How is sample size related to the Central Limit Theorem?

The Central Limit Theorem (CLT) states that when independent random samples are taken from a population, the distribution of the sample means will approach a normal distribution as the sample size increases, regardless of the shape of the population distribution. This fundamental principle reveals that larger sample sizes yield more reliable approximations of normality for the sample mean, which is crucial for many statistical analyses that assume normality.

When the sample size is increased, the variability of the sample means decreases, leading to a tighter clustering of those means around the true population mean. This effectively enhances the reliability of the sample mean as a predictor of the population mean. As a result, even if the population from which the samples are drawn is not normally distributed, the distribution of the sample means will become approximately normal when the sample size is sufficiently large. This underpins the importance of using larger samples in statistical inference and hypothesis testing.

The other options do not accurately describe the relationship of sample size to the Central Limit Theorem. For example, while a larger sample size does lead to a more accurate estimation of population parameters, that is not the focus of the Central Limit Theorem specifically.