A study on proper sample size for the use of the Central Limit Theorem on skewed distributions.

• Main Authors: Li-Sheng Hsu, 許力升
• Other Authors: Wei-Hou Cheng
• Format: Others
• Language: zh-TW
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/73567983070965855446

碩士 === 淡江大學 === 數學學系碩士班 === 98 === When we make statistical inferences about the population mean based on the sample mean , we often rely on the central limit theorem to obtain the （approximate）sampling distribution of . The central limit theorem is an asymptotic result, hence the sample size has to be sufficiently large for the application to be appropriate. Yet there does not seem to be much discussion on how large qualifies for “sufficiently large”. General suggestions have been made which include, for example, , or . But we do know that if the population distribution is very skewed, then it takes bigger sample size for the distribution of the sample mean to be close to normal distribution. We would like to explore in more details about the appropriateness of the application of the central limit theorem under these circumstances. We used computer to simulate random samples from gamma, mixed normal and Bernoulli distributions and found that when the population standard deviation is unknown and has to be replaced by the sample standard deviation, cautions have to be taken when one applies the central limit theorem and makes decisions based on the result of the inferences, because the significant levels and confidence coefficients may not be what we expected.