How does the standard error of the mean behave as sample size increases?

• A. Increases as sample size increases.
• B. Stays the same regardless of sample size.
• C. Varies unpredictably with sample size.
• D. Decreases as sample size increases.

Answer: (D)

The standard error of the mean reflects how precisely the sample mean estimates the population mean. It depends on the variability in the data and on how many observations you average. As you increase the sample size, you average out more random fluctuation, so the distribution of sample means becomes tighter around the true population mean. Mathematically, SEM is the standard deviation (σ) divided by the square root of the sample size (n), or the sample standard deviation (s) over √n when σ is unknown. Because n sits in the denominator under a square root, increasing n makes SEM smaller. In other words, larger samples give more precise estimates of the population mean, not more variable ones. For example, going from 25 to 100 observations reduces the SEM by about half, illustrating the gain in precision with bigger samples.