Which statement about confidence intervals is true?

Which statement about confidence intervals is true?

• A. Wider intervals imply more precise estimation.
• B. Narrower intervals imply more precision.
• C. They give the exact true value.
• D. If the study were repeated many times, a specified proportion of calculated intervals would contain the true value.

Answer: (D)

Confidence intervals express a range around a study estimate that reflects uncertainty about the population parameter. The defining idea is that if you repeated the study many times and calculated a new interval each time using the same method, a fixed proportion (such as 95%) of those intervals would contain the true value. This long-run performance is what the statement is capturing. Wider intervals are less precise, not more, and do not guarantee inclusion of the true value in a single study. Narrower intervals are more precise, but a single interval cannot promise to contain the true value; only the long-run proportion across many repetitions matches the confidence level. Confidence intervals do not give the exact true value—they provide a plausible range.

Confidence intervals express a range around a study estimate that reflects uncertainty about the population parameter. The defining idea is that if you repeated the study many times and calculated a new interval each time using the same method, a fixed proportion (such as 95%) of those intervals would contain the true value. This long-run performance is what the statement is capturing. Wider intervals are less precise, not more, and do not guarantee inclusion of the true value in a single study. Narrower intervals are more precise, but a single interval cannot promise to contain the true value; only the long-run proportion across many repetitions matches the confidence level. Confidence intervals do not give the exact true value—they provide a plausible range.