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:

1. The data are numeric
2. 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)
3. 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.

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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