Confidence interval - why not porbability

[bobo2]

Wikipedia: "the confidence level represents the frequency (i.e. the proportion) of possible confidence intervals that contain the true value of the unknown population parameter"

Some say the following is incorrect:
The chance that the true population value is in the confidence interval is the confidence level.

Why is it incorrect?
Is it only the issue that the real value is not a random variable?

 

[Karabiner]

Personally, I found this explanation helpful: https://statmodeling.stat.columbia.edu/2016/11/23/abraham-lincoln-confidence-intervals/

With kind regards

Karabiner

 

[bobo2]

Thanks you Karabiner, this a very good explanation!

 

[obh]

So can you say that the chance that the true population value is in the true confidence interval is the confidence level,
but since we know only the estimate confidence interval, we won't get the exact confidence level (as a probability)?

 

[Dason]

What exactly would you mean by "true confidence interval"?

 

[obh]

You calculate the confidence interval beasted on the estimate mean and estimate standard deviation (for example)
If you would know the mean and the population's standard deviation you may say that
"The chance that the true population value is in the confidence interval is the confidence level"

But of course the egg and the chicken ...
In this case, what I called the "confidence interval" is actually something a bit else because you know the exact mean ...

PS, A good example for the original question, if you calculate the CI twice and get the following result:
sample1: [10,20]
sample2: [10.1,19.7]
You can't say that the probability that the mean is inside the CI is 0.95 in both cases.