A computed 95% confidence interval does cover the true value with probability 0.95 if epistemically interpreted

Dan Hedlin

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arXiv · 2402.10000

A computed 95% confidence interval does cover the true value with probability 0.95 if epistemically interpreted

Dan Hedlin

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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.

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Dan Hedlin. 2024-02-15. A computed 95% confidence interval does cover the true value with probability 0.95 if epistemically interpreted. https://arxiv.org/abs/2402.10000

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