What does a 95% confidence interval imply about the population parameter across repeated samples?

What does a 95% confidence interval imply about the population parameter across repeated samples?

• A. In 95% of samples, the interval would contain the population parameter
• B. The interval contains the population parameter with 95% probability in this sample
• C. 95% of data fall inside the interval
• D. The interval is guaranteed to contain the parameter

Answer: (A)

A 95% confidence interval reflects how the estimation procedure behaves across repeated samples, not a probability about this one interval. If you could take many samples and compute a 95% interval from each, about 95% of those intervals would contain the true population parameter. The parameter itself is fixed, so for any given interval you’ve calculated, it either contains it or it doesn’t. The 95% refers to long-run coverage of the method, assuming the data come from the same population and the usual statistical assumptions hold. It’s not that 95% of the data lie inside the interval, and it isn’t a guarantee that this particular interval will contain the parameter.

A 95% confidence interval reflects how the estimation procedure behaves across repeated samples, not a probability about this one interval. If you could take many samples and compute a 95% interval from each, about 95% of those intervals would contain the true population parameter. The parameter itself is fixed, so for any given interval you’ve calculated, it either contains it or it doesn’t. The 95% refers to long-run coverage of the method, assuming the data come from the same population and the usual statistical assumptions hold. It’s not that 95% of the data lie inside the interval, and it isn’t a guarantee that this particular interval will contain the parameter.