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 38

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

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Definitions:

Cognitive Dissonance Theory

A theory suggesting that inconsistency among beliefs, attitudes, and behaviors causes discomfort, leading individuals to adjust them to reduce the discomfort.

Situational Attributions

The process of attributing a person's behavior to external or environmental factors instead of to internal personality traits.

Fundamental Attribution Error

A common bias in social psychology where individuals attribute others' actions to their personality or disposition rather than situational factors affecting those actions.

Foot-In-The-Door Phenomenon

The tactic of influencing a person to agree to a large request by first getting them to agree to a modest request.