Exhibit 7-12: an Investigator Is Studying the Effect of Two

Exhibit 7-12: An investigator is studying the effect of two physical fitness programs (M and N) on boys and girls.The experimental design is a 2 * 2 factorial design.The results of the investigation might be one of the following four conditions.
$\begin{array}{l}\begin{array}{lll}&\text { Condition (a) }\\&\mathrm{M} & \mathrm{N} \\\text { Boys }&\mathrm{X}=50 & \mathrm{X}=60 \\\text { Girls }&\mathrm{X}=60 & \mathrm{X}=50\end{array}\begin{array}{lll}&\text { Condition (b) }\\&\mathrm{M} & \mathrm{N} \\\text { Boys }&\mathrm{X}=50 & \mathrm{X}=60 \\\text { Girls }&\mathrm{X}=40 & \mathrm{X}=60\end{array}\end{array}$

$\begin{array}{l}\begin{array}{lll}&\text { Condition (c) }\\&\mathrm{M} & \mathrm{N} \\\text { Boys }&\mathrm{X}=50 & \mathrm{X}=40 \\\text { Girls }&\mathrm{Y}=60 & \mathrm{Y}=50\end{array}\begin{array}{lll}&\text { Condition (d) }\\&\mathrm{M} \quad\quad\quad\quad\quad\quad\quad\quad \mathrm{N} \\&\text { None of these condition }\\\\\end{array}\end{array}$

-What is the relationship between the standard deviation of a population and the standard deviation of means of samples randomly selected from the population?

A) The standard deviation of the distribution of sample means is larger than that of the population.
B) The standard deviation of the population is larger than that of the distribution of sample means.
C) They are equal to one another.
D) It is impossible to determine the relationship with the available data.