What happens to the standard error as sample size increases?

As the sample size increases, the standard error decreases. This relationship is rooted in the concept of variability within a sample. The standard error is a measure of how much the sample mean is expected to vary from the true population mean. When you take larger samples, the sample mean tends to get closer to the true population mean because larger samples provide a better overall representation of the population.

The formula for standard error is the standard deviation divided by the square root of the sample size. As the sample size increases, the denominator (the square root of the sample size) increases, leading to a smaller value for the standard error. Hence, with a larger sample size, the estimates become more precise, meaning the standard error reflects this increased precision by decreasing.

Understanding this concept is vital for interpreting statistical results, as it helps in assessing the reliability of estimates derived from sample data.