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Psy-Kosh comments on A Request for Open Problems - Less Wrong
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You can do better than that. If the distance between the two data points is 7/4, you can shrink the 100% confidence interval to 1/4, etc. (The extreme case is as the distance between the two data points approaches 2, your 100% confidence interval approaches size zero.)
EDIT: whoops, I was stupid. Corrected 3/4 to 7/4 and 1 to 2. There, now it should be right