How do you interpret confidence intervals in statistics?
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.