As sample size increases, the standard error of the mean tends to which of the following?

As sample size increases, the standard error of the mean tends to which of the following?

• A. It decreases
• B. It increases
• C. It approaches zero
• D. It remains unpredictable

Answer: (C)

As you collect more data, the sample mean becomes a more precise estimate of the true population mean. The standard error of the mean is the standard deviation of the sampling distribution of the mean, and it shrinks as the sample size grows. For a population with finite variance, the standard error is σ/√n (or s/√n when using the sample standard deviation). Since √n increases without bound, σ/√n gets smaller and tends toward zero as n becomes very large. So the standard error of the mean approaches zero with increasing sample size. For intuition, if σ = 10, the SEM is 10/√n, giving 2 at n=25 and 1 at n=100, illustrating the shrinking spread of sample means.

As you collect more data, the sample mean becomes a more precise estimate of the true population mean. The standard error of the mean is the standard deviation of the sampling distribution of the mean, and it shrinks as the sample size grows. For a population with finite variance, the standard error is σ/√n (or s/√n when using the sample standard deviation). Since √n increases without bound, σ/√n gets smaller and tends toward zero as n becomes very large. So the standard error of the mean approaches zero with increasing sample size. For intuition, if σ = 10, the SEM is 10/√n, giving 2 at n=25 and 1 at n=100, illustrating the shrinking spread of sample means.