# Chapter 4 One-sample \(t\)-test Assumptions

For the one-sample \(t\)-test to be valid, we need to make some ** assumptions**. These assumptions can be summarised as follows:

**One-sample \(t\)-test Assumptions:**

- The data are numeric
- Observations are independent of one another (that is, the sample is a simple random sample and each individual within the population has an equal chance of being selected)
- The sample mean, \(\overline{X}\), is normally distributed.

For the most part in this subject, we will assume that the first two assumptions have been met. Checking for normality is therefore the assumption we will spend most of our time on. In the following sections, we will learn how to check whether the underlying distribution is normal, how the Central Limit Theorem applies, and finally, we will summarise this process with some rules guiding the normality assumption decision.