### Introduction

This Section introduces you to the basic ideas of hypothesis testing in a non-mathematical way by using a problem solving approach to highlight the concepts as they are needed. We only consider situations involving a single sample.

In Section 41.3 we will introduce you to situations involving two samples and while the basic ideas will follow through, their practical application is a little more complex than that met in this Workbook. However, once you have learned how to apply the basic ideas of hypothesis testing covered in this Workbook, you should be capable of applying hypothesis testing to a very wide range of practical problems and learning about methods of hypothesis testing which are not covered here.

#### Prerequisites

- be familiar with the results and concepts met in the study of probability
- be familiar with a range of statistical distributions
- understand the term hypothesis
- understand the concepts of Type I error and Type II error

#### Learning Outcomes

- apply the ideas of hypothesis testing to a range of problems underpinned by elementary statistical distributions and involving only a single sample.

#### Contents

1 Tests of proportion1.1 Problem 1

1.2 Extracts from the normal probability integral table

1.3 Problem 2

2 Tests for population means

2.1 Tests concerning a single mean

2.2 General comments about tests concerning a population mean

2.3 General comments on the $t$ -test

2.4 Tests concerning paired data