How do you interpret a confidence interval?

A confidence interval provides a range of values that is likely to contain the true population parameter. It reflects the uncertainty around a sample estimate and quantifies how confident we are that this range captures the actual value in the population. For instance, if we construct a 95% confidence interval for a population mean, it means that if we took many samples and constructed confidence intervals in the same way, approximately 95% of those intervals would contain the true population mean.

This interpretation is fundamental in statistics as it allows researchers to convey both the estimate and the associated uncertainty in a clear manner. Thus, when we state a confidence interval, we are not claiming to know the population parameter exactly; rather, we indicate a range within which we believe the parameter is likely to fall, based on the data collected and the level of confidence we choose. This is distinct from more absolute claims about specific values or data range representation, which is why the other options do not accurately capture the purpose and meaning of a confidence interval.