Abstract
The normal approximation of the confidence level of the standard confidence intervals leaves an error of the order O(1/n) (and not only O(n -1/2)). We use the first order term in the error to obtain simple lower bounds for the sample size.
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Höglund, T. Bounds for the sample size to justify normal approximation of the confidence level. Ann Inst Stat Math 43, 565–578 (1991). https://doi.org/10.1007/BF00053373
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DOI: https://doi.org/10.1007/BF00053373