What does a 95% confidence interval for a population mean represent?

• A. The true mean has a 95% probability of lying in the interval.
• B. The true mean is likely to be within the interval, with 95% confidence.
• C. The interval estimates the mean with 95% confidence but does not imply probability about the true mean.
• D. If the study were repeated many times, 95% of the intervals would capture the true mean.

Answer: (D)

A 95% confidence interval conveys how reliable the estimation method is across many samples. If we could repeat the study many times and compute a new interval each time, about 95% of those intervals would contain the true population mean. The true mean is fixed, so for any single interval it either lies inside or it doesn’t; the 95% refers to the long-run performance of the method, not to a probability for this specific interval. Among the options, the statement about repeated samples—where 95% of the intervals would capture the true mean—best captures this long-run reliability of the procedure.