What effect does greater uncertainty or a smaller sample size have on the width of a confidence interval?

• A. Larger sample size.
• B. Greater uncertainty or smaller sample size.
• C. A more precise estimate.
• D. Lower variability.

Answer: (B)

The width of a confidence interval reflects how imprecise our estimate is, and it grows with the standard error. The standard error measures how much the sample estimate would vary if we repeated the study. It gets larger when there’s more uncertainty about the parameter or when the sample size is smaller. Since the margin of error is the standard error scaled by a critical value (MOE = z* × SE), increasing SE widens the interval.

So, greater uncertainty or a smaller sample size leads to a wider confidence interval. The other options describe conditions that would reduce the standard error and produce a more precise, narrower interval: a larger sample size lowers SE, lower variability reduces SE, and both would tighten the interval.