As the sample size increases while keeping other factors constant, the margin of error will

As the sample size increases while keeping other factors constant, the margin of error will

• A. Increase
• B. Decrease
• C. Stay the same
• D. Fluctuate

Answer: (B)

As the sample size grows while keeping everything else constant, the margin of error gets smaller. This happens because the margin of error is tied to the standard error of the estimate, which is proportional to 1 over the square root of the sample size (for a given population standard deviation, or its estimate). When you increase n, sqrt(n) increases, so the standard error decreases, and since the margin of error is a fixed multiplier (like a z or t value) times the standard error, the margin of error shrinks as well. Doubling the sample size reduces the margin of error by about 1 over sqrt(2), not by half, illustrating the 1/sqrt(n) relationship. With the confidence level unchanged, the interval becomes tighter, so the margin of error decreases.

As the sample size grows while keeping everything else constant, the margin of error gets smaller. This happens because the margin of error is tied to the standard error of the estimate, which is proportional to 1 over the square root of the sample size (for a given population standard deviation, or its estimate). When you increase n, sqrt(n) increases, so the standard error decreases, and since the margin of error is a fixed multiplier (like a z or t value) times the standard error, the margin of error shrinks as well. Doubling the sample size reduces the margin of error by about 1 over sqrt(2), not by half, illustrating the 1/sqrt(n) relationship. With the confidence level unchanged, the interval becomes tighter, so the margin of error decreases.