抽样调查分层抽样实验报告

1、实验报告实验项目分层随机抽样实验日期实验地点实验目的掌握分层随机抽样及其简单估计实验内容1、掌握分层随机抽样的抽取方法及各层样本统计量的汇总方法2、掌握分层随机抽样总体均值、总体总量、总体比例的简单估计方法3、掌握分层随机抽样样本量确定及在各层的分配方法4、比估计、回归估计方法实验思考题：1、某调查员欲从某大学所有学生中抽样调查学生平均生活费支出情况，假设该调查员已经完成了抽样，并获得样本情况(见样本文件)，请根据此样本分别按性别、家庭所在地分层，并计算各层的样本量、平均生活费支出、生活费支出的方差及标准差。(1) 先对数据按照家庭所在地进行排序：【数据】T【排序】，选择“家庭所在地”(2)

2、再对数据进行分类汇总：【数据】t【分类汇总】，“分类字段”选择“家庭所在地”“汇总方式”选择“平均值”，“选定汇总项”选择“平均月生活费”，在对话框下方选择“汇总结果显示在数据下方”；再做两次分类汇总，“汇总方式”分别选择“计数”和“标准偏差”。最后得到表1-1所示结果：表1-1家庭所在地平均月生活费大型城市平均值614.5348837大型城市计数86大型城市标准偏差300.0849173乡镇地区平均值529.4117647乡镇地区计数68乡镇地区标准偏差219.0950339中小城市平均值618.6440678中小城市计数118中小城市标准偏差202.5264159总计平均值595.0367

3、647总计数272总计标准偏差243.4439223(3) 在SPSS软件中得出的计算结果:选择dialyzeCoitjpare Mears工,然后在出现的对话框中分别在“ Dependent list ”框中选入“家庭所在地”，在“ IndependentList ”框中选入“平均月生活费”，得到如表1-2所示结果：表1-2Report平均月生活费家庭所在地MeanNStd. Deviation大型城市614.5386300.085乡镇地区529.4168219.095中小城市618.64118202.526Total595.04272243.444诜择歸Bl Aggrege .，在出现的对

4、话框中选择“ function ”选择估计量，得到如图1-2所示结果：图1-1图1-2家庭所在平均月 i|平均月旦TG1453300.082乡镇地区529.41219.103中水城市618.64202.534|选择AnalyzeDes 匚 riprtig Statistics乓E炯述，出现如下图所示对话框，并按照下图1-3中所选项进行操作：得到如下图表的结果Case Processing Summary家庭所在地ValidCasesMissingTotalNPercentNPercentNPercent平均月生活费大型城市86100.0%0.0%86100.0%乡镇地区68100.0%0.0%

5、68100.0%中小城市118100.0%0.0%118100.0%Descriptives家庭所在地StatisticStd. Error平均月生活费大型城市Mean614.5332.35995% ConfidenceLower Bound550.20Interval for MeanUpper Bound678.875% Trimmed Mean592.51Median500.00Variance90050.958Std. Deviation300.085Minimum100Maximum2500Range2400Interquartile Range300.00Skewness3.116

6、.260Kurtosis17.407.514乡镇地区Mean529.4126.56995% ConfidenceLower Bound476.38Interval for MeanUpper Bound582.445% Trimmed Mean518.46Median500.00Variance48002.634Std. Deviation219.095Minimum200Maximum1000Range800Interquartile Range200.00Skewness.996.291Kurtosis.172.574中小城市Mean618.6418.64495% ConfidenceLo

7、wer Bound581.72Interval for MeanUpper Bound655.575% Trimmed Mean612.34Median600.00Variance41016.949Std. Deviation202.526Minimum200Maximum1200Range1000Interquartile Range300.00Skewness.686.223Kurtosis.168.442平均月生活费 Siem-and-Leaf Plot for 家庭所在二大型城市FrequencyStem & LeafLOO08.00036.00019.00010.00010.0011

8、.0011. 00 Ext rentes12333333344444444445555555555555555555555555566666666666666667778888888888000000000020=2500)St em width: Each leaf:10001 case(s)黎雜聲蟲氏Plot琢Frequency Stem fe Leaf2.00213.00315.00416.0057.0064.0073.0088.00 Extremes050000000000005 000000000005555 0000000000000000 000000000000000=1000

9、)Steik width: Each leaf:1001 case(s)平均月生活费 Stem-and-Leaf Plot for 家庭所在二中小城市FrequencyStem & Leaf1.008.0010.0033.0027.008.0016.003.0010.00 .002.00234567890120000000550000000005000000000000000000000000000000005 ooooooooooooooooooooooooooo oooooooo0000000000000000000000000000000Stem width:Each leaf:1001

10、 case(s)2000 1*461000 |0 -平均月生活1费3000-1000N =86大型城市家庭所在地2、教材129页第3.3题层11010202203510503020030V168118乡镇地区中小城市样本20100 103020040501020203050400300层样本1101020201001030202203510500405010202030200303050400300(1)数据结构、运用Excel的计算步骤及结果如下:层NhWhyhWh2s2Sh1 fh咛(1人)/片WhS：WhSh12560.303311.20.09294.49.7160.96090.8345

11、6885528.6331752.94702324200.497625.50.248302.517.3930.97627.312630556150.533188.65504931680.1991200.04355.618.8560.94051.32491782970.7740923.753363sum844156.70.379752.545.9652.87769.472117241249.9404415.35543总体均值估计 总体均值估计 方差总体均值估计 标准差V(yst)Wh M/N20.06789.472123.077681.04830.29614第h层的层权：WhNhN总样本量比例分配

12、185.907奈曼分配175.381比例分配奈曼分配奈曼分配层权n156.388833.659w10.192n292.512998.853w20.564n337.005142.869w30.244sum185.907175.3811nhyhyhi5 i 1第h层的样本均值:nh第h层的样本方差：s2(yhi Yh)2 /g 1)i 1v(yst)()2U /210% *20.06781.96)21.0483L总体均值估计：Y ystWh y =20.0678hh总体均值方差：L1fV(Y) ?(ysJWh2hs2h=9.472hnh下面计算两种分配方法的样本量及每层要抽的样本量:1.比例分配：

13、L2WhSh比例分配的样本量：nh Mean95%Lower BoundConfidenceUpper BoundInterval for=185.907(r Y)Mean5% Trimmed Mean N WhS2u /2N h 1比例分配的层权为：Wh Wh故：qW2n =56.3888取整得n1 =57n2W2n =92.5129取整得n2 =93W3n =37.0051取整得n3 =382.奈曼分配:L2(WhSh)2奈曼分配的样本量为:(UY)2L2WhS：=175.381L奈曼分配的层权为：wh WhSh / WhShh 1故：qW2n =33.659取整得m =34w2n =98

14、.853取整得n2 =99n3W3n =42.869取整得n3 =43(2)在SPSS中的计算均值与方差的结果如下:StatisticStd. Error11.203.0724.2518.1510.78样本DescriptivesVarianceStd. DeviationMinimumMaximumRangeInterquartile RangeSkewnessKurtosis94.4009.7160303018.50.668-.040.6871.3342样本Mean25.005.42695%Lower Bound12.72ConfidenceUpper BoundInterval for3

15、7.28Mean5% Trimmed Mean25.00Median20.00Variance294.444Std. Deviation17.159Minimum0Maximum50Range50Interquartile Range32.50Skewness.330.687Kurtosis-1.0011.3343样本Mean20.005.96395%Lower Bound6.51ConfidenceUpper BoundInterval for33.49Mean5% Trimmed Mean19.44Median25.00Variance355.556Std. Deviation18.856

16、Minimum0Maximum50Range50Interquartile Range32.50Skewness.124.687Kurtosis-1.5081.334403020100-106050403020100-106050403020100-10N =10样本N =10样本10样本3、教材130页第3.4题Whah0.1827 0.21 280.14270.0926 0.16 280.2229wh2 Phqh帀1层WhnhPhshA2WhA2qhnh 1Wh*Sh10.18270.90.090.03240.10.0001010.05420.21280.930.0622220.04410

17、.0666679.46E-050.05238330.14270.90.090.01960.16.08E-050.04240.09260.870.1155560.00810.1333333.23E-050.03059450.16280.930.0622220.02560.0666675.49E-050.03991160.22290.970.0322220.04840.0333335.38E-050.039491sum11655.50.4522220.17820.50.0003970.25838总体比例估计 总体比例估计方差0.9240.000396981比例分配层权w10.18总体比例估计标准差

18、0.019924378w20.21V2.60308E-05w30.14w40.09w50.16总样本量w60.22比例分配2662.655644奈曼分配2564.651673比例分配奈曼分配奈曼分配层权n1479.278016 535.9991w10.208995n2559.1576853 519.9509w20.202737n3372.7717902 416.8882w30.162552n4239.639008 303.6744w40.118408n5426.0249031396.1531w50.154467n6585.7842418 391.9861w60.152842SUM2662.655644 2564.6521公式：（1） 总体比例P的简单估计量：Y P, Yh Ph, yst Ph.按照总体均值估计量的公式，可推出总体比例（成数）p的估计量为:LLf?tWh 氏WhPh=0.924hh(2)总体比例P的方差为V（P；t）Ph(1 Ph)Wh2(1fh)