How do you interpret confidence intervals?

• A. A range within which the true population parameter lies with a specified probability (e.g., 95%).
• B. The exact value of the population parameter is contained in the interval.
• C. The probability that the population parameter lies within this fixed interval is 100%.
• D. The interval contains 100% of future sample means.

Answer: (A)

Confidence intervals express a range that would capture the true population parameter in a certain proportion of repeated samples. If you see a 95% confidence interval, that means that if you repeated the study many times and computed a new interval each time, about 95% of those intervals would contain the actual parameter. It’s about the method’s long-run performance, not the fate of this single interval. The interval does not guarantee that the exact parameter lies inside with 95% probability for this one interval, nor does it claim that 100% of future sample means will fall inside. Precision improves with larger samples or less variability, which tightens the interval and makes the estimate more informative.