Which of the following is NOT correct about the Central Limit Theorem?

The Central Limit Theorem states that when taking many samples from a population and calculating their averages, these averages will form a normal distribution, even if the original population isn't normally distributed. The standard rule requires a sample size of $n \geq 30$.

Statement 1: "When sample size increases, the sample mean becomes close to the population mean"

This is correct. This describes the Law of Large Numbers. As sample size increases, the sample mean provides a more accurate estimate of the population mean.

Statement 2: "When sample size increases, the sampling distribution of the mean approaches a normal distribution"

This is correct. This is the core principle of the Central Limit Theorem. Regardless of the shape of the parent population, the distribution of sample means becomes approximately normal as sample size increases.

Statement 3: "A sample size of less than 30 is sufficient for CLT"

This is incorrect. The Central Limit Theorem requires a sample size of $n \geq 30$ (30 or more). A sample size of less than 30 does not meet the standard threshold, and the theorem may not hold reliably.

Statement 4: "A sample size of 30 or more is sufficient for CLT"

This is correct. This follows the standard rule that $n \geq 30$ is the threshold for the Central Limit Theorem to apply.

Statements 3 and 4 are contradictory. Statement 3 claims less than 30 is sufficient, while Statement 4 correctly states 30 or more is sufficient. Only Statement 4 aligns with the Central Limit Theorem.

Therefore, the answer is Statement 3.