Question

what happens to the variance of the sampling distribution of the sample means when the sample size increases

Answer 1

The variance of the sampling distribution of the sample means is given as,

$var(\bar x_i)={\sigma^2\over n}$ where $\sigma^2$ is the population variance and $n$ is the sample size. Clearly, the sample size is on the denominator side of this formula. Therefore, when the sample size is increased the variability of each sampling distribution decreases.