What "95% coverage" says about your one interval

Question

You run 100 independent experiments and build a 95% confidence interval from each. A colleague asks two things: "About how many of these cover the true parameter?" and "For the one specific interval I'm looking at, is there a 95% chance it covers the truth?" Answer both, and explain why the two questions have different kinds of answers.

Accepted Answer

How many cover the truth. Coverage is a property of the procedure: each interval independently has a 95\% chance of covering the true parameter, so out of 100 you expect about 95 to cover it (the count is roughly Binomial(100, 0.95), so typically 93 to 97). "About 95" is the right answer. The one specific interval. Once a particular interval is computed, the randomness is gone. The true parameter is a fixed number, and the realized interval either contains it or it does not, there is no 95\% left to attach to that single fixed interval. The 95\% lived in the procedure before the data were see…

What "95% coverage" says about your one interval

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