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?

---

Definitions:

Biological Forces

The natural, physiological drivers behind the growth, behavior, and adaptation of organisms.

Personality

The amalgam of different characteristics that constitute an individual's specific identity.

Creative Power

The innate or developed ability to generate original ideas, solutions, or artistic expressions.

Genetic Factors

Elements within an organism's genes that can influence its traits and characteristics, including physical appearance, behavior, and susceptibility to diseases.