# Confidence interval interpretation [duplicate]

Why it's said when we estimate a parameter, from 100 confidence intervals, 95 will have the parameter. And why it is incorrect to say that is a 95% probability that the true parameter is in the confidence interval? Thank you in advance.

• You generate the confidence interval once. Suppose it is constructed to be a 95% confidence interval. The true value of the parameter is unknown but fixed. So the actual interval may include it or it might not. The interval was constructed in such a way that if we repeated the process a large number of times approximately 95% of the intervals will contain the true parameter value and the rest will not. For the given interval we cannot assess a probability because the parameter is a fixed quantity and not random. Commented Apr 24, 2017 at 21:23
• @Alexis There has been so much discussion about this issue on this site that I was not sure it was important enough to make it an answer. But if you and the OP think I should make it an answer I will do that. Commented Apr 24, 2017 at 22:25
• As gung mentions there is a lot of interesting information in the link he gave. Commented Apr 25, 2017 at 0:26
• Although some of the answers in the link go beyond confidence intervals for a mean this question and my answer are more general. The concept goes back to Neyman and is different from Fisher's concept of fiducial inference. Commented Apr 25, 2017 at 0:52
• I explained why the question is not an exact duplicate of the referenced post. I see that the OP has used the self-study tag. I am not quite sure why it requires that tag which I am very much acquainted with. Commented Apr 25, 2017 at 17:38