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Population parameters and sample estimates

The mean study score for the population of all Year 12 students taking a particular subject is an example of a population parameter. It is important to make the distinction between this population parameter and a sample estimate. In practice, we are interested in finding out about an unknown population parameter, the mean \(\mu\). This has a fixed but unknown value: it is a number. We collect data from a random sample in order to obtain a sample estimate of this population parameter. As we have illustrated repeatedly, it is most unlikely that different samples from the same population will give the same estimate: rather, they will vary.

The unknown population parameter, the true mean, is \(\mu\). An estimate we obtain from a single sample, the sample mean, is the point estimate \(\bar{x}\). The aim of the methods we describe later in this module is to infer something about the parameter of a population from the sample. This is an inference because there is uncertainty about the parameter. We can however, quantify this uncertainty, and the theory we have been looking at, based on the distribution of sample means, is what is required for this task.

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