Which statement accurately describes a 95% confidence interval when the study is repeated many times?

• A. If the study were repeated many times, about 95% of the constructed intervals would contain the parameter.
• B. The interval contains the true parameter with 95% probability for this study.
• C. The interval is guaranteed to contain the parameter with 95% certainty.
• D. The interval implies the parameter lies within 95% of observed sample values.

Answer: (A)

The main idea is the long-run behavior of the method that constructs the interval. A 95% confidence interval is built so that, if you could repeat the entire study many times and compute a new interval each time using the same method, about 95% of those intervals would contain the true parameter. This describes how the procedure performs across many samples, not the chance for this single interval to contain the parameter. For this particular study, the interval either does or does not contain the parameter; the 95% claim refers to the method's performance over repeated repetitions, not a probability for this one case. The other interpretations mix up probability with a single fixed result or imply a guaranteed or wrong kind of relationship between the interval and the observed data.