1、實驗報告實驗項目分層隨機抽樣實驗日期實驗地點實驗目的掌握分層隨機抽樣及其簡單估計實驗內容1、掌握分層隨機抽樣的抽取方法及各層樣本統計量的匯總方法2、掌握分層隨機抽樣總體均值、總體總量、總體比例的簡單估計方法3、掌握分層隨機抽樣樣本量確定及在各層的分配方法4、比估計、回歸估計方法實驗思考題：1、某調查員欲從某大學所有學生中抽樣調查學生平均生活費支出情況，假設該調查員已經完成了抽樣，并獲得樣本情況(見樣本文件)，請根據此樣本分別按性別、家庭所在地分層，并計算各層的樣本量、平均生活費支出、生活費支出的方差及標準差。(1) 先對數據按照家庭所在地進行排序：【數據】T【排序】，選擇“家庭所在地”(2)

2、再對數據進行分類匯總：【數據】t【分類匯總】，“分類字段”選擇“家庭所在地”“匯總方式”選擇“平均值”，“選定匯總項”選擇“平均月生活費”，在對話框下方選擇“匯總結果顯示在數據下方”；再做兩次分類匯總，“匯總方式”分別選擇“計數”和“標準偏差”。最后得到表1-1所示結果：表1-1家庭所在地平均月生活費大型城市平均值614.5348837大型城市計數86大型城市標準偏差300.0849173鄉鎮地區平均值529.4117647鄉鎮地區計數68鄉鎮地區標準偏差219.0950339中小城市平均值618.6440678中小城市計數118中小城市標準偏差202.5264159總計平均值595.0367

3、647總計數272總計標準偏差243.4439223(3) 在SPSS軟件中得出的計算結果:選擇dialyzeCoitjpare Mears工,然后在出現的對話框中分別在“ Dependent list ”框中選入“家庭所在地”，在“ IndependentList ”框中選入“平均月生活費”，得到如表1-2所示結果：表1-2Report平均月生活費家庭所在地MeanNStd. Deviation大型城市614.5386300.085鄉鎮地區529.4168219.095中小城市618.64118202.526Total595.04272243.444詵擇歸Bl Aggrege .，在出現的對

4、話框中選擇“ function ”選擇估計量，得到如圖1-2所示結果：圖1-1圖1-2家庭所在平均月 i|平均月旦TG1453300.082鄉鎮地區529.41219.103中水城市618.64202.534|選擇AnalyzeDes 匚 riprtig Statistics乓E炯述，出現如下圖所示對話框，并按照下圖1-3中所選項進行操作：得到如下圖表的結果Case Processing Summary家庭所在地ValidCasesMissingTotalNPercentNPercentNPercent平均月生活費大型城市86100.0%0.0%86100.0%鄉鎮地區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平均月生活費大型城市Mean614.5332.35995% ConfidenceLower Bound550.20Interval for MeanUpper Bound678.875% Trimmed Mean592.51Median500.00Variance90050.958Std. Deviation300.085Minimum100Maximum2500Range2400Interquartile Range300.00Skewness3.116

6、.260Kurtosis17.407.514鄉鎮地區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平均月生活費 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)平均月生活費 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費3000-1000N =86大型城市家庭所在地2、教材129頁第3.3題層11010202203510503020030V168118鄉鎮地區中小城市樣本20100 103020040501020203050400300層樣本1101020201001030202203510500405010202030200303050400300(1)數據結構、運用Excel的計算步驟及結果如下:層NhWhyhWh2s2Sh1 fh嚀(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總體均值估計 總體均值估計 方差總體均值估計 標準差V(yst)Wh M/N20.06789.472123.077681.04830.29614第h層的層權：WhNhN總樣本量比例分配

12、185.907奈曼分配175.381比例分配奈曼分配奈曼分配層權n156.388833.659w10.192n292.512998.853w20.564n337.005142.869w30.244sum185.907175.3811nhyhyhi5 i 1第h層的樣本均值:nh第h層的樣本方差：s2(yhi Yh)2 /g 1)i 1v(yst)()2U /210% *20.06781.96)21.0483L總體均值估計：Y ystWh y =20.0678hh總體均值方差：L1fV(Y) ?(ysJWh2hs2h=9.472hnh下面計算兩種分配方法的樣本量及每層要抽的樣本量:1.比例分配：

13、L2WhSh比例分配的樣本量：nh Mean95%Lower BoundConfidenceUpper BoundInterval for=185.907(r Y)Mean5% Trimmed Mean N WhS2u /2N h 1比例分配的層權為：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奈曼分配的樣本量為:(UY)2L2WhS：=175.381L奈曼分配的層權為：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中的計算均值與方差的結果如下:StatisticStd. Error11.203.0724.2518.1510.78樣本DescriptivesVarianceStd. DeviationMinimumMaximumRangeInterquartile RangeSkewnessKurtosis94.4009.7160303018.50.668-.040.6871.3342樣本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樣本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樣本N =10樣本10樣本3、教材130頁第3.4題Whah0.1827 0.21 280.14270.0926 0.16 280.2229wh2 Phqh帀1層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總體比例估計 總體比例估計方差0.9240.000396981比例分配層權w10.18總體比例估計標準差

18、0.019924378w20.21V2.60308E-05w30.14w40.09w50.16總樣本量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層權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） 總體比例P的簡單估計量：Y P, Yh Ph, yst Ph.按照總體均值估計量的公式，可推出總體比例（成數）p的估計量為:LLf?tWh 氏WhPh=0.924hh(2)總體比例P的方差為V（P；t）Ph(1 Ph)Wh2(1fh)