Interpreting a 95% confidence interval means which of the following?

• A. There is a 95% chance the true parameter lies in this interval.
• B. If the study were repeated many times, about 95% of such intervals would contain the true parameter.
• C. 95% of the data fall within the interval.
• D. The interval contains 95% of the sample values.

Answer: (B)

The key idea is that a 95% confidence interval reflects long-run coverage over many repeated samples, not a probability for this single interval. If you repeated the study many times and built a 95% interval from each sample, about 95% of those intervals would contain the true parameter. The parameter itself is fixed, while the interval is random because it depends on the sample.

The other statements mix up what the interval describes. A single interval isn’t a statement about a 95% probability that the parameter lies inside this exact range. It also isn’t about what percentage of observed data fall inside the interval, nor about how many sample values happen to lie within it. Those interpretations misapply the concept, which is about long-run frequency of the method’s success in capturing the true parameter.