Question

Select the true statement about the relationship between sample size and the standard deviation of distribution of sample means, also known as the standard error. a.) Sample size does not have an impact on standard error. b.) As sample size decreases, standard error decreases. c.) As sample size increases, standard error decreases. d.) As sample size increases, standard error increases.

Answer 1

Answer:  c.) As sample size increases, standard error decreases.

Explanation:

The standard error (SE) is found by computing $SE = \frac{\sigma}{\sqrt{n}}$ where $\sigma$ (greek letter sigma) is the population standard deviation. If sigma is unknown, then you can use the sample standard deviation to estimate it.

The n in the denominator means that as it increases, the SE will decrease, and vice versa. Think of it like a see-saw.

So as we have a larger sample, the SE will decrease to indicate we are more accurate. The SE is a measure how spread out the xbar distribution is.