If the sample size increases, what happens to the standard error of the mean?

When the sample size increases, the standard error of the mean decreases. This relationship is rooted in the formula for the standard error, which is calculated as the standard deviation of the population divided by the square root of the sample size. As the sample size increases, the denominator of this formula (the square root of the sample size) becomes larger, leading to a smaller value for the standard error.

A smaller standard error indicates that the sample mean is likely to be a more accurate estimate of the population mean. This reflects a reduction in the variability of sample means, suggesting that as you gather more data, the precision of the estimates improves. Therefore, the correct answer is that it decreases when the sample size increases.