# Chapter 9: Inferences for Two Population Means

Chapters 7 and 8 introduced how to obtain a confidence interval and perform a hypothesis test for the population mean *[latex]\mu[/latex]* based on a simple random sample from a population with mean [latex]\mu[/latex]. This chapter covers how to obtain a confidence interval and conduct a hypothesis test for the difference between population means [latex]\mu_1[/latex] – [latex]\mu_2[/latex].

Learning Objectives

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

- Explain the sampling distribution of the difference between two sample means [latex]\bar{X_1} - \bar{X_2}[/latex] for two independent samples.
- State the assumptions for inferences about the difference between two population means based on two independent samples.
- Obtain and interpret a [latex](1 – \alpha) \times 100\%[/latex] two-mean conference interval for [latex]\mu_1[/latex] – [latex]\mu_2[/latex].
- Conduct a two-mean (sample)
*t-test*. - Determine whether two samples are independent or paired.
- Obtain and interpret a paired
*t-*confidence interval. - Conduct a paired
*t-test*. - Explain the relationship between the results of a hypothesis test at significance level [latex]\alpha[/latex] and the corresponding [latex](1 – \alpha) \times 100\%[/latex] confidence interval.