If a study reports a 95% CI for the mean of (2.1, 5.7), which interpretation is correct?

• A. The true mean has a 95% probability of lying between 2.1 and 5.7.
• B. If the study were repeated many times, 95% of the intervals would contain the true mean.
• C. The true mean is certainly between 2.1 and 5.7.
• D. The interval contains 95% of the population values.

Answer: (B)

A confidence interval for a mean expresses how often the estimation method would capture the true population mean if we repeated the study many times. The true mean is fixed, while the interval we compute from each sample varies. So a 95% interval means that in repeated samples, about 95% of the intervals would contain the true mean. For this interval, we can’t say there is a 95% probability that the true mean lies between 2.1 and 5.7, because the parameter isn’t random—the interval method is. We also wouldn’t claim the true mean is certainly between those values; there’s still uncertainty from sampling. And this interval does not say that 95% of population values lie in it—that would be about individual observations, not the mean. The correct interpretation is that, in the long run, 95% of similarly constructed intervals would cover the true mean.