Three Randomly Selected Households Are Surveyed as a Pilot Project

question 62

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 1, 4, and 8. Consider the values of 1, 4, and 8 to be a population. Assume that samples of size n = 2 are randomly selected with replacement from the population of 1, 4, and 8. The nine different samples are as follows: (1, 1), (1, 4), (1, 8), (4, 1), (4, 4), (4, 8), (8, 1), (8, 4), and (8, 8).
(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?

Understand fundamental concepts and properties related to the sum of variances and expected values.

Calculate and interpret the mean and standard deviation of derived distributions in practical contexts.

Understand and apply the concept of covariance and correlation in the context of bivariate distributions.

Know the characteristics of independent random variables and their impact on sums, variances, and covariances.

---

Definitions:

Newsworthy

A quality or characteristic of events or information that makes them interesting, important, or relevant enough to be reported in the news.

Discretionary Funds

Discretionary funds refer to money available for spending on non-essential items or activities, often allocated after necessary expenses have been covered.

Worthwhile Cause

A meaningful, important, or valuable goal, project, or mission that merits time, effort, and resources.

Place Blame

The act of attributing fault or responsibility for a mistake or wrongdoing to someone.