《样本容量的选取》PPT课件

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第五节样本容量的选取二、Z检验法的OC函数三、t检验法的OC函数一、施行特征函数四、小结 一、施行特征函数在一些实际问题中,我们除了希望控制犯第I类错误的概率外,往往还希望控制犯第II类错误的概率.以上在进行假设检验时,总是根据问题的需要,预先给出显著性水平以控制犯第I类错误的概率,而犯第II类错误的概率则依赖于样本容量的选择.在本节中,我们将阐明如何选取样本的容量使得犯第II类错误的概率控制在预先给定的限度内,为此,引入施行特征函数. 施行特征函数的定义:施行特征函数的作用:适当地选取样本的容量,的概率控制在预先给定的限度内.使得犯第II类错误 二、Z检验法的OC函数1.右边检验问题 此OC函数的图形如下:此OC函数的性质如下: 犯第II类错误的概率不超过给定的就能使犯第II类错误的概率不超过给定的 2.左边检验问题就能使犯第II类错误的概率不超过给定的 3.双边检验问题 此OC函数的图形如下:就能使犯第II类错误的概率不超过给定的 例1(工业产品质量抽验方案)设有一大批产品,解 三、t检验法的OC函数1.右边检验问题 错误的概率不超过犯第II类 2.左边检验问题犯第II类错误的概率不超过给定的 3.双边检验问题犯第II类错误的概率不超过给定的 例2 解附表5-1附表5-2 解例3附表5-3 4.求样本容量的一种近似方法怎样确定所需样本容量? 否则再按上述方法重复进行.一般,容量n.只需试少数几次就可以得到所求的样本 5.两个正态总体均值差的t检验问题当分别自两个总体取得的相互独立的样本容量可以查附表8得到所需的样本容量. 当分别自两个总体取得的相互独立的本容量.可以查附表8得到所需的样误的概率小于或等于犯第II类错 例4需比较两种汽车用的燃料的辛烷值,则使用燃料A.解燃料的辛烷值越高,料A价格便宜,因此,因燃料B较燃如果两者辛烷值相同时,使用燃料B.但若含量的均值差设两总体的分布均可认为是正态的,而两个样本相互独立.则燃料质量越好.问应采用那种燃料?得数据 所取的样本容量水平为0.1的F检验知:犯第II类错误的概率不超过经附表5-4 现n=12,故已近似地满足要求.右边检验的拒绝域为由样本观察值算得补充例题 右边检验左边检验双边检验四、小结两种检验法的OC函数如表 0.050.100.150.200.250.300.350.400.450.500.550.600.650.700.750.800.850.900.951.0012270139101451229771329072522410170554019805544331565453627135438302211463226199392822178342419158302117137271915126241714116211513105191411951813118599128641199045109886734117846851269367544121765444341863453728155338322413463327211240292419103526211693122191592821171382519161272317141172116131061399011563109854710185663711081685330906655432575554636216347393118554134271647353024144231272113372824191233252117112923191610272118149251916139110134781259958115977745927762371007563513083635342267153453622614639312053403428174736302516413227221437292420133426221812312420171128221916100.050.100.150.200.250.300.350.400.450.500.550.600.650.700.750.800.850.900.951.000.50.20.10.050.010.50.20.10.050.010.50.20.10.050.010.50.20.10.050.01显　　　著　　　性　　　水　　　平单边检验双边检验附表5-1均值的t检验的样本容量13返回 0.050.100.150.200.250.300.350.400.450.500.550.600.650.700.750.800.850.900.951.0012270139101451229771329072522410170554019805544331565453627135438302211463226199392822178342419158302117137271915126241714116211513105191411951813118599128641199045109886734117846851269367544121765444341863453728155338322413463327211240292419103526211693122191592821171382519161272317141172116131061399011563109854710185663711081685330906655432575554636216347393118554134271647353024144231272113372824191233252117112923191610272118149251916139110134781259958115977745927762371007563513083635342267153453622614639312053403428174736302516413227221437292420133426221812312420171128221916100.050.100.150.200.250.300.350.400.450.500.550.600.650.700.750.800.850.900.951.000.50.20.10.050.010.50.20.10.050.010.50.20.10.050.010.50.20.10.050.01显　　　著　　　性　　　水　　　平单边检验双边检验附表5-2均值的t检验的样本容量返回0.01 附表5-3均值的t检验的样本容量0.050.100.150.200.250.300.350.400.450.500.550.600.650.700.750.800.850.900.951.0012270139101451229771329072522410170554019805544331565453627135438302211463226199392822178342419158302117137271915126241714116211513105191411951813118599128641199045109886734117846851269367544121765444341863453728155338322413463327211240292419103526211693122191592821171382519161272317141172116131061399011563109854710185663711081685330906655432575554636216347393118554134271647353024144231272113372824191233252117112923191610272118149251916139110134781259958115977745927762371007563513083635342267153453622614639312053403428174736302516413227221437292420133426221812312420171128221916100.050.100.150.200.250.300.350.400.450.500.550.600.650.700.750.800.850.900.951.000.50.20.10.050.010.50.20.10.050.010.50.20.10.050.010.50.20.10.050.01显　　　著　　　性　　　水　　　平单边检验双边检验返回68 附表5-4均值的t检验的样本容量单边检验双边检验显　　　著　　　性　　　水　　　平0.010.050.10.20.50.010.050.10.20.50.010.050.10.20.50.010.050.10.20.51.11.21.31.41.51.61.71.81.92.02.12.22.32.42.53.03.54.0241916149211614128181513118161312107151211971311108612109861210986119876108875108779876977687768776766565562116141281814121071613119614111096131098612109751198710877108769776876687658667667666555181311961512108514109712987118761087697658768667657676656651511971310861187610875976866865767566651.11.21.31.41.51.61.71.81.92.02.12.22.32.42.53.03.54.08返回