Solve the Problem. -Three Randomly Selected Households Are Surveyed as a Pilot Project

question 145

Essay

Solve the problem.
-Three randomly selected households are surveyed as a pilot project for a larger survey to be conducted later.
The numbers of people in the households are 1, 4, and 7. Consider the values of 1, 4, and 7 to be a population.
Assume that samples of size n = 2 are randomly selected with replacement from the population of 1, 4, and 7.
The nine different samples are as follows:
(1, 1), (1, 4), (1, 7), (4, 1), (4, 4), (4, 7), (7, 1), (7, 4), and (7, 7). (i) Construct a probability distribution table that
describes the sampling distribution of the proportion of even numbers when samples of size n = 2 are randomly
selected. (ii) Does the mean of the sample proportions target the value of the population proportion? (iii) Does
the sample proportion make a good estimator of the population proportion?

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Definitions:

Effort Justification

A phenomenon in which individuals attribute greater value to outcomes they had to put effort into achieving, often to reduce cognitive dissonance.

Ingratiation Theory

A psychological theory that explores how people attempt to make themselves appear more likable to others, often through flattery or other strategic behaviors.

Self-Serving Bias

The tendency to attribute positive outcomes to internal factors and negative ones to external factors, thereby protecting self-esteem.

Peripheral Route

A concept in persuasion that refers to the influence of cues that are not directly related to the message content, such as the attractiveness or credibility of the source.