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

question 148

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 2, 4, and 10. Consider the values of 2, 4, and 10 to be a population.
Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 4, and 10.
The nine different samples are as follows: (2, 2), (2, 4), (2, 10), (4, 2), (4, 4), (4, 10), (10, 2), (10, 4), and (10, 10). (i)
Find the mean of each of the nine samples, then summarize the sampling distribution of the means in the format
of a table representing the probability distribution. (ii) Compare the population mean to the mean of the sample
means. (iii) Do the sample means target the value of the population mean? In general, do means make good
estimators of population means? Why or why not?

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Definitions:

Imagination Inflation

The phenomenon where vividly imagining an event can increase confidence that it actually occurred.

Source Amnesia

A memory disorder where an individual is unable to remember the source of a specific memory while retaining the factual content.

Sensory Memory

It is the shortest-term element of memory which acts as a buffer for stimuli received through the senses, lasting typically less than a second.

Proactive Interference

A phenomenon where old information hinders the recall of newly learned information.