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A statistical tolerance interval bounds a stated proportion of the population, not just its mean. The half-width is k x sample standard deviation, where k exceeds the normal z-score for the coverage because the mean and standard deviation are themselves estimated from a finite sample. k shrinks towards z as sample size grows.
Tolerance interval
Limits = mean +/- k x s, with k inflated above the normal z-score for finite sample size
A confidence interval bounds the population mean. A tolerance interval bounds where individual future observations will fall, which is what matters for specification setting.
With 10 observations the standard deviation estimate is itself uncertain, so the interval must be widened to retain coverage. Published k-factor tables should be used where the interval has contractual weight.