# Chapter 2 What is a hypothesis test?

Recall our previous example where 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?* ** Hypothesis testing** provides a formal framework from which questions such as this can be addressed using information from a collected sample.

When carrying out a formal hypothesis test, we normally consider two hypotheses:

- The
, denoted \(H_0\)*null hypothesis* - The
, denoted \(H_1\).*alternative hypothesis*

In our example above, we would define the null and alternative hypotheses as follows:

\[H_0:\mu = 5\;\;\text{versus}\;\;H_1:\mu \neq 5,\] where:

- \(\mu\) denotes the average cholesterol level of patients from this population
- \(H_0\) denotes the null hypothesis that the average cholesterol level of patients from this population is
to 5*equal* - \(H_1\) denotes the null hypothesis that the average cholesterol level of patients from this population is
to 5.*not equal*

When we carry out a hypothesis test, to start out with, we ** assume the null hypothesis to be true**. If our sample provides evidence that this was not a reasonable assumption to make, then we

**and therefore have evidence in favour of the**

*reject the null hypothesis***.**

*alternative hypothesis*We will now consider an example.