How is a confidence level of 95% interpreted?

A confidence level of 95% is interpreted as an indication that approximately 95 out of 100 confidence intervals constructed from random samples will contain the true population parameter. This means that if you were to take multiple random samples from the population and calculate a confidence interval for each sample, about 95% of those intervals would include the actual value of the parameter being estimated.

This concept is rooted in the framework of inferential statistics, where we use sample data to make inferences about a broader population. A confidence interval provides a range of values derived from the sample that is likely to include the population parameter, and the confidence level reflects the reliability of this range. Thus, the interpretation emphasizes the toolbox of statistical inference rather than asserting certainty about a single sample or a guaranteed outcome.

In essence, the confidence level quantifies our level of confidence in the method used to estimate the parameter, rather than guaranteeing that any individual interval will capture the parameter or that sample outcomes will be identical.