A graphical approach for verification of the central limit theorem
Suresh Kumar Veluchamy · Digital Scholarship - UNLV (University of Nevada Reno) · 2019
The distribution of the sample mean, when sampling from a normally distributed population, is known to be normal. When sampling is done from a non-normal population, the above result holds when the number of samples (n) is sufficiently large. This important result is known as the Central Limit Theorem (CLT). The CLT plays a very important role in statistical inference. The logical question that arises is: how large does n have to be before the CLT can be used? No one answer is available in the statistical literature, since n depends on the extent of nonnormality present in the underlying population. A rule of thumb given in almost every introductory applied statistics text is that n = 30 is sufficient for most cases. In this thesis, the method of bootstrap is used to develop a graphical approach to determine if the CLT will be valid for any given random sample. A computer program in C#.NET is developed and Monte Carlo simulation is used to demonstrate the program.