Because once you have collected the data there is nothing random.
is either 0 or 1.
can be .95...
The is a rv, is not.
This is why we make up this term confidence, it is NOT a probability interval.
NOW a prediction interval is something different. That new observation is random
and there is a probability associated with that event.
BUT is a constant. It may be unknown, but unless you're a Bayesian, ew, it's constant.
The point of the first paragraph is the strong law of large numbers.
IF WE resample over and over again, then approximately 95 percent (or what ever is your [tex]1-\alpha/math])
wewill contain that unknown constant about that many times.
I had my students do that with 100 samples of 100 exponentials last year.
The intervals contained 93-97 precent of the time quite often.
It was a nice example.
I first made them generate 100 U(0,1) then transform them to Exp( ) rvs.
Then obtain one 95% CI for and repeat.
Finally count how many contained .