Question

Why does the standard error of the mean decrease as the sample size, n, increases?

Answer 1

Solution: -

As you increase your sample size, the standard error of the mean will become smaller. With bigger sample sizes, the sample mean becomes a more accurate estimate of the parametric mean, so the standard error of the mean becomes smaller.

Because n is in the denominator of the standard error formula, the standard error decreases as n increases.

As sample size increases, the range decreases, which means variability decreases. Let's look more closely at the smallest of the small samples then, the rate at which results get less variable slows down. As we test a larger and larger sample, variability keeps decreasing, but very slowly