Minimum Sample Size Ensuring Validity of Classical Confidence Intervals for Means of Skewed and Platykurtic Distributions

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Abstract
COCHRAN (1953) and BARTCH (1957) gave formulae for the magnitude of the sample size (n) ensuring the validity of the limiting normal distribution of the sample mean x(n) obtained from a non‐normal distribution with marked asymmetry and kurtosis.These formulae have been checked empirically in this paper using (a) simulated data with given asymmetry and kurtosis and (b) real data gathered from a coronary heart disease study. We find that our results are in general agreement with Bartch's formula. However, in a number of cases, the asymptotic normal distribution is attained for smaller sample size than that required by Bartch's formula.