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1、第三章样本均数的抽样误差与置信区间联系：数据 /变量在离散点或区间上 分布分布 特征数应用样本数据 x频数分布表频数分布图描述指标 (x , sx )参考值范围x1.96Sx随机变量 X概率分布表概率分布图总体参数 (,x )置信区间X ,误差 x(,x )x1.96Sx3.1样本均数的分布 从同一总体中独立抽取多份样本, 他们的均数常大小不一, 这说明样本均数存在变异。通过电脑实验来认识样本均数的变异规律一、正态总体样本均数的分布实验 3.1 从正态分布总体抽样的实验假定正常男子的红血球计数服从正态分布N(4.6602, 0.5746 2)，随机抽取1000 份样本 ,每份含 n 5 个个体
2、。样本均数依然是一个随机变量, 且(1) 各样本均数未必等于总体均数( x，误差？ )；(2) 样本均数之间存在差异 ( xa x b ， 变异 )；(3) 样本均数的分布很有规律 ,围绕着总体均数 ,中间多、两边少 ,左右基本对称(对称、正态？ ) ；(4) 样本均数的变异范围较原变量变异范围大大缩小(5) 随着样本量的增大 , 样本均数变异范围逐渐缩小( SxSx ) ；( SxSxn )。表 3_2n=5n=10n=303.74.14.54.95.35.73.74.14.54.95.35.73.74.14.54.95.35.7(a)(b)(c)图 3.1从正态分布总体抽样的实验结果原正态
3、总体N(4.6602, 0.57462)；直方图是样本均数的分布（Luo: 这里横坐标为 x ，若改为 ( x) 便是误差分布图的形状不变）实 3_1a表 3.1从 N(4.6602, 0.5746 2) 中随机抽样 ,样本量为 5, 100 份独立样本的均数、标准差和总体均数的95%置信区间 ( 单位： 10 12 /L)样本标准差样本均数标准差95% 置信区间号均数95% 置信区间号15.00.56884.2939, 5.7062514.48.40063.9827, 4.977324.72.34704.2891, 5.1509524.32.54873.6388, 5.001234.24.5
4、7633.5246, 4.9554534.88.37324.4167, 5.343444.64.59493.9014, 5.3786544.68.35244.2425, 5.117554.60.40054.1028, 5.0972554.80.58664.0717, 5.528364.80.81863.7837, 5.8163564.52.35044.0850, 4.955074.68.45024.1211, 5.2389574.88.68694.0272, 5.732884.32.82253.2989, 5.3411584.80.52324.1505, 5.449594.72.59643.9
5、796, 5.4604594.80.27944.4531, 5.1469104.40.44963.8418, 4.9582604.76.58234.0371, 5.4830114.60.56833.8944, 5.3056614.76.70833.8807, 5.6394124.60.34014.1778, 5.0222624.12.57933.4008, 4.8392134.60.66483.7746, 5.4254634.72.44194.1714, 5.2686144.76.62743.9811, 5.5389644.44.28184.0902, 4.7898154.20.68863.3
6、451, 5.0549654.921.02673.6454, 6.1947164.64.30914.2562, 5.0238664.80.71913.9073, 5.6927174.96.42234.4357, 5.4843674.72.43614.1786, 5.2614184.96.40834.4532, 5.4669684.84.58734.1109, 5.5691194.68.58753.9506, 5.4094694.36.48923.7527, 4.9673204.84.53404.1771, 5.5030704.76.33534.3437, 5.1763214.92.28524.
7、5659, 5.2741714.40.43093.8650, 4.9350224.60.45174.0392, 5.1608724.68.68803.8259, 5.5341234.44.43333.9021, 4.9779734.60.43014.0661, 5.1339244.96.37114.4993, 5.4207744.48.64113.6841, 5.2759254.64.47424.0513, 5.228775*4.16.39273.6724, 4.6476264.96.53494.2959, 5.6241764.52.54873.8388, 5.2012274.48.47783
8、.8868, 5.0732774.36.39303.8721, 4.8479284.68.38184.2061, 5.153978*5.04.20524.7853, 5.2947294.68.62893.8992, 5.4608794.56.99633.3231, 5.7969305.28.64674.4771, 6.0829804.80.62434.0249, 5.5751314.84.67244.0053, 5.674781*4.00.20903.7405, 4.2595324.52.32034.1224, 4.9176824.64.34144.2162, 5.0638334.76.584
9、14.0348, 5.4852835.04.40504.5372, 5.5428344.48.20844.2213, 4.7388844.52.53533.8555, 5.1845355.04.66464.2149, 5.8651854.44.32764.0333, 4.8467364.56.39124.0743, 5.0457864.60.37974.1287, 5.0713374.68.51834.0366, 5.3234874.48.28014.1322, 4.8278384.80.74453.8758, 5.7242884.64.24734.3330, 4.9471394.72.726
10、03.8187, 5.621389*5.32.39824.8256, 5.8144404.68.85673.6165, 5.7435904.92.34734.4888, 5.3512414.561.02413.2887, 5.8313914.72.29414.3548, 5.0852424.76.67863.9175, 5.6025924.44.42733.9096, 4.9704435.04.51764.3974, 5.6826934.48.35944.0338, 4.9262444.52.36584.0659, 4.9741944.92.44564.3668, 5.4732454.52.5
11、9443.7821, 5.2580954.64.47584.0494, 5.2306464.72.50244.0963, 5.3437964.76.85163.7027, 5.8173475.12.63544.3312, 5.9088974.64.45604.0739, 5.2061484.76.58374.0354, 5.4846984.36.33683.9419, 4.778149*4.04.35953.5937, 4.4863994.56.61973.7907, 5.3293504.52.60943.7634, 5.27661004.60.45664.0331, 5.1669* 由这份样
12、本估计的 95% 置信区间实际上并未复盖总体均数图 3_1表 3.2从 N(4.6602, 0.5746 2)中随机抽取 1000份独立样本 , 其均数的频数分布组段下限 (1012 /L)频数频率 (%)累积频率 (%)3.60-10.10.13.80-50.50.64.00-323.23.84.20-11711.715.54.40-22922.938.44.60-30430.468.84.80-21821.890.65.00-767.698.25.20-151.599.75.40-30.3100.0合计1000100.0理论上可以证明, 从正态分布N(,2)的总体中随机抽取含量为 n 的样本，其样本均数XN( ,2 /n) 。 样本均数的标准差习惯上又称为样本均数的
