# Interpretaton of confidence interval

I have read two books that explicitly state that the $(1-\alpha)$% confidence interval should be interpreted as:

If you construct 100 such confidence intervals, $\alpha$ of them are expected to not contain the true population statistic and $(1-\alpha)$ of them are expected to contain the true population statistic.

and not as

There is a $(1-\alpha)$% probability that the true population statistic is contained in the confidence interval.

In my view, they both equivalent: If you make the first statement, you implicitly make the second statement. You are looking at any one arbitrary confidence interval, which in itself is a random variable, the generic confidence interval should, therefore, be subject to the second statement. Do things change when this random variable is actually realized?

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I struggled with this concept for quite a while, but an intuitive explanation for it I found on Wikipedia (as background context a $95\%$ confidence interval of the number of voters voting for a particular party was found to be $[36\%,44\%])$:
I think confidence intervals are better understood in the following way. There is an infinite set of constant open intervals. Some of them cover the population statistic $\theta$ and some of them don't. Now the (random) confidence interval is just a mechanism to draw an interval from this set. So the $(1-\alpha)\%$ is the chance of picking a constant interval that covers $\theta$. But whatever interval is drawn (or realized), since each of these interval is constant, the probability that it contains $\theta$ can only be $0$ or $1$.