摘要
According to the central limit theorem, if X1, X2, …X_υ is a random sample drawn from X^2(1), then, when υ → ∞, the distribution function of the sample mean The equation is abbreviated would asymptotically approximate to N [1, 2/υ], or the distribution function of The equation is abbreviated would approximate to the standard normal distribution N(0, 1). Also, the distribution function of The equation is abbreviated would asymptotically approximate to the normal distribution N(υ, 2υ). Many statistics textbooks or applied statistics research accept the use of a sample size of υ≥ 30 for the assumption of N(υ, 2υ) approximating to The equation is abbreviated . Therefore, in the present study, computer simulation was adopted to test the required sample size υ for the normal distribution to approximate to the X^2 distribution. This information is useful for the applications of the central limit theorem.
延伸閱讀
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