What does a 95% confidence interval represent?

What does a 95% confidence interval represent?

• A. If the study were repeated many times, 95% of the calculated intervals would contain the true parameter.
• B. There is a 95% probability that the true parameter lies in this interval.
• C. 95% of study participants have values within the interval.
• D. The interval contains the true parameter with 5% probability.

Answer: (A)

A 95% confidence interval reflects how often a chosen method would capture the true population parameter if we could repeat the study many times. The 95% means that, in the long run, about 95% of the intervals produced by this procedure would contain the true parameter. It does not imply a 95% probability that the parameter lies in this specific interval, since the parameter is fixed and the interval either contains it or it does not. It also isn’t about the proportions of study participants within the interval. The 95% level is about the performance of the interval-generation method across repeated samples and depends on the data’s variability and the sample size.

A 95% confidence interval reflects how often a chosen method would capture the true population parameter if we could repeat the study many times. The 95% means that, in the long run, about 95% of the intervals produced by this procedure would contain the true parameter. It does not imply a 95% probability that the parameter lies in this specific interval, since the parameter is fixed and the interval either contains it or it does not. It also isn’t about the proportions of study participants within the interval. The 95% level is about the performance of the interval-generation method across repeated samples and depends on the data’s variability and the sample size.