Interpret a 95% confidence interval in repeated sampling?

• A. It guarantees the true parameter lies in this interval for this study.
• B. It implies the probability that the parameter lies within this fixed interval is 95%.
• C. If we repeated the study many times, about 95% of the calculated intervals would contain the true parameter.
• D. It indicates that 95% of observations fall inside the interval.

Answer: (C)

The main idea here is how a confidence interval performs across repeated samples, not what happens in a single study. A 95% confidence interval is built so that, if you could repeat the entire sampling process many times and compute a new interval each time using the same method, about 95% of those intervals would contain the true parameter. The true parameter is fixed; each study’s interval varies because of sampling variability.

So for one particular study, you don’t assign a probability to whether this interval contains the parameter. The 95% figure refers to the long-run success rate of the method. It’s not saying that there’s a 95% chance the parameter lies in this fixed interval. It also isn’t about where most data points fall—the interval is about the unknown parameter, not about the observed data.

That’s why the statement describing repeated sampling and the long-run coverage is the best fit.