When is <i>n</i> large enough? Looking for the right sample size to estimate proportions

The central limit theorem indicates that when the sample size goes to infinite, the sampling distribution of means tends to follow a normal distribution; it is the basis for the most usual confidence interval and sample size formulas. This study analyzes what sample size is large enough to assume that the distribution of the estimator of a proportion follows a Normal distribution. Also, we propose the use of a correction factor in sample size formulas to ensure a confidence level even when the central limit theorem does not apply for these distributions.中心极限定理（Central Limit Theorem）指出，当样本量趋于无穷大时，样本均值的抽样分布将趋近于正态分布；该定理是当前最常用的置信区间与样本量计算公式的理论基础。本研究分析了何种样本规模足以保证比例估计量的分布服从正态分布。此外，本研究提出在样本量计算公式中引入校正因子，以确保即便中心极限定理不适用于此类分布时，仍能达到预设的置信水平。