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单击此处编辑母版标题样式,第五节 正态总体均值与方差的区间估计,一、单个总体的情况,二、两个总体的情况,一、单个总体 的情况,由上节例2可知:,1.,包糖机某日开工包了12包糖,称得质量(单位:克)分别为506,500,495,488,504,486,505,513,521,520,512,485.假设重量服从正态分布,解,附表2-1,例,1,附表2-2,查表得,推导过程如下:,解,有一大批糖果,现从中随机地取16袋,称得重量(克)如下:,设袋装糖果的重量服从正态分布,试求总体均值,附表3-1,例,2,就是说估计袋装糖果重量的均值在500.4克与507.1克之间,这个估计的可信程度为95%.,这个误差的可信度为95%.,解,附表3-2,例,3,(续例1)如果只假设糖包的重量服从正态分布,推导过程如下:,根据第六章第二节定理二知,2.,进一步可得:,注意,:在密度函数不对称时,习惯上仍取对称的分位点来确定置信区间(如图).,(,续例,2),求例2中总体标准差,的置信度为0.95的置信区间.,解,代入公式得标准差的置信区间,附表4-1,附表4-2,例,4,解,例,5,(,续例,1),二、两个总体 的情况,讨论两个整体总体均值差和方差比的估计问题.,推导过程如下:,1.,例,6,为比较,两种型号步枪子弹的枪口速度,随机地取,型子弹10发,得到枪口速度的平均值为,随机地取,型子弹20发,得枪口速度平均值为,假设两总体都可认为近似,地服从正态分布,且由生产过程可认为它们的方差,相等,求两总体均值差,信区间.,解,由题意,两总体样本独立且方差相等(但未知),推导过程如下:,2.,根据,F,分布的定义,知,解,例,7,研究由机器,A,和机器,B,生产的钢管内径,随,机抽取机器,A,生产的管子 18 只,测得样本方差为,均未知,求方差比,区间.,设两样本相互独,抽取机器,B,生产的管子 13 只,测,得样本方差为,立,且设由机器,A,和机器,B,生产的钢管内径分别服,从正态分布,信,小结,附表2-1,标准正态分布表,z,0,1,2,3,4,5,6,7,8,9,0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0,1.1,1.2,1.3,1.4,1.5,1.6,0.5000,0.5398,0.5793,0.6179,0.6554,0.6915,0.7257,0.7580,0.7881,0.8159,0.8413,0.8643,0.8849,0.9032,0.9192,0.9332,0.9452,0.5040,0.5438,0.5832,0.6217,0.6591,0.6950,0.7291,0.7611,0.7910,0.8186,0.8438,0.8665,0.8869,0.9049,0.9207,0.9345,0.9463,0.5080,0.5478,0.5871,0.6255,0.6628,0.6985,0.7324,0.7642,0.7939,0.8212,0.8461,0.8686,0.8888,0.9066,0.9222,0.9357,0.9474,0.5120,0.5517,0.5910,0.6293,0.6664,0.7019,0.7357,0.7673,0.7967,0.8238,0.8485,0.8708,0.8907,0.9082,0.9236,0.9370,0.9484,0.5160,0.5557,0.5948,0.6331,0.6700,0.7054,0.7389,0.7703,0.7995,0.8264,0.8508,0.8729,0.8925,0.9099,0.9251,0.9382,0.9495,0.5199,0.5596,0.5987,0.6368,0.6736,0.7088,0.7422,0.7734,0.8023,0.8289,0.8531,0.8749,0.8944,0.9115,0.9265,0.9394,0.9505,0.5239,0.5636,0.6026,0.6406,0.6772,0.7123,0.7454,0.7764,0.8051,0.8315,0.8554,0.8770,0.8962,0.9131,0.9278,0.9406,0.9515,0.5279,0.5675,0.6064,0.6443,0.6808,0.7157,0.7486,0.7794,0.8078,0.8340,0.8577,0.8790,0.8980,0.9147,0.9292,0.9418,0.9525,0.5319,0.5714,0.6103,0.6480,0.6844,0.7190,0.7517,0.7823,0.8106,0.8365,0.8599,0.8810,0.8997,0.9162,0.9306,0.9430,0.9535,0.5359,0.5753,0.6141,0.6517,0.6879,0.7224,0.7549,0.7852,0.8133,0.8389,0.8621,0.8830,0.9015,0.9177,0.9319,0.9441,0.9545,1.645,z,0,1,2,3,4,5,6,7,8,9,1.6,1.7,1.8,1.9,2.0,2.1,2.2,2.3,2.4,2.5,2.6,2.7,2.8,2.9,3.0,0.9452,0.9554,0.9641,0.9713,0.9772,0.9821,0.9861,0.9893,0.9918,0.9938,0.9953,0.9965,0.9974,0.9981,0.9987,0.9463,0.9564,0.9648,0.9719,0.9778,0.9826,0.9864,0.9896,0.9920,0.9940,0.9955,0.9966,0.9975,0.9982,0.9990,0.9474,0.9573,0.9656,0.9726,0.9783,0.9830,0.9868,0.9898,0.9922,0.9941,0.9956,0.9967,0.9976,0.9982,0.9993,0.9484,0.9582,0.9664,0.9732,0.9788,0.9834,0.9871,0.9901,0.9925,0.9943,0.9957,0.9968,0.9977,0.9983,0.9995,0.9495,0.9591,0.9671,0.9738,0.9793,0.9838,0.9871,0.9904,0.9927,0.9945,0.9959,0.9969,0.9977,0.9984,0.9997,0.9505,0.9599,0.9678,0.9744,0.9798,0.9842,0.9878,0.9906,0.9929,0.9946,0.9960,0.9970,0.9978,0.9984,0.9998,0.9515,0.9608,0.9686,0.9750,0.9803,0.9846,0.9881,0.9909,0.9931,0.9948,0.9961,0.9971,0.9979,0.9985,0.9998,0.9525,0.9616,0.9693,0.9756,0.9808,0.9850,0.9884,0.9911,0.9932,0.9949,0.9962,0.9972,0.9979,0.9985,0.9999,0.9535,0.9625,0.9700,0.9762,0.9812,0.9854,0.9887,0.9913,0.9934,0.9951,0.9963,0.9973,0.9980,0.9986,0.9999,0.9545,0.9633,0.9706,0.9767,0.9817,0.9858,0.9890,0.9916,0.9936,0.9952,0.9964,0.9974,0.9981,0.9986,1.0000,1.96,附表2-,2,标准正态分布表,附表3-1,=0.25,0.10,0.05,0.025,0.01,0.005,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1.0000,0.8165,0.7649,0.7407,0.7267,0.7176,0.7111,0.7064,0.7027,0.6998,0.6974,0.6955,0.6938,0.6924,0.6912,0.6901,3.0777,1.8856,1.6377,1.5332,1.4759,1.4398,1.4149,1.3968,1.3830,1.3722,1.3634,1.3562,1.3502,1.3450,1.3406,1.3368,6.3138,2.9200,2.3534,2.1318,2.0150,1.9432,1.8946,1.8595,1.8331,1.8125,1.7959,1.7823,1.7709,1.7613,1.7531,1.7459,12.7062,4.3027,3.1824,2.7764,2.5706,2.4469,2.3646,2.3060,2.2622,2.2281,2.2010,2.1788,2.1604,2.1448,2.1315,2.1199,31.8207,6.9646,4.5407,3.7469,3.3649,3.1427,2.9980,2.8965,2.8214,2.7638,2.7181,2.6810,2.6503,2.6245,2.6025,2.5835,63.6574,9.9248,5.8409,4.6041,4.0322,3.7074,3.4995,3.3554,3.2498,3.1693,3.1058,3.0545,3.0123,2.9768,2.9467,2.9208,分布表,2.1315,=0.25,0.10,0.05,0.025,0.01,0.005,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1.0000,0.8165,0.7649,0.7407,0.7267,0.7176,0.7111,0.7064,0.7027,0.6998,0.6974,0.6955,0.6938,0.6924,0.6912,0.6901,3.0777,1.8856,1.6377,1.5332,1.4759,1.4398,1.4149,1.3968,1.3830,1.3722,1.3634,1.3562,1.3502,1.3450,1.3406,1.3368,6.3138,2.9200,2.3534,2.1318,2.0150,1.9432,1.8946,1.8595,1.8331,1.8125,1.7959,1.7823,1.7709,1.7613,1.7531,1.7459,12.7062,4.3027,3.1824,2.7764,2.5706,2.4469,2.3646,2.3060,2.2622,2.2281,2.2010,2.1788,2.1604,2.1448,2.1315,2.1199,31.8207,6.9646,4.5407,3.7469,3.3649,3.1427,2.9980,2.8965,2.8214,2.7638,2.7181,2.6810,2.6503,2.6245,2.6025,2.5835,63.6574,9.9248,5.8409,4.6041,4.0322,3.7074,3.4995,3.3554,3.2498,3.1693,3.1058,3.0545,3.0123,2.9768,2.9467,2.9208,2.2021,附表3-,2,分布表,附表4-2,=0.995,0.99,0.975,0.95,0.90,0.75,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,0.010,0.072,0.207,0.412,0.676,0.989,1.344,1.735,2.156,2.603,3.074,3.565,4.075,4.601,5.142,
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