Question: When calculating one-sided confidence (or tolerance) intervals from the formula X + kS, the value of k (Table A.4.2) for 50% confidence for any percentile

When calculating one-sided confidence (or tolerance) intervals from the formula X + kS, the value of k (Table A.4.2) for 50% confidence for any percentile

(except the median) differs from the equivalent percentile of the unit normal distribution. For example, when estimating the 95%ile with n = 20 data, k = 1.6712, only becoming the unit normal percentile (1.6449) for infinite sample size. Can you explain this?

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