How does increasing sample size affect the width of a confidence interval?

How does increasing sample size affect the width of a confidence interval?

• A. It widens the interval, reducing precision.
• B. It has no effect on the interval width.
• C. It narrows the interval, providing more precise estimates.
• D. It changes the point estimate but not the interval.

Answer: (C)

Increasing sample size reduces the standard error of the estimator. The confidence interval is built as the point estimate plus and minus a margin of error that depends on that standard error. Since the standard error decreases roughly with 1/√n, larger samples make the margin of error smaller and the interval tighter. This means you get a more precise estimate around the same or similar point estimate. Even with the t distribution used when the population variance is unknown, the same idea applies: more data lowers the standard error and narrows the interval. So, increasing sample size narrows the confidence interval, providing more precise estimates.

Increasing sample size reduces the standard error of the estimator. The confidence interval is built as the point estimate plus and minus a margin of error that depends on that standard error. Since the standard error decreases roughly with 1/√n, larger samples make the margin of error smaller and the interval tighter. This means you get a more precise estimate around the same or similar point estimate. Even with the t distribution used when the population variance is unknown, the same idea applies: more data lowers the standard error and narrows the interval. So, increasing sample size narrows the confidence interval, providing more precise estimates.