R软件计算题--统计学专业

.,例4.15P179（一个正态总体的区间估计）为估计一件物体的重量a，将其称了10次，得到的重量（单位：kg）为10.1,10,9.8,10.5,9.7,10.1,9.9,10.2,10.3,9.9，假设所称出物体重量服从正态分布求该物体重量a的置信系数为0.95的置信区间。,x-c(10.1,10,9.8,10.5,9.7,10.1,9.9,10.2,10.3,9.9)t.test(x)程序结果：OneSamplet-testdata:xt=131.59,df=9,p-value=4.296e-16alternativehypothesis:truemeanisnotequalto095percentconfidenceinterval:9.87722510.222775sampleestimates:meanofx10.05得到的区间估计为：9.88,10.22,.,例4.18P185(均值差的区间估计）现从生产线上随机抽取样本x1,x2，x12和y1,y2，y17，都服从正态分布，其均值分别为u1=201.1,u2=499.7，标准差分别为2.4,4.7。给定置信系数0.95，试求u1-u2的区间估计。,x-rnorm(12,501.1,2.4)y-rnorm(17,499.7,4.7)两样本方差不同t.test(x,y)程序结果：WelchTwoSamplet-testdata:xandyt=-0.6471,df=25.304,p-value=0.5234alternativehypothesis:truedifferenceinmeansisnotequalto095percentconfidenceinterval:-3.6571211.907620sampleestimates:meanofxmeanofy500.7888501.6635u1-u2的置信系数为0.95的区间估计为-3.66,1.91方差相同t.test(x,y,var.equal=TRUE),.,例4.19P186(配对数据情形下均值差的区间估计）抽查患者10名。记录下治疗前后血红蛋白的含量数据。试求治疗前后变化的区间估计。（a=0.05）。,x-c(11.3,15.0,15.0,13.5,12.8,10.0,11.0,12.0,13.0,12.3)y-c(14.0,13.8,14.0,13.5,13.5,12.0,14.7,11.4,13.8,12.0)t.test(x-y)程序结果：OneSamplet-testdata:x-yt=-1.3066,df=9,p-value=0.2237alternativehypothesis:truemeanisnotequalto095percentconfidenceinterval:-1.85728810.4972881sampleestimates:meanofx-0.68治疗前后变化的区间估计为-1.86,0.497,.,例4.22P193（一个总体求均值的单侧置信区间估计）从一批灯泡中随机地取5只作寿命试验测得寿命以小时计为10501100112012501280设灯泡的寿命服从正态分布.求灯泡寿命平均值的置信度为0.95的单侧置信下限,x-c(1050,1100,1120,1250,1280)t.test(x,alternative=greater)程序结果：OneSamplet-testdata:xt=26.003,df=4,p-value=6.497e-06alternativehypothesis:truemeanisgreaterthan095percentconfidenceinterval:1064.9Infsampleestimates:meanofx116095%的灯泡寿命在1064.9小时以上,.,习题4.6P201甲、乙两种稻种分布播种在10块试验田中，每块试验田甲、乙稻种各种一半，假设两稻种产量X,Y均服从正态分布，且方差相等，收获后10块试验田的产量如下所示（单位：千克）。求出两稻种产量的期望差u1-u2的置信区间（a=0.05).,x-c(140,137,136,140,145,148,140,135,144,141)y-c(135,118,115,140,128,131,130,115,131,125)t.test(x,y,var.equal=T)程序结果TwoSamplet-testdata:xandyt=4.6287,df=18,p-value=0.0002087alternativehypothesis:truedifferenceinmeansisnotequalto095percentconfidenceinterval:7.53626120.063739sampleestimates:meanofxmeanofy140.6126.8置信区间为7.536261,20.063739,.,习题4.7甲、乙两组生产同种导线，现从甲组生产的导线中随机抽取4根，从乙组生产的导线中随机抽取5根，它们的电阻值分别为：甲：0.143,0.142,0.143,0.137；乙：0.140,0.142,0.136,0.138,0.140；假设两组电阻值分别服从正态分布，方差相同但未知，试求u1-u2的置信系数为0.95的区间估计。,x-c(0.143,0.142,0.143,0.137)y-c(0.140,0.142,0.136,0.138,0.140)a-rnorm(4,mean(x),var(x)b-rnorm(5,mean(y),var(y)t.test(a,b)程序结果：WelchTwoSamplet-testdata:aandbt=636.28,df=5.788,p-value=3.028e-15alternativehypothesis:truedifferenceinmeansisnotequalto095percentconfidenceinterval:0.0020414400.002057343sampleestimates:meanofxmeanofy0.14124940.1392000区间为：0.00204,0.00205,.,例5.2P209（单个正态总体均值的假设检验）某种元件的寿命X（小时），服从正态分布,其中f方差和均值均未知，16只元件的寿命如下：问是否有理由认为元件的平均寿命大于255小时。,x-c(159,280,101,212,224,379,179,264,222,362,168,250,149,260,485,170)t.test(x,alternative=greater,mu=225)程序结果：OneSamplet-testdata:xt=0.66852,df=15,p-value=0.257alternativehypothesis:truemeanisgreaterthan22595percentconfidenceinterval:198.2321Infsampleestimates:meanofx241.5计算出P值为0.257大于0.05，所以，接受原假设，即认为元件的平均寿命不大于255小时,.,例5.6P221（二项分布总体的假设检验）有一批蔬菜种子的平均发芽率为P=0.85,现在随机抽取500粒，用种衣剂进行浸种处理，结果有445粒发芽，问种衣剂有无效果。,binom.test(445,500,p=0.85)程序结果：Exactbinomialtestdata:445and500numberofsuccesses=445,numberoftrials=500,p-value=0.01207alternativehypothesis:trueprobabilityofsuccessisnotequalto0.8595percentconfidenceinterval:0.85923420.9160509sampleestimates:probabilityofsuccess0.89P值=0.012070.05，拒绝原假设，认为种衣剂对种子发芽率有显著效果。,.,习题5.1P249正常男子血小板计数均值为225*109/L,今测得20名男性油漆作业工人的血小板计数值如下。问油漆工人的血小板计数与正常成年男子有无差异？,x-c(220,188,162,230,145,160,237,188,247,113,126,245,164,231,250,183,190,158,224,175)t.test(x,alternative=two.side,mu=225)程序结果：OneSamplet-testdata:xt=-3.5588,df=19,p-value=0.002096alternativehypothesis:truemeanisnotequalto22595percentconfidenceinterval:172.2743211.3257sampleestimates:meanofx191.8P值=0.0020960.05,拒绝原假设，认为油漆工人的血小板计数与正常成年男子有差异。,.,习题5.3为研究某铁剂治疗和饮食治疗营养性缺铁性贫血的效果，将16名患者按年龄、体重、病程和病情相近的原则配成8对，分别使用饮食疗法和补充铁剂治疗的方法，三个月后测得两种患者血红蛋白如表5.1所示，问两种方法治疗后的患者血红蛋白有无差异.,x0.05,接受原假设，两种方法治疗后的患者血红蛋白无差异,.,例6.2P257（回归方程的显著性检验）求例6.1的回归方程，并对相应的方程做检验。,x-c(0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.20,0.21,0.23)y-c(42.0,43.5,45.0,45.5,45.0,47.5,49.0,53.0,50.0,55.0,55.0,60.0)lm.sol|t|)(Intercept)28.4931.58018.045.88e-09*x130.8359.68313.519.50e-08*-Signif.codes:0*0.001*0.01*0.05.0.11Residualstandarderror:1.319on10degreesoffreedomMultipleR-squared:0.9481,AdjustedR-squared:0.9429F-statistic:182.6on1and10DF,p-value:9.505e-08,.,例6.4P260（预测）求例6.1中X=x0=0.16时相应的Y的概率为0.95的预测区间,new-data.frame(x=0.16)lm.pred-predict(lm.sol,new,interval=prediction,level=0.95)lm.pred程序结果：fitlwrupr49.4263946.3662152.48657预测值为49.43，预测区间46.37,52.49,.,例6.5P261（全面展示一元回归模型的计算过程）Forbes数据,X-matrix(c(194.5,20.79,1.3179,131.79,194.3,20.79,1.3179,131.79,197.9,22.40,1.3502,135.02,198.4,22.67,1.3555,135.55,199.4,23.15,1.3646,136.46,199.9,23.35,1.3683,136.83,200.9,23.89,1.3782,137.82,201.1,23.99,1.3800,138.00,201.4,24.02,1.3806,138.06,201.3,24.01,1.3805,138.05,203.6,25.14,1.4004,140.04,204.6,26.57,1.4244,142.44,209.5,28.49,1.4547,145.47,208.6,27.76,1.4434,144.34,210.7,29.04,1.4630,146.30,211.9,29.88,1.4754,147.54,212.2,30.06,1.4780,147.80),ncol=4,byrow=T,dimnames=list(1:17,c(F,h,log,log100)forbes-data.frame(X)plot(forbes$F,forbes$log100)程序结果是出现散点图,.,lm.sol|t|)(Intercept)-42.130873.33895-12.622.17e-09*F0.895460.0164554.452e-16*-Signif.codes:0*0.001*0.01*0.05.0.11Residualstandarderror:0.3789on15degreesoffreedomMultipleR-squared:0.995,AdjustedR-squared:0.9946F-statistic:2965on1and15DF,p-value:2.2e-16,.,abline(lm.sol)程序结果：得到散点图和相应的回归直线y.res|t|)(Intercept)-41.301801.00038-41.295.01e-16*F0.890960.00493180.732e-16*-Signif.codes:0*0.001*0.01*0.05.0.11Residualstandarderror:0.1133on14degreesoffreedomMultipleR-squared:0.9996,AdjustedR-squared:0.9995F-statistic:3.266e+04on1and14DF,p-value:2.2e-16,.,例6.14P292某公司为了研究产品的营销策略，对产品的销售情况进行了调查，设Y为某地区该产品的家庭人均购买量（单位：元），X为家庭收入（单位：元），表6.8给出了53个家庭的数据。试通过这些数据建立Y与X的关系。,X-scan()6792921012493582115699721891097207818181700747203016434143541276745435540874154310297101434837174813811428125517773702316113046377072480879078340612426581746468111441317873560149522211526Y-scan()0.790.440.560.792.703.644.739.505.346.855.845.213.254.433.160.500.171.880.771.390.561.565.280.644.000.314.204.883.487.582.634.990.598.194.790.511.744.103.940.963.290.443.242.145.710.641.900.518.3314.945.113.853.93,.,lm.sol|t|)(Intercept)-0.83130370.4416121-1.8820.0655.X0.00368280.000333911.0304.11e-15*-Signif.codes:0*0.001*0.01*0.05.0.11Residualstandarderror:1.577on51degreesoffreedomMultipleR-squared:0.7046,AdjustedR-squared:0.6988F-statistic:121.7on1and51DF,p-value:4.106e-15y.rst-rstandard(lm.sol);y.fit-predict(lm.sol)plot(y.rsty.fit)abline(0.1,0.5);abline(-0.1,-0.5)程序结果：画出了标准化后的残差图,.,lm.new|t|)(Intercept)5.822e-011.299e-014.4814.22e-05*X9.529e-049.824e-059.6993.61e-13*-Signif.codes:0*0.001*0.01*0.05.0.11Residualstandarderror:0.464on51degreesoffreedomMultipleR-squared:0.6485,AdjustedR-squared:0.6416F-statistic:94.08on1and51DF,p-value:3.614e-13yn.rst-rstandard(lm.new);yn.fit-predict(lm.new)plot(yn.rstyn.fit),.,习题6.1P331为估计山上积雪融化后对下游灌溉的影响，在山上建立一个观测站，测量最大积雪深度X（米）与当年灌溉面积Y（公颂），测得连续10年的数据如表6.1所示。,snow|t|)x385.515.0975.746.17e-14*-Signif.codes:0*0.001*0.01*0.05.0.11Residualstandarderror:104.6on9degreesoffreedomMultipleR-squared:0.9984,AdjustedR-squared:0.9983F-statistic:5736on1and9DF,p-value:6.169e-14,.,现测得今年的数据是X=7m，给出今年灌溉面积的预测值与相应的区间估计。（a=0.05）,4）X-data.frame(x=7)lm.pred-predict(lm.sol,X,interval=prediction,level=0.95)lm.pred#拟合新数据，并生成置信区间程序结果：fitlwrup