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:

Volume

A measure of the amount of space occupied by a substance, such as a gas, liquid, or solid.

°C

A unit of measurement for temperature on the Celsius scale, where 0°C represents the freezing point of water and 100°C represents the boiling point at sea level.

Gas Law

A set of laws that describe the behavior of gases in relation to pressure, volume, temperature, and quantity.

Mole

A mole is a unit of measurement used in chemistry to quantify the amount of substance, equivalent to approximately 6.022 x 10^23 particles, atoms, molecules, ions, or electrons.