Which statement regarding the sampling distribution of sample means is incorrect?

The statement about the standard deviation of the sampling distribution being the standard deviation of the population is correct in essence but requires clarification regarding its context. The standard deviation of the sampling distribution, commonly referred to as the standard error, is indeed derived from the population standard deviation but is adjusted by the sample size. The standard error is calculated as the population standard deviation divided by the square root of the sample size.

This adjustment is crucial because it shows how the variability of the sample means decreases with larger sample sizes, reinforcing the accuracy of estimates derived from those samples.

In contrast, the other statements align with established statistical principles: the mean of the sampling distribution does indeed equal the population mean as established by the Central Limit Theorem; the distribution becoming more normal with larger sample sizes is a fundamental concept, emphasizing how sample means tend to form a normal distribution regardless of the shape of the population distribution as the sample size increases; and the standard error being derived from the standard deviation of samples—while combining the concept of variability into the context of sampling distributions—highlights the effects of sample size on this measure.

Thus, the statement regarding the standard deviation of the sampling distribution being the standard deviation of the population is misleading without including the sample size adjustment required to