In this chapter, our goal is to estimate the value of an unknown population parameter, such as a population mean or a proportion from a binomial population. For example, we might want to know the mean gas mileage for a new car model, the average expected life of a flat-screen computer monitor, or the proportion of Iraq War veterans with post-traumatic stress syndrome.

You’ll see that different techniques are used for estimating a mean or proportion, depending on whether a sample contains a large or small number of measurements. Nevertheless, our objectives remain the same: We want to use the sample information to estimate the population parameter of interest (called the target parameter) and to assess the reliability of the estimate.

Often, there are one or more key words in the statement of the problem that indicate the appropriate target parameter. Some key words associated with the parameters covered in this chapter are listed in the following box:

For the examples given in the first paragraph of this section, the words mean in “mean gas mileage” and average in “average life expectancy” imply that the target parameter is the population mean $\mu .$ The word proportion in “proportion of Iraq War veterans with post-traumatic stress syndrome” indicates that the target parameter is the binomial proportion p.

In addition to key words and phrases, the type of data (quantitative or qualitative) collected is indicative of the target parameter. With quantitative data, you are likely to be estimating the mean or variance of the data. With qualitative data with two outcomes (success or failure), the binomial proportion of successes is likely to be the parameter of interest.

A single number calculated from the sample that estimates a target population parameter is called a point estimator. For example, we’ll use the sample mean, $\overline{x}$, to estimate the population mean $\mu$. Consequently, $\overline{x}$ is a point estimator. Similarly, we’ll learn that the sample proportion of successes, denoted $\widehat{p}$, is a point estimator for the binomial proportion p and that the sample variance s² is a point estimator for the population variance ${\sigma }^2$. Also, we will attach a measure of reliability to our estimate by obtaining an interval estimator—a range of numbers that contains the target parameter with a high degree of confidence. For this reason the interval estimate is also called a confidence interval.

We consider methods for estimating a population mean in Sections 5.2 and 5.3. Estimating a population proportion is presented in Section 5.4. We show how to determine the sample sizes necessary for reliable estimates of the target parameters in Section 5.5. Finally, in optional Section 5.6 we discuss estimation of a population variance.