The variance of the sampling distribution of sample mean
decreases as the sample size,n,increases.

Question

The variance of the sampling distribution of sample mean  
decreases as the sample size,n,increases.

Quizplus · Accepted Answer

The variance of the sampling distribution of the sample mean decreases as the sample size, n, increases. This is due to the Central Limit Theorem, which states that as the sample size increases, the distribution of sample means tends to approach a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. As the standard deviation of the sampling distribution decreases, the variance also decreases.

The Variance of the Sampling Distribution of Sample Mean