### Introduction

In Section 40.1 we have seen that the sampling distribution of the sample mean, when the data come from a normal distribution (and even, in large samples, when they do not) is itself a normal distribution. This allowed us to find a confidence interval for the population mean. It is also often useful to find a confidence interval for the population variance. This is important, for example, in quality control. However the distribution of the sample variance is not normal. To find a confidence interval for the population variance we need to use another distribution called the “chi-squared” distribution.

#### Prerequisites

- understand and be able to calculate means and variances
- understand the concepts of continuous probability distributions
- understand and be able to calculate a confidence interval for the mean of a normal distribution

#### Learning Outcomes

- find probabilities using a chi-squared distribution
- find a confidence interval for the variance of a normal distribution

#### Contents

1 Interval estimation for the variance1.1 The chi-squared random variable

1.2 Degrees of freedom

1.3 Constructing a confidence interval for the variance