Which statement about confidence intervals is correct?

Which statement about confidence intervals is correct?

• A. The range of values in which a specified probability of the means of repeated samples would be expected to fall.
• B. The population mean is always within the interval.
• C. It contains 99% of sample means.
• D. It represents the exact population parameter.

Answer: (A)

Confidence intervals express the uncertainty around estimating a population mean. They are built from the sample data to form a range that, at a chosen confidence level, would contain the true mean if we repeated the study many times and constructed an interval each time. This long-run behavior is what the statement captures: a range of values where a specified probability of the population mean would fall across repeated samples. It doesn’t guarantee the population mean lies inside a single interval from one sample, nor does it claim the interval contains 99% of sample means, nor that it gives the exact population parameter. This framing best describes what a confidence interval represents.

Confidence intervals express the uncertainty around estimating a population mean. They are built from the sample data to form a range that, at a chosen confidence level, would contain the true mean if we repeated the study many times and constructed an interval each time. This long-run behavior is what the statement captures: a range of values where a specified probability of the population mean would fall across repeated samples. It doesn’t guarantee the population mean lies inside a single interval from one sample, nor does it claim the interval contains 99% of sample means, nor that it gives the exact population parameter. This framing best describes what a confidence interval represents.