When using bootstrapping to create a confidence interval, what is true about the width of that confidence interval?
A) A wide interval indicates that the estimate is highly accurate.
B) A narrow interval results in lower confidence.
C) A narrow interval indicates that the estimate for the mean is not very precise.
D) A wide interval indicates that the estimate for the mean is not very precise.

Question

Quizplus · Accepted Answer

A wide interval in a bootstrap confidence interval indicates that there is a large amount of variability in the data and/or that the sample size is small, both of which lead to imprecise estimates for the mean. Therefore, D is the correct choice as it reflects this understanding. A narrow interval, on the other hand, indicates a more precise estimate for the mean as there is less variability in the data and/or the sample size is larger, and thus choice B is incorrect. A wide interval cannot indicate high accuracy (A) as wide intervals are by definition less precise, and a narrow interval also does not necessarily mean less confidence (B). Finally, C is incorrect because a narrow interval indicates a precise estimate, not an imprecise one.

When Using Bootstrapping to Create a Confidence Interval, What Is