What happens to the standard error as the sample size increases?

The standard error measures the variability of a sample mean from the population mean. It is calculated by taking the standard deviation of the sample and dividing it by the square root of the sample size. As the sample size increases, the denominator in this formula—the square root of the sample size—also increases. This leads to a smaller value for the standard error.

In practical terms, a smaller standard error indicates that the sample mean is reflecting the true population mean more accurately, meaning that larger samples tend to produce more reliable estimates. This concept is foundational in statistics, as it underlies many inferential statistical tests and confidence interval calculations. Thus, as the sample size grows, the standard error diminishes, reinforcing the principle that larger samples yield more precise estimates of population parameters.