What does a confidence interval interpretation refer to?

• A. In repeated sampling, a specified proportion of such intervals would contain the true parameter.
• B. There is a 95% probability that the parameter lies in this particular interval.
• C. The interval contains the true parameter with certainty.
• D. It reflects the range of a single observation's possible values.

Answer: (A)

Confidence intervals express a long-run frequency property of the estimation method. If we could repeat the study many times and compute a new interval each time, a specified proportion of those intervals would contain the true population parameter.

For a 95% confidence interval, that means about 95% of the intervals produced in repeated samples would capture the true parameter. This reflects the method’s performance across many samples, not the certainty of this single interval.

The idea that the parameter lies in this particular interval with 95% probability is a common misconception. The parameter is fixed; the interval is random because it depends on the random sample. Similarly, saying the interval contains the true parameter with certainty ignores sampling variability. Also, this interval targets the population parameter, not a single observed value—that would be a prediction interval for future observations, not a confidence interval.