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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2402.10000 |
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| _version_ | 1866929244386361344 |
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| author | Hedlin, Dan |
| author_facet | Hedlin, Dan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10000 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A computed 95% confidence interval does cover the true value with probability 0.95 if epistemically interpreted Hedlin, Dan Other Statistics 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. |
| title | A computed 95% confidence interval does cover the true value with probability 0.95 if epistemically interpreted |
| topic | Other Statistics |
| url | https://arxiv.org/abs/2402.10000 |