Three Randomly Selected Households Are Surveyed as a Pilot Project

question 60

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 5, 6, and 10. Consider the values of 5, 6, and 10 to be a population. Assume that samples of size n = 2 are randomly selected with replacement from the population of 5, 6, and 10. The nine different samples are as follows:
(5, 5), (5, 6), (5, 10), (6, 5), (6, 6), (6, 10), (10, 5), (10, 6), and (10, 10).
(i) Find the variance of each of the nine samples, then summarize the sampling distribution of the variances in the format of a table representing the probability distribution.
(ii) Compare the population variance to the mean of the sample variances.
(iii) Do the sample variances target the value of the population variance? In general, do variances make good estimators of population variances? Why or why not?

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Definitions:

Hurdle Rate

The minimum rate of return on an investment that a company or investor expects to earn, used as a benchmark for funding projects.

Capital Outlay

Expenditure for acquiring, maintaining, or improving fixed assets such as buildings, equipment, or land, that have a long-term use or value.

Capital Budgeting

The process of evaluating and selecting long-term investments that are in line with the goal of shareholder wealth maximization.

Post-audits

Reviews conducted after the completion of a project or process to assess its success, efficiency, and adherence to budget and timelines.