If the confidence level increases, what happens to the width of the CI?

If the confidence level increases, what happens to the width of the CI?

• A. Narrower CI
• B. Wider CI
• C. No change
• D. It depends on sample size

Answer: (B)

Increasing the confidence level means you want to be more certain that the interval contains the true parameter. To achieve this, you must widen the range of values you’re considering. In practice, the confidence interval is the estimate plus and minus a margin of error that grows with the critical value associated with that confidence level (the z* or t* factor). As you move from, say, 90% to 95% to 99% confidence, that critical value increases, so the margin of error grows and the interval becomes wider. Therefore, with a fixed sample size, a higher confidence level yields a wider confidence interval.

Increasing the confidence level means you want to be more certain that the interval contains the true parameter. To achieve this, you must widen the range of values you’re considering. In practice, the confidence interval is the estimate plus and minus a margin of error that grows with the critical value associated with that confidence level (the z* or t* factor). As you move from, say, 90% to 95% to 99% confidence, that critical value increases, so the margin of error grows and the interval becomes wider. Therefore, with a fixed sample size, a higher confidence level yields a wider confidence interval.