What is a 95% confidence interval and what does it imply about the estimate?

• A. A 95% CI is the range that contains 95% of observed sample values.
• B. A 95% CI is the range in which 95% of samples would produce an estimate.
• C. A 95% CI is the range within which the true parameter lies with 95% probability in repeated samples.
• D. A 95% CI is the observed data range from the current sample.

Answer: (C)

A 95% confidence interval expresses how precisely we’ve estimated a population value from the data. It’s the range around our sample estimate that, if we could repeat the study many times and compute a new interval each time, would capture the true parameter in about 95% of those repeats. In other words, the method used to build the interval has a long-run property: 95% of the intervals it produces would contain the actual value we're trying to estimate.

This doesn’t mean there’s a 95% chance that the true parameter lies in this single interval, because the true value is fixed and the interval either contains it or it doesn’t. It also isn’t about 95% of observed data falling inside the interval, nor about 95% of samples producing the same estimate within this interval. The interval reflects the method’s reliability across repeated samples and the precision of the estimate: wider intervals indicate more uncertainty, while narrower ones indicate more precise estimates, assuming the model and sampling assumptions hold.