例 6.6.7easy一级题目发布者: ai-batch题干对某事件 AAA 作 120 次观察，AAA 发生 36 次。试给出事件 AAA 发生概率 ppp 的 0.95 置信区间。答案点击展开后可查看解析解析此处 n=120n = 120n=120，xˉ=36/120=0.3\bar{x} = 36/120 = 0.3xˉ=36/120=0.3，而 u0.975=1.96u_{0.975} = 1.96u0.975=1.96，于是 ppp 的 0.95（双侧）置信下限和上限分别为 p^L=0.3−1.96×0.3×0.7120=0.218,\hat{p}_L = 0.3 - 1.96 \times \sqrt{\frac{0.3 \times 0.7}{120}} = 0.218,p^L=0.3−1.96×1200.3×0.7=0.218, p^U=0.3+1.96×0.3×0.7120=0.382,\hat{p}_U = 0.3 + 1.96 \times \sqrt{\frac{0.3 \times 0.7}{120}} = 0.382,p^U=0.3+1.96×1200.3×0.7=0.382, 故所求的近似置信区间为 [0.218, 0.382][0.218,\; 0.382][0.218,0.382]。