The Probability Distribution Shown Below Describes a Population of Measurements $\begin{array}{c|ccc}\mathrm{x} & 0 & 2 & 4 \\\hline \mathrm{p}(\mathrm{x}) & 1 / 3 & 1 / 3 & 1 / 3\end{array}$

question 8

Multiple Choice

The probability distribution shown below describes a population of measurements.
$\begin{array}{c|ccc}\mathrm{x} & 0 & 2 & 4 \\\hline \mathrm{p}(\mathrm{x}) & 1 / 3 & 1 / 3 & 1 / 3\end{array}$
Suppose that we took repeated random samples of $n = 2$ observations from the population described above. Which of the following would represent the sampling distribution of the sample mean?

• A)
• \(\begin{array}{c|ccccc}
• \overline{\mathrm{x}} & 0 & 1 & 2 & 3 & 4 \\
• \hline \mathrm{p}(\overline{\mathrm{x}}) & 1 / 5 & 1 / 5 & 1 / 5 & 1 / 5 & 1 / 5
• \end{array}\)
• B)
• \(\begin{array}{c|ccccc}
• \overline{\mathrm{x}} & 0 & 1 & 2 & 3 & 4 \\
• \hline \mathrm{p}(\overline{\mathrm{x}}) & 2 / 9 & 2 / 9 & 1 / 9 & 2 / 9 & 2 / 9
• \end{array}\)
• C)
• \(\begin{array}{c|ccc}
• \bar{x} & 0 & 2 & 4 \\
• \hline \mathrm{p}(\bar{x}) & 1 / 3 & 1 / 3 & 1 / 3
• \end{array}\)

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Definitions:

Factor Structure

The pattern and relationship of underlying factors identified through factor analysis that explains the variability among observed variables.

Psychological Construct

An abstract concept or category used to describe and understand psychological phenomena that are not directly observable, such as intelligence or motivation.

Comparative Research Framework

A methodology that involves comparing two or more groups, entities, or cases, in real-life or experimental settings, to draw conclusions about their similarities or differences.

Psychological Variables

Factors that can be varied or measured in experiments or studies that reflect emotional, cognitive, and behavioral aspects of individuals.