# STM1001 Topic 5: Hypothesis Testing

*2022-08-26*

# Introduction

Having learnt in the previous topic about the distribution of the sample mean, \(\overline{X}\), we are now ready to learn how we can use that distribution to help us draw ** inferences** about the population mean \(\mu\).

For example, suppose it was believed that in general, the average cholesterol level was \(\mu = 5.0\) mmol/L. Further suppose the cholesterol levels of 72 patients were measured, and we wanted to ascertain: *Is the average cholesterol level of patients from this population different from 5.0 mmol/L?*

To answer this question, we can use perhaps the most famous technique in Statistics: ** Hypothesis Testing**.

In this topic, we will learn what hypothesis tests are and how to carry them out using an example throughout. We will also learn what assumptions we need to make to carry out these hypothesis tests, and check whether or not these assumptions have been met.