Given:

The provided statement is, “As sample size increases, the sampling distribution of \(\overline{x}\) becomes more and more skewed.”

The central limit theorem is one of the important concepts of the large sample theory. It can be stated, “If the size of a sample increases, the population mean can be approximated by the sample mean and the population standard deviation becomes approximately equal to the ratio of the sample standard deviation and the square root of the sample size.”

In other words,central limit theorem, for a sufficiently large sample size, the sampling distributions of the mean tend to be normal distribution, irrespective of the distribution of the population.

Therefore, as sample size increases the sampling distribution of \(\overline{x}\) becomes less and less skewed. Hence, the provided statements are false.