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

question 178

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 3, 6, and 10. Consider the values of 3, 6, and 10 to be a population.
Assume that samples of size n = 2 are randomly selected with replacement from the population of 3, 6, and 10.
The nine different samples are as follows:
(3, 3), (3, 6), (3, 10), (6, 3), (6, 6), (6, 10), (10, 3), (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:

Respiratory Arrest

Respiratory arrest is a critical condition that occurs when breathing completely stops, requiring immediate medical intervention to restore respiration.

Concussion

A jarring injury to the brain; the most common type of head injury.

Jarring Injury

A type of injury typically caused by a sudden and forceful impact, often leading to concussion or other trauma.

Semi-Fowler's Position

A seating position where the patient is inclined at an angle between 15 to 45 degrees; often used to promote comfort and respiratory function.