# Chapter 10: Inferences for Population Proportions

**Overview**

Chapters 8 and 9 introduced inferences for population means. This chapter focuses on inferences for another population parameter: **the population proportion p**, defined as the proportion (or percentage) of a population with a specified attribute. For example, the proportion of times that athletes wearing blue uniforms win a judo match, the proportion of customers who respond to an advertisement, and the proportion of women who have arthritis.

Learning Objectives

As a result of completing this chapter, you will be able to do the following:

- Explain why the sample proportion [latex]\hat{p} = \frac{x}{n}[/latex] is a special type of sample mean [latex]\bar{x} = \frac{\sum x_i}{n}[/latex].
- Describe the sampling distribution of the sample proportion [latex]\hat{p}[/latex].
- Conduct a one-proportion
*z-test*. - Obtain a [latex](1 - \alpha) \times 100%[/latex] confidence interval for the population proportion [latex]p[/latex].
- Describe the sampling distribution of the difference between two sample proportions [latex](\hat{p}_1 - \hat{p}_2)[/latex].
- Conduct a two-proportion
*z-test*. - Obtain a [latex](1 - \alpha) \times 100%[/latex] confidence interval for the difference between two population proportions [latex](p_1 - p_2)[/latex].