Three Randomly Selected Households Are Surveyed as a Pilot Project $\mathrm { n } = 2$

question 142

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 3, 8, and 10. Consider the values of 3, 8, and 10 to be a population. Assume that samples of size n $\mathrm { n } = 2$ 2 are randomly selected with replacement from the population of 3, 8, and 10. The nine different samples are as follows: (3, 3), (3, 8), (3, 10), (8, 3), (8, 8), (8, 10), (10, 3), (10, 8), 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:

Net Income

The total earnings of a company after subtracting all expenses from revenues.

Common Stock

A form of corporate equity ownership, a type of security representing ownership in a corporation and a claim on part of the corporation's assets and earnings.

Declaration Date

The specific date on which a company's board of directors announces the issuance of a dividend to shareholders.

Common Stock

Represents ownership interests in a corporation, giving holders voting rights and a share in the company's profitability through dividends.