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We’ve already covered most of the key ideas of statistical inference in Topic 4 with our discussion of sampling variation and the sampling distribution, and the illustration of confidence intervals and hypothesis tests.  

This theme will help you to understand why the normal distribution is so important in statistics and when it can be used for inference. To achieve this goal we first talk about something called the central limit theorem which underpins the use of the normal distribution for many analyses.

We will then look at the central limit theorem in practice by estimating confidence intervals and performing hypothesis tests for a single sample mean and single sample proportion. Nothing new is introduced here, we are just bringing together ideas already discussed and showing practical examples that use a solitary sample.