Three Randomly Selected Households Are Surveyed as a Pilot Project

question 160

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, 6, and 7. Consider the values of 3, 6, and 7 to be a population. Assume that samples of size n = 2 are randomly selected with replacement from the population of 3, 6, and 7. The nine different samples are as follows:
(3, 3), (3, 6), (3, 7), (6, 3), (6, 6), (6, 7), (7, 3), (7, 6), and (7, 7).
(i) Construct a probability distribution table that describes the sampling distribution of the proportion of even numbers when samples of size n = 2 are randomly selected.
(ii) Does the mean of the sample proportions target the value of the population proportion?
(iii) Does the sample proportion make a good estimator of the population proportion?

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Definitions:

Borrowed Money

Funds that an individual or entity obtains from another party under the condition of future repayment with interest, which can be used for various purposes.

Debt Paying Ability

Debt paying ability indicates an entity's capacity to repay its debt obligations based on its financial situation, including liquidity ratios and income.

Acid-test Ratio

A stringent indicator of a company's liquidity, calculating its ability to cover short-term obligations with its most liquid assets, excluding inventory.

Inventory Turnover

A measure of how often a company's inventory is sold and replaced over a certain period of time, indicating efficiency in inventory management.