Which theorem states that as sample size increases, the distribution of sample means approaches a normal distribution?

The Central Limit Theorem is a fundamental concept in statistics that asserts that as the size of a sample increases, the distribution of sample means will approach a normal distribution, regardless of the shape of the original population distribution from which the samples are drawn. This theorem is crucial because it allows researchers to make inferences about population parameters even when the underlying data is not normally distributed, as long as the sample size is sufficiently large.

This property of the Central Limit Theorem enables the use of various statistical techniques and hypothesis testing that rely on the assumption of normality. Essentially, it provides a foundation for many statistical methods, making it possible to apply normal distribution properties when analyzing data in psychological research and other fields.

The other options do not accurately describe this concept. The Law of Large Numbers speaks to the idea that as a sample size increases, the sample average converges to the expected value, which is related but does not specifically address the distribution of sample means. The Sampling Theorem is a more general concept that deals with the reconstruction of signals from samples, not specifically the distribution of sample means. The Normal Distribution Law refers to the characteristics and properties of the normal distribution itself but does not encompass the specific behavior of sample means as described by the Central Limit Theorem