matlab的参数估计与假设检验

1、参数估计与假设检验1 .常见分布的参数估计mm）如从某工厂生产的滚珠中随机抽取10个，测得滚珠的直径（单位下：2 5.14.8115.1115.2615.0815.1715.1214.9515.0514.87滚珠直径服从正太分布，但是N （ ,2）不知道。（90%勺置信区间）x=15.1414.8115.1115.2615.0815.1715.1214.9515.0514.87;muhat,sigmahat,muci,sigmaci=normfit(x,0.1)muhat =15.0560sigmahat =0.1397muci =14.975015.1370sigmaci =0.10190.

2、2298二、总体标准差知道时的单个正态总体均值的U检验。1.某切割机正常工作时，切割的金属棒的长度服从正态分布N (100,4)从该切割机的一批金属棒中随机抽取十五根，测得他们的长度如下：02100103.假设总体方差不变，试检验该切割机工作是否正常，及总体均值是否等于 100mm?取显著水平=0.05.假设如下：H0:=0=100, H1:0利用MATLAB里面的ztest函数:x=97 102 105 112 99 103 102 94 100 95 105 98 102 100 103 h,p,muci,zval=ztest(x,100,2,0.05)h =1 %h=1代表拒绝原假设P

3、=0.0282%muci =100.12102.1455zval =2.1947那么是否H0:0,H1: 0x=97 102 105 112 99 103 102 94 100 95 105 98 102 100 103h,p,muci,zval=ztest(x,100,2,0.05, ' right ' )h =1p =0.0141muci =100.2839Infzval =2.1947拒绝H0,接受H1。即认为总体均值大于100.三、总体标准差未知时的单个正态总体的t检验（ttest）。例：化肥厂用自动包装机包装肥料，某日测得9包化肥的质量（单位：kg）如下：49.450

4、.550.751.749.847.949.251.448.9设每包化肥的质量服从正太分布，是否可以认为每包的平均质量为50kg?取显著水平=0.05假设：H0:=0=50, H1:0x=49.450.550.751.749.847.949.251.448.9 ;h,p,muci,stats=ttest(x,50,0.05)h =0p =0.8961muci =48.994350.8945stats =tstat:-df:0.1348%t检验统计量的观测值t8% t检验统计量的自由度sd:1.2360%样本标准差 x5 / 1419.3四、总体标准差未知时的两个正态总体的均值比较t检验例：甲、乙

5、两台机床加工同一产品，这两台机床加工的产品中随机抽取若干件，测得直径为(单位：mm)为：甲机床：20 .120.020.219.919.320.620.219.919. 119.9已机床：18 .619.120.020.020.019.719.919.620. 2设甲、乙两个机床加工的产品的直径服从正态分布N(1,12)和 N(2,2),试比较甲、乙两个机床加工产品的直径是否有显著差别.取显著水平为0.05假设：2H0:12,H1:1.1 2x=20.120.620.219.920.019.919.11.9 9 ;y=18.619.120.020.020.019.719.919.620.2;a

6、lpha=0.05;tail='both'7/ 14vartype='equal'h,p,muci,stats=ttest2(x,y,alpha,tail,vartype)h =0p =0.3191muci =-0.23460.6791stats =tstat:1.0263df:17sd:0.4713接受H02检验五、总体均值未知时的单个正态总体方差的根据第三个例子的化肥的方差是否等于1.10 取显著水平0.05假设：H0: 28 / 14448.9;1.5,H1: 202x=49.450.550.751.749.847.949.251.448.9;var0=1

7、.5 ;alpha=0.05;tail=both '；h,p,varci,stats=vartest(x,var0,alpha,tail)x=49.450.550.751.749.847.949.251.var0=1.6 ;alpha=0.05;tail='both'h,p,varci,stats=vartest(x,var0,alpha,tail)h =0p =0.83varci =0.69705.6072stats =chisqstat:8.1481df:8%8受F检验六、总体均值未知时的两个正态总体方差的比较取第四个例子，比较甲与乙的产品的方差是否一样?假设：H0

8、:10 / 1420.022,H1:1222x=20.120.019.320.620.219.920.019.919.119.9 ;y=18.619.120.020.019.719.919.620.2;alpha=0.05;tail= both ;h,p,varci,stats=vartest2(x,y,alpha,tail)x=20.120.019.320.620.219.920.019.919.119.9 ;y=12 / 1418.619.120.020.020.019.719.919.620.2;alpha=0.05;tail='both'h,p,varci,stats=vartes