Award Date

1-1-2007

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Committee Member

Ashok K. Singh

Number of Pages

67

Abstract

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.

Keywords

Approach; Central; Graphical; Limit; Theorem; Verification

Controlled Subject

Statistics

File Format

pdf

File Size

1003.52 KB

Degree Grantor

University of Nevada, Las Vegas

Language

English

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