##
Overview
Section* *

This lesson starts with the rationale for using auxiliary information about the population to estimate the unknown population parameter of interest. It then motivates the ratio estimates and the condition appropriate for ratio estimates to be used. An example of using a ratio estimate when the population size is unknown is given in section 4.1. In section 4.2, an example of using ratio estimate when the population size is given. We then discuss the sample size needed for a specified margin of error and confidence level when the ratio estimate is used. At the end of section 4.2, a small population example is given to illustrate that the ratio estimate is biased and also to demonstrate that the ratio estimate is indeed better than the expansion estimate when the condition for using the ratio estimate is satisfied.

Lesson 4: Ch. 7.1, 7.2 of *Sampling *by Steven Thompson, 3rd edition.

## Objectives

- Identify the appropriate reasons and situations for utilizing ratio estimates,
- Evaluate the conditions for determining the feasibility of using a ratio estimate,
- Compute the ratio estimate and its estimated variance,
- Compute confidence interval based on ratio estimates,
- Compute the sample size needed when the ratio estimate is used,
- Recognize the biasedness of the ratio estimate that is demonstrated by a small population example, and
- Recognize the improved performance of the ratio estimate over the expansion estimate when the appropriate conditions for using the ratio estimate are met.