Solve the Problem. -Three Randomly Selected Households Are Surveyed as a Pilot Project

question 36

Essay

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

---

Definitions:

Effective Communication

A process of exchanging information clearly and efficiently between individuals or groups.

Medical Decisions

Choices made by patients and healthcare professionals regarding the course of treatment or interventions based on clinical judgement and patient preferences.

Nonmaleficence

A fundamental principle in medical ethics that obligates healthcare providers to avoid causing harm to patients.

Autonomy

The right or condition of self-governance, especially in the context of making personal health decisions.