A computed 95% confidence interval does cover the true value with probability 0.95 if epistemically interpreted
Abstract
Suppose the lifetime of a large sample of batteries in routine use is measured. A confidence interval is computed to 394 plus/minus 1.96 times 4.6 days. The standard interpretation is that if we repeatedly draw samples and compute confidence intervals, about 95% of the intervals will cover the unknown true lifetime. What can be said about the particular interval 394 plus/minus 1.96 times 4.6 has not been clear. We clarify this by using an epistemic interpretation of probability. The conclusion is that a realised (computed) confidence interval covers the parameter with the probability given by the confidence level is a valid statement, unless there are relevant and recognisable subsets of the sample.
 Publication:

arXiv eprints
 Pub Date:
 February 2024
 DOI:
 10.48550/arXiv.2402.10000
 arXiv:
 arXiv:2402.10000
 Bibcode:
 2024arXiv240210000H
 Keywords:

 Statistics  Other Statistics
 EPrint:
 11 pages