Bootstrapping enables confidence intervals without relying on parametric assumptions. Which statement best describes this benefit?

Bootstrapping enables confidence intervals without relying on parametric assumptions. Which statement best describes this benefit?

• A. It eliminates the need to assume a specific parametric form for the sampling distribution.
• B. It guarantees normality of the data.
• C. It always yields the narrowest confidence interval.
• D. It increases the sample size.

Answer: (A)

Bootstrapping uses the observed data to approximate the distribution of a statistic without assuming a specific parametric form for the population. By repeatedly resampling with replacement from the data and computing the statistic each time, you build an empirical distribution of that statistic. Confidence intervals are then derived from this empirical distribution (for example, by taking appropriate percentiles). Because you’re basing the interval on the data’s own variability rather than on a assumed normal or other parametric shape, you don’t need a parametric model of the sampling distribution. The other statements aren’t correct: bootstrapping does not guarantee that the data are normal, it does not inherently produce the narrowest possible interval, and it does not increase the actual sample size (it uses the same data to simulate many resamples).

Bootstrapping uses the observed data to approximate the distribution of a statistic without assuming a specific parametric form for the population. By repeatedly resampling with replacement from the data and computing the statistic each time, you build an empirical distribution of that statistic. Confidence intervals are then derived from this empirical distribution (for example, by taking appropriate percentiles). Because you’re basing the interval on the data’s own variability rather than on a assumed normal or other parametric shape, you don’t need a parametric model of the sampling distribution.

The other statements aren’t correct: bootstrapping does not guarantee that the data are normal, it does not inherently produce the narrowest possible interval, and it does not increase the actual sample size (it uses the same data to simulate many resamples).