Three Randomly Selected Households Are Surveyed as a Pilot Project

question 26

Essay

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 2, 3, and 8. Consider the
values of 2, 3, and 8 to be a population. Assume that samples of size n = 2 are randomly
selected with replacement from the population of 2, 3, and 8. The nine different samples are
as follows:
(2, 2), (2, 3), (2, 8), (3, 2), (3, 3), (3, 8), (8, 2), (8, 3), and (8, 8).
(i)Find the range of each of the nine samples, then summarize the sampling distribution of the
ranges in the format of a table representing the probability distribution. (ii)Compare the
population range to the mean of the sample ranges. (iii)Do the sample ranges target the value
of the population range? In general, do ranges make good estimators of population ranges?
Why or why not?

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Definitions:

Drive-Reduction Theory

A theory of motivation proposing that the primary motivation of all organisms is to reduce their drives, such as hunger, thirst, or the need for warmth.

Stimulus Motive Theory

The concept that behavior is motivated by a desire to increase stimulation in order to maintain an optimal level of arousal.

Evolutionary Theory

A scientific theory that explains how species change over time through mechanisms like natural selection and genetic variation.

Cognitive Appraisal Theory

A theory in psychology that describes the process in which an individual evaluates and interprets a situation, influencing their emotional reaction.