Chapter 4 The distribution of the sample mean

Given a sample of data, it can be very useful to ascertain what the associated distribution of the sample mean would be. Once we know what this distribution is, it makes it much easier to draw conclusions, or make inferences, about the population mean based on our sample.

In this chapter, we discuss how to ascertain the distribution of the sample mean. We will consider the following three scenarios:

1. It is known that the underlying population distribution is normal
2. The underlying population distribution is not known, and the sample size is 30 or more
3. The underlying population distribution is not known, and the sample size is less than 30

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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