##
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 ratio estimate when the population size is unknown is given in section 4.1. In section 4.2, an example for using ratio estimate when the population size is known 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

- know why and when to use ratio estimates,
- check the condition to see whether one can use the 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,
- learn about the biasedness of the ratio estimate via a small population example, and
- see that the ratio estimate does perform better than the expansion estimate when the condition for using the ratio estimate is satisfied.