If sample size increases, what happens to the width of the CI?

If sample size increases, what happens to the width of the CI?

• A. No change
• B. Narrower CI
• C. Wider CI
• D. It depends on population variance

Answer: (B)

Increasing the sample size makes the estimate more precise, so at a fixed confidence level the confidence interval becomes narrower. The width is driven by the margin of error, which is the critical value times the standard error. The standard error shrinks as n grows, since it is proportional to 1/√n. So as you collect more data, your uncertainty about the mean decreases and the interval tightens. Even if you’re using the sample standard deviation and a t-distribution, the general idea holds: with larger n, the standard error gets smaller and the interval narrows (the t-quantile also approaches the z-value for large n). The only thing that can counteract this is changing the confidence level; with a fixed level, more data leads to a narrower CI.

Increasing the sample size makes the estimate more precise, so at a fixed confidence level the confidence interval becomes narrower. The width is driven by the margin of error, which is the critical value times the standard error. The standard error shrinks as n grows, since it is proportional to 1/√n. So as you collect more data, your uncertainty about the mean decreases and the interval tightens. Even if you’re using the sample standard deviation and a t-distribution, the general idea holds: with larger n, the standard error gets smaller and the interval narrows (the t-quantile also approaches the z-value for large n). The only thing that can counteract this is changing the confidence level; with a fixed level, more data leads to a narrower CI.