What a 95% confidence interval really claims

Question

State precisely what a 95% confidence interval means, and name the most common ways it is misinterpreted.

Accepted Answer

Definition. A confidence interval is built by a procedure applied to random data. A 95\% confidence interval is a random interval [L(	ext{data}), U(	ext{data})] such that, over repeated sampling, \mathbb{P}\big(L \le 	heta \le U\big) = 0.95, where the interval is random and the true parameter 	heta is a fixed, unknown constant. The guarantee is about the method: if you repeated the experiment many times and formed an interval each time, about 95\% of those intervals would contain the true 	heta. Common misconceptions. 1. "There is a 95\% probability the true value lies in this interval."…

What a 95% confidence interval really claims

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