Which description best captures the meaning of a confidence level in interval estimation?

• A. The probability that the interval contains the true parameter.
• B. The process of selecting a sample to estimate a parameter.
• C. Typically selecting a level like 95%, reflecting the desired long-run proportion of intervals that contain the true parameter.
• D. It is determined after collecting data to maximize precision.

Answer: (C)

A confidence level expresses how often the interval estimation method would capture the true parameter if we could repeat the study many times. If we set it at 95%, that means that, across many repeated samples and the intervals built from them using the same method, about 95% of those intervals would contain the true parameter. This describes the performance of the method over repeated sampling, not the probability that any single, specific interval contains the parameter. The level is chosen before looking at the data and affects how wide the interval tends to be: higher confidence gives wider intervals to ensure the desired coverage. It is not about selecting a sample process after the data are collected to maximize precision, nor is it the probability for one particular interval.