On the Evaluation of Sample Size Required for a Good Approximation by the Normal Curve for Some Statistics
On the Evaluation of Sample Size Required for a Good Approximation by the Normal Curve for Some Statistics

Summary/Abstract: Testing hypotheses or evaluation confidence intervals requires knowledge of some statistics’ distributions. It is convenient if the probability distribution of the statistic converges to normal distribution when the sample size is sufficiently large. This paper examines the problem of how to evaluate sample size in order to determine that a statistic’s distribution does not depart from normal distribution by more than an assumed amount. Two procedures are proposed to evaluate the necessary sample size. The first is based on Berry-Esseen inequality while the second is based on simulation procedure. In order to evaluate the necessary sample size, the distribution of the sample mean is generated by replicating samples of a fixed size. Next, the normal distribution of the evaluated sample means is tested. The size of the generated samples is gradually increased until the hypothesis on the normality of the sample mean distribution is not rejected. This procedure is applied in the cases of statistics other than sample mean.

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