Which statement describes the effect of increasing sample size on the confidence interval for a proportion?

Which statement describes the effect of increasing sample size on the confidence interval for a proportion?

• A. It widens the interval.
• B. It narrows the interval.
• C. It does not affect the interval width.
• D. It biases the estimate.

Answer: (B)

Increasing sample size makes the confidence interval for a proportion narrower. The width of the interval is tied to the margin of error, which depends on the standard error of the sample proportion: sqrt(p(1-p)/n). As n grows, this standard error gets smaller, so the margin of error decreases and the interval tightens. The confidence level you choose stays the same, so the probability the interval contains the true proportion doesn’t change, but your estimate becomes more precise with more data. Also, the estimator itself is unbiased, and increasing sample size reduces sampling variability rather than introducing bias.

Increasing sample size makes the confidence interval for a proportion narrower. The width of the interval is tied to the margin of error, which depends on the standard error of the sample proportion: sqrt(p(1-p)/n). As n grows, this standard error gets smaller, so the margin of error decreases and the interval tightens. The confidence level you choose stays the same, so the probability the interval contains the true proportion doesn’t change, but your estimate becomes more precise with more data. Also, the estimator itself is unbiased, and increasing sample size reduces sampling variability rather than introducing bias.