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I just read that a (1 - alpha)*100% confidence interval cannot be interpreted as follows: The probability that mu is in the confidence interval is (1 - alpha)*100%. That is counterintuitive from the proof from NYU below. In particular, doesn't the last line imply that the probability that mu is in the confidence interval is (1 - alpha)*100%? If not, can someone explain why? What am I missing?

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  • $\begingroup$ It can be interpreted as: The probability that mu is in the confidence interval is (1 - alpha)*100%. That is the correct interpretation and the definition of the confidence interval. But, when you have an observed dataset and construct a confidence interval from that dataset, it is not correct to interpret that there is a probability of (1 - alpha)*100% that mu is in that specific confidence interval. $\endgroup$ – John L Jan 21 at 16:24