We frequently collect data on categorical variables. When we record categorical variables, our data consist of counts or of percents obtained from counts. In these settings, our goal is to say something about the corresponding population proportions.

The methods detailed in this chapter will help us answer questions such as

• Do experts think that the use of robots will have a negative effect on job opportunities?
• What percent of people who own a particular version of a smartphone will upgrade within the next year?
• What proportion of U.S. adults consume the recommended five servings of fruits and vegetables per day?

Just as in the case of inference about population means, we may be concerned with a single population or with comparing two populations. Inference about one or two proportions is very similar to inference about means, which we discussed in Chapter 7. In particular, inference for both means and proportions is based on sampling distributions that are approximately Normal.

We begin in Section 8.1 with inference about a single population proportion. Section 8.2 concerns methods for comparing two proportions.