A Simulation Approach to Studying Normality of Sampling Distribution

Ibrahim, S.A.

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Keywords: Normal Distribution, Sampling Distribution, Central Limit Theorem, Simulation.


The normality of sampling distribution is crucial for statistical inference; and sampling distribution is the source of all
knowledge in statistical analysis. In this article, sampling distributions of means for normal and uniform distributions were
studied using a simulation approach. Data used were simulated from R software. It was found that the mean of the sampling
distribution of means for all sample size n considered for each distribution were in a neighborhood of the true population
mean with a little bias. It was also found that the standard deviation (also called standard error) of sampling distribution of
means agree quite closely with the formula based estimate, and standard error decreased as sample size n increased for both
distributions considered. Finally, it was observed that the histogram visualized the meaning of Central Limit Theory and the
shape of the sampling distribution of means approximate normal for each sample size n and for the population distributions
considered. Since the sampling distribution of means is approximately normal, this justifies the use of statistical procedure
based on normal distribution theory to estimate confidence intervals of 
even when working with non-normal data.