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

question 12

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 median of each of the nine samples, then summarize the sampling distribution of the medians in the
format of a table representing the probability distribution. (ii) Compare the population median to the mean of
the sample medians. (iii) Do the sample medians target the value of the population median? In general, do
medians make good estimators of population medians? Why or why not?

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Definitions:

Rich Countries

Nations with high levels of income per capita, often characterized by strong economies, advanced infrastructure, and a high standard of living.

Per Capita Real Income

The average income earned per person in a given area, adjusted for inflation, reflecting the true purchasing power of the populace.

Percent Per Year

A rate that expresses the change of a quantity over one year as a percentage of the initial quantity.

Productivity

A measure of the efficiency with which goods and services are produced, often expressed as output per unit of labor.