independently selected.