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

.