How to correctly understand confidence intervals and confidence level [duplicate]

Question

I recently read an online discussion about confidence levels and confidence intervals. To be honest, I'm confused. What's the bottom line there?

For a specific statement, say,

Foobar is 3.45 (with CI = [3.08, 3.82] at 99% confidence level)

my understanding is that if the experiment/measurement is done many times by drawing different random samples, then 99% of the times, the CI deduced based on each of the random sample will contain the true value of population statistic. But what exactly does the specific CI of [3.08, 3.82] mean? Is there any positive logic statement that can be made that use [3.08, 3.82] as a parameter?

Answer 1

If, as you said, you repeat the experiment a large number of times in 99% of these excercises the true value you are estimating will be located in the confidence interval generated in that particular instance. C[3.08, 3.82] is the interval generated from that particular sample, it is a closed set containing the real numbers from 3.08 to 3.82. Confidence intervals are completely based on a frecuentist conception of probability. These can be tricky as you should definetly not think about "confindence" in terms of probabilies. You can't say things like the true value is between 3.08 and 3.82 with a probability of 0.99 because the interval will most likely change when building it upon another sample. The notion of confidence is solely what was stated before.