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.

These notes have been prepared by Amanda J. Shaker. The copyright for the material in these notes resides with the author named above, with the Department of Mathematics and Statistics and with La Trobe University. Copyright in this work is vested in La Trobe University including all La Trobe University branding and naming. Unless otherwise stated, material within this work is licensed under a Creative Commons Attribution-Non Commercial-Non Derivatives License CC BY-NC-ND