# 4: Foundations for Inference

Statistical inference is concerned primarily with understanding the quality of parameter estimates. For example, a classic inferential question is, "How sure are we that the estimated mean, \( \bar {x}\), is near the true population mean, \(\mu\)?" While the equations and details change depending on the setting, the foundations for inference are the same throughout all of statistics. We introduce these common themes in Sections 4.1-4.4 by discussing inference about the population mean, \(\mu\), and set the stage for other parameters and scenarios in Section 4.5. Some advanced considerations are discussed in Section 4.6. Understanding this chapter will make the rest of this book, and indeed the rest of statistics, seem much more familiar.

### Contributors

- David M Diez (Google/YouTube)
- Christopher D Barr (Harvard School of Public Health)
- Mine Çetinkaya-Rundel (Duke University)