Central Limit Theorem
The central limit theorem states that when an infinite number of successive random samples are taken from a population, the distribution of sample means calculated for each sample will become approximately normally distributed with mean μ and standard deviation σ/√N (∼N(μ, σ/√N)) as the sample size (N) becomes larger, irrespective of the shape of the population distribution.

Hypothesis Tests
How does the central limit theorem help us when we are testing hypotheses about sample means? Even if we do not know the distribution of scores in the original population, we know that the sampling distribution of the means will be approximately normally distributed with mean μ and standard deviation σ/√N, if the sample is relatively large. Knowing the properties of the sampling distribution allows us to continue with the test, even if we don't know what the population distribution looks like.

Now that you have reviewed all three components of the central limit theorem, test your knowledge with practice exercises.