If variability increases, the width of a confidence interval will generally:

If variability increases, the width of a confidence interval will generally:

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

Answer: (B)

Increasing variability makes the estimate less precise, which shows up as a larger standard error. The confidence interval width is driven by the margin of error, which scales with that standard error. So, with a fixed sample size and confidence level, more spread in the data raises the standard error, increases the margin of error, and the interval becomes wider. The other options don’t fit this direct effect: a narrower interval would imply less variability, no change would mean no change in uncertainty, and while sample size does influence width, the primary impact of higher variability is to widen the interval.

Increasing variability makes the estimate less precise, which shows up as a larger standard error. The confidence interval width is driven by the margin of error, which scales with that standard error. So, with a fixed sample size and confidence level, more spread in the data raises the standard error, increases the margin of error, and the interval becomes wider. The other options don’t fit this direct effect: a narrower interval would imply less variability, no change would mean no change in uncertainty, and while sample size does influence width, the primary impact of higher variability is to widen the interval.