# Lesson 30: Confidence Intervals for One Mean

### Introduction

In this lesson, we'll learn how to calculate a confidence interval for a population mean. As we'll soon see, a confidence interval is an interval (or range) of values that we can be really confident contains the true unknown population mean. We'll get our feet wet by first learning how to calculate a confidence interval for a population mean (called a **Z****-interval**) by making the unrealistic assumption that we know the population variance. (Why would we know the population variance but not the population mean?!) Then, we'll derive a formula for a confidence interval for a population mean (called a **t****-interval**) for the more realistic situation that we don't know the population variance. We'll also spend some time working on understanding the "confidence part" of an interval, as well as learning what factors affect the length of an interval.

### Objectives

- To learn how to calculate a confidence interval for a population mean.
- To understand the statistical interpretation of confidence.
- To learn what factors affect the length of an interval.
- To understand the steps involved in each of the proofs in the lesson.
- To be able to apply the methods learned in the lesson to new problems.