In statistical sampling, what is the minimum sample size for applying the Central Limit Theorem effectively?

The Central Limit Theorem (CLT) states that, given a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution. This is particularly important when conducting statistical analyses, as many inferential statistics rely on assumptions of normality.

For most practical applications, a minimum sample size of 30 is generally recommended to effectively apply the CLT. This guideline stems from empirical observations that, when samples reach this size, the means of those samples tend to form a normal distribution, even if the underlying population does not. This threshold helps ensure that analyses such as confidence intervals and hypothesis tests yield reliable results.

While smaller sample sizes can still yield useful information, they may not adequately approximate normality, especially if the original population is significantly skewed or has outliers. Therefore, a sample size of 30 serves as a reliable benchmark for applying the Central Limit Theorem effectively, providing sufficient data points to approach the behavior of a normal distribution for the sample means in most cases.