Taking skewness into consideration when applying the Central Limit Theorem

• Main Authors: Hsin-Chieh Wong, 翁新傑
• Other Authors: Wei-Hou Cheng
• Format: Others
• Language: zh-TW
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/33497105000547600709

碩士 === 淡江大學 === 數學學系碩士班 === 100 === When applying the central limit theorem on statistical inference, sample size n has to be large, but different text books give different suggestions on how large the sample size should be. We observed that the skewness of the population plays an important role in this matter. When the distribution of the population is very skewed, it takes a bigger sample size for the distribution of the sample mean X.bar to get close to the normal distribution. In this paper we are interested in the problem of testing H_0:μ=μ_0vs.H_1:μ>μ_0. In Li-Sheng Hsu’s master’s thesis he noted that when the population standard deviation is unknown and has to be replaced by the sample standard deviation, the probability of a Type I error is often a lot smaller than the designated α of 0.05. In this paper we want to take skewness into consideration and try to cut down the difference between the actual and designated significant levels. Edgeworth expansion was used and we were successful in making adjustments to the critical value to achieve our goal, shown by the results of computer simulations.