What does the 95% represent in a 95% confidence interval?

Verified step by step guidance

1. Understand that a confidence interval is a range of values, derived from sample data, that is likely to contain the true population parameter (such as a mean or proportion).
2. Recognize that the 95% in a 95% confidence interval refers to the confidence level, which quantifies the degree of certainty we have about the interval capturing the true parameter.
3. Interpret the 95% confidence level as meaning that if we were to take many random samples from the population and construct a confidence interval from each sample, approximately 95% of those intervals would contain the true population parameter.
4. Note that the 95% confidence does not mean there is a 95% probability that the specific interval calculated from your sample contains the true parameter; rather, it reflects the long-run success rate of the method used to generate the interval.
5. Summarize that the 95% confidence level expresses the reliability of the estimation process, indicating that the method used will produce intervals capturing the true parameter 95% of the time in repeated sampling.

Key Concepts

Confidence Interval

A confidence interval is a range of values, derived from sample data, that is likely to contain the true population parameter. It provides an estimated range that reflects the uncertainty inherent in sampling.

Confidence Level

The confidence level, such as 95%, indicates the proportion of times that the confidence interval would contain the true population parameter if the same sampling procedure were repeated many times. It reflects the degree of certainty in the interval estimate.

Interpretation of 95% Confidence

A 95% confidence means that if we were to take many samples and build confidence intervals from each, about 95% of those intervals would include the true population parameter. It does not mean there is a 95% probability the parameter lies within a single calculated interval.