Question

How do you interpret confidence intervals in statistics?

Answer 1

Confidence interval is the interval where we believe the true parameter lies, and the belief is quantified as the level of confidence of that interval.

For example, if I construct a 95% confidence interval for the mean using some sample data, and suppose the interval is (5, 8) then I am 95% confident that the true mean is within 5 to 8.

Here, 95% is not the probability, because true mean is not a random quantity, it is either inside the interval or it is not. But I am 95% confident because the method works on 95% of the random sample.