本論文之目的是要建造母體比例(依據所觀測到的成功次數和總試驗 次數)之最佳(optimum)信賴區間. 此處 "最佳" 意指: 1. 信賴係數 愈接近先前訂定的(pre-fixed)信賴水準愈好. 2. 信賴區間的寬度愈短 愈好 3. 信賴區間符合三個特性: 對稱性(symmetricity), 端點的單調 性(monotonicity of the end-points), 和寬度的凹性 (concavity of the width). 首先, 我們回顧以中央極限定理這種漸近( approximate)的方法而造的信賴區間.一般來說, 這種以漸近方法所得到 的信賴係數小於我們先前訂定的信賴水準.然後我們回顧Clopper 和 Pearson 提出的變換法(inversion method);並進一步詳加探討 Sterne- Crow,Blyth-Still 和 Casella 等人的研究結果. 最後,我們製作了一 個信賴區間表, 試驗次數是從 1 到 50, 信賴水準是90%, 95% 和99%. The purpose of this thesis is to construct optimum confidence intervalsfor the populaion proportion for each observed number of successes and totalnumber of trials. "Optimum" is in the sense that: 1. The confidence coefficients are as close to the pre-fixed confidence levels as possible. 2.e widths of the intervals are as short as possible. 3. The intervals satisfy the three properties: symmetricity, monotonicity of the end-points, and concavity of the width. We first review the approximate methods of construction confidence intervalsusing the Central Limit Theorem. The approximate methods generally give confidence coefficients lower than the pre-fixed confidence levels. We then review the confidence intervals constructed by the inversion method of Clopper and Pearson. The results by Sterne-Crow, Blyth-Still and Casella are reviewedin some details. Finally, we compiled a table for the total numbers of trials from 1 to 50at three confidence levels 90%, 95% and 99%.
