WHAT DOES THE CENTRAL LIMIT THEOREM SAY ABOUT THE TRADITIONAL SAMPLE SIZE THAT SEPARATES A LARGE SAMPLE SIZE FROM A SMALL SAMPLE SIZE?

http://en.wikipedia.org/wiki/Central_limit_theorem

https://www.khanacademy.org/math/probability/statistics-inferential/sampling_distribution/v/central-limit-theorem

The Central Limit Theorem states that for a large enough sample size, the distribution of the sample means will approach a normal distribution, regardless of the shape of the population distribution. This means that even if the population from which we are drawing our samples is not normally distributed, if we have a large enough sample size, the distribution of sample means will become approximately normal.

However, the Central Limit Theorem does not provide a specific cutoff between a large sample size and a small sample size. The definition of a large sample size is not fixed and may vary depending on the context and the specific statistical analysis being conducted.

In practice, statisticians generally consider a sample size of 30 or more to be large enough for the Central Limit Theorem to apply, as long as the population distribution is not heavily skewed or has extreme outliers. However, it is important to note that this is a common guideline and not an absolute rule.

To summarize, the Central Limit Theorem does not provide a precise definition of a large or small sample size, but a sample size of 30 or more is often considered large enough for the theorem to hold.