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JGWeissman comments on What is Bayesianism? - Less Wrong
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My intuition would be that the interval should be bounded above by 12 - epsilon, since the probability that we got one component that failed at the theoretically fastest rate seems unlikely (probability zero?).
If by epsilon, you mean a specific number greater than 0, the only reason to shave off an interval of length epsilon from the high end of the confidence interval is if you can get the probability contained in that epsilon-length interval back from a smaller interval attached to the low end of the confidence interval. (I haven't work through the math, and the pdf link is giving me "404 not found", but presumably this is not the case in this problem.)
Thanks, that makes sense, although it still butts up closely against my intuition.
The link's a 404 because it includes a comma by accident -- here's one that works: http://bayes.wustl.edu/etj/articles/confidence.pdf.