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.