Understanding the Central Limit Theorem is necessary to understand hypothesis tests of means. 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.

The following tutorial demonstrates three different components of the central limit theorem.

1. successive sampling from a population
2. increasing sample size
3. population distribution

Keep in mind that this theorem applies only to the mean and not other statistics.

Let's begin with successive sampling.