Comment author:Jordan
28 February 2010 01:39:30AM
0 points
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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?).

Comment author:JGWeissman
28 February 2010 02:13:15AM
2 points
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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.)

## Comments (211)

BestMy 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?).

You can treat the interval as open at 12.0 if you like; it makes no difference.

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.)

*2 points [-]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.

Thanks, that makes sense, although it still butts up closely against my intuition.