How does increasing sample size affect the standard error?

How does increasing sample size affect the standard error?

• A. SE remains constant as n increases.
• B. SE decreases as n increases.
• C. SE increases as n increases.
• D. SE decreases linearly with n.

Answer: (B)

Increasing the sample size lowers the standard error of the mean because the sample mean becomes a more precise estimator of the population mean. The standard error is roughly the population standard deviation divided by the square root of the sample size (SE ≈ σ/√n, or s/√n in practice). As n grows, the denominator grows like the square root of n, so SE shrinks. The reduction isn’t linear—doubling the sample size reduces SE by a factor of about 1/√2, not by half. For example, if SE is 4 at n = 100, increasing to n = 400 would cut SE to about 2. So, larger samples give more precise estimates, while maintaining the inverse square root relationship.

Increasing the sample size lowers the standard error of the mean because the sample mean becomes a more precise estimator of the population mean. The standard error is roughly the population standard deviation divided by the square root of the sample size (SE ≈ σ/√n, or s/√n in practice). As n grows, the denominator grows like the square root of n, so SE shrinks. The reduction isn’t linear—doubling the sample size reduces SE by a factor of about 1/√2, not by half. For example, if SE is 4 at n = 100, increasing to n = 400 would cut SE to about 2. So, larger samples give more precise estimates, while maintaining the inverse square root relationship.