抽樣調(diào)查2(共8頁(yè))

1、實(shí) 驗(yàn)（實(shí)訓(xùn)）報(bào) 告項(xiàng) 目 名 稱 簡(jiǎn)單(jindn)隨機(jī)抽樣(三)，分層抽樣 所屬(sush)課程名稱 抽樣調(diào)查(chu yn dio ch) 項(xiàng) 目 類 型 綜合性實(shí)驗(yàn) 實(shí)驗(yàn)(實(shí)訓(xùn))日期 2015年 5月 13日 班 級(jí) 14應(yīng)用統(tǒng)計(jì)C 學(xué) 號(hào) 姓 名 指導(dǎo)教師 羅 季 浙江財(cái)經(jīng)大學(xué)教務(wù)處制實(shí)驗(yàn)(shyn)名稱: 簡(jiǎn)單(jindn)隨機(jī)抽樣(三)，分層抽樣實(shí)驗(yàn)(shyn)目的: 編寫R程序解決簡(jiǎn)單隨機(jī)抽樣及分層抽樣中的統(tǒng)計(jì)問(wèn)題實(shí)驗(yàn)要求: 解題，編寫R程序，實(shí)現(xiàn).調(diào)查某個(gè)地區(qū)的養(yǎng)牛頭數(shù)，以村作為抽樣單元。根據(jù)村的海拔高度和人口密度劃分成四層，每層取10個(gè)村作為樣本單元，經(jīng)過(guò)調(diào)查獲得下列數(shù)據(jù)層

2、村總數(shù)樣本村養(yǎng)牛頭數(shù)1 2 3 4 5 6 7 8 9 10 12341411470525581499743 84 98 0 10 44 0 124 13 050 147 62 87 84 158 170 104 56 160228 262 110 232 139 178 334 0 63 22017 34 25 34 36 0 25 7 15 31 要求：估計(jì)該地區(qū)養(yǎng)?？傤^數(shù)及其估計(jì)量的變異系數(shù)。求分層隨機(jī)抽樣的設(shè)計(jì)效應(yīng)。若樣本量不變采用Neyman分配可以減少方差多少？某鄉(xiāng)欲估計(jì)今年的小麥總產(chǎn)量，全縣共實(shí)驗(yàn)過(guò)程:一，(1)N1-1411N2-4705N3-2558N4-14997y1-c(

3、43,84,98,0,10,44,0,124,13,0)y2-c(50,147,62,87,84,158,170,104,56,160) y3-c(228,262,110,232,139,178,334,0,63,220)y4-c(17,34,25,34,36,0,25,7,15,31) N-N1+N2+N3+N4W1-N1/NW2-N2/NW3-N3/NW4-N4/Nybar1-mean(y1)ybar2-mean(y2)ybar3-mean(y3)ybar4-mean(y4)ybar-W1*ybar1+W2*ybar2+W3*ybar3+W4*ybar4Y-N*ybarY1 1353572

4、VY-(N1*(N1-n)*var(y1)/n+(N2*(N2-n)*var(y2)/n+(N3*(N3-n)*var(y3)/n+(N4*(N4-n)*var(y4)/nSY-sqrt(VY)/YSY1 0.09098019估計(jì)(gj)該地區(qū)養(yǎng)牛總頭數(shù)1353572及其估計(jì)量的變異系數(shù)0.09098019(2)N1-1411N2-4705N3-2558N4-14997y1-c(43,84,98,0,10,44,0,124,13,0)y2-c(50,147,62,87,84,158,170,104,56,160) y3-c(228,262,110,232,139,178,334,0,63,22

5、0)y4-c(17,34,25,34,36,0,25,7,15,31) N-N1+N2+N3+N4W1-N1/NW2-N2/NW3-N3/NW4-N4/Nybar1-mean(y1)ybar2-mean(y2)ybar3-mean(y3)ybar4-mean(y4)ybar-W1*ybar1+W2*ybar2+W3*ybar3+W4*ybar4vybar-(W12*var(y1)+W22*var(y2)+W32*var(y3)+W42*var(y4)/10-(W1*var(y1)+W2*var(y2)+W3*var(y3)+W4*var(y4)/Nvsrs=(N-10)/(10*(N-1)*(

6、W12*var(y1)+W22*var(y2)+W32*var(y3)+W42*var(y4)-(W12*var(y1)+W22*var(y2)+W32*var(y3)+W42*var(y4)/10+W1*ybar2+W2*ybar2+W3*ybar2+W4*ybar2-ybar2+vyabr)deff-vybar/vsrsdeff1 1.011586 (3)y1-c(43,84,98,0,10,44,0,124,13,0) y2-c(50,147,62,87,84,158,170,104,56,160) y3-c(228,262,110,232,139,178,334,0,63,220) y

7、4-c(17,34,25,34,36,0,25,7,15,31) N1-1411 N2-4705 N3-2558 N4-14997 N-N1+N2+N3+N4n-40n1-n*N1*sd(y1)/(N1*sd(y1)+N2*sd(y2)+N3*sd(y3)+N4*sd(y4)n2-n*N2*sd(y2)/(N1*sd(y1)+N2*sd(y2)+N3*sd(y3)+N4*sd(y4)n3-n*N3*sd(y3)/(N1*sd(y1)+N2*sd(y2)+N3*sd(y3)+N4*sd(y4) n4-n*N4*sd(y4)/(N1*sd(y1)+N2*sd(y2)+N3*sd(y3)+N4*sd

8、(y4) w1-N1/N w2-N2/N w3-N3/N w4-N4/Nybar1-mean(y1) ybar2-mean(y2) ybar3-mean(y3) ybar4-mean(y4) ybar-w1*ybar1+w2*ybar2+w3*ybar3+w4*ybar4Y-N*ybar v-(w12*var(y1)/4+w22*var(y2)/12+w32*var(y3)/14+w42*var(y4)/10)-(1/N)*(w1*var(y1)+w2*var(y2)+w3*var(y3)+w4*var(y4)v1 23.40882第一(dy)小題的方差是vybar-(W12*var(y1)+

9、W22*var(y2)+W32*var(y3)+W42*var(y4)/10-(W1*var(y1)+W2*var(y2)+W3*var(y3)+W4*var(y4)/NVbar1 27.065952,方差可以(ky)減少：27.06595-23.40882=3.65713第二(d r)題有123個(gè)村，按簡(jiǎn)單隨機(jī)抽樣抽取13個(gè)村作為樣本，取得資料如下：樣本村去年的小麥產(chǎn)量（百斤）今年的小麥產(chǎn)量（百斤）12345678910111213550720150010206209809281200135017506707291530610780160010306001050977144015702210

10、9808651710若已知去年(qnin)的小麥總產(chǎn)量為128200（百斤），采用比估計(jì)法估計(jì)今年(jnnin)的小麥總產(chǎn)量和置信度為95%的置信區(qū)間;采用回歸估計(jì)(gj)法估計(jì)今年的小麥總產(chǎn)量和置信度為95%的置信區(qū)間;比較兩種估計(jì)方法的精確度。Q-function(Yr,sd,alpha)u-qnorm(1-alpha/2)q1-Yr-u*sdq2-Yr+u*sdQ-c(q1,q2)x-c(550,720,1500,1020,620,980,928,1200,1350,1750,670,729,1530)y-c(610,780,1600,1030,600,1050,977,1440,157

11、0,2210,980,865,1710)xbar-mean(x)ybar-mean(y)N-123n-13X-128200varx-var(x)vary-var(y)R-ybar/xbarYrbar-R*Xsxy-cov(x,y)f-n/Nvaryrbar-(1-f)*(varx+R2*vary-2*R*sxy)/nvarYrbar-N2*varyrbarsd-sqrt(varYrbar)alpha-0.05u-qnorm(1-alpha/2)C-Q (Yrbar,sd,alpha)1 133950.5 157937.0總量估計(jì)量為145943.8，置信區(qū)間為133950.5 157937.0

12、（2）Q-function(Yr,sd,alpha)u-qnorm(1-alpha/2)q1-Yr-u*sdq2-Yr+u*sdQ-c(q1,q2)x-c(550,720,1500,1020,620,980,928,1200,1350,1750,670,729,1530)y-c(610,780,1600,1030,600,1050,977,1440,1570,2210,980,865,1710)N-123n-13f-n/NX-128200 xbar-mean(x)ybar-mean(y)Xbar-X/Nvarx-var(x)vary-var(y)sxy-cov(x,y)a-sxy/varxyl

13、r-ybar+a*(Xbar-xbar)Ylr-N*ylrse-sqrt(n-1)*(vary-a*sxy)/(n-2)vYlr-N2*(1-f)*se2/nsd-sqrt(vYlr)alpha-0.05u-qnorm(1-alpha/2)C-Q(Ylr,sd,alpha) 1 138552.4 153337.8，置信區(qū)間為138552.4 153337.8（3）比估計(jì)(gj)：Yrbar= 145943.8，sd= 6119.111回歸估計(jì)：Ylbar=145945.1，sd= 3771.863回歸估計(jì)(gj)比比估計(jì)精度更高。某縣欲調(diào)查某種農(nóng)作物的產(chǎn)量，由于平原和山區(qū)的產(chǎn)量有差別，故擬劃分

14、平原和山區(qū)兩層采用分層抽樣。同時(shí)當(dāng)年產(chǎn)量與去年產(chǎn)量之間有相關(guān)關(guān)系，故還計(jì)劃采用比估計(jì)(gj)方法。已知平原共有120個(gè)村，去年總產(chǎn)量為24500（百斤），山區(qū)共有180個(gè)村，去年總產(chǎn)為21200（百斤）。現(xiàn)從平原用簡(jiǎn)單隨機(jī)抽樣抽取6個(gè)村，從山區(qū)抽取9個(gè)村，兩年的產(chǎn)量資料如下： 平原 山區(qū)樣本去年產(chǎn)量（百斤）當(dāng)年產(chǎn)量（百斤）123456 2041438225627519821016075280300190樣本去年產(chǎn)量（百斤）當(dāng)年產(chǎn)量（百斤）123456789137189119631031071596387150200125601101001807590 試用分別比估計(jì)與聯(lián)合比估計(jì)分別估計(jì)當(dāng)年(d

15、ngnin)的總產(chǎn)量，給出估計(jì)量的標(biāo)準(zhǔn)誤，并對(duì)上述兩種結(jié)果進(jìn)行比較和分析。第三(d sn)題x1-c(204,143,82,256,275,198)x2-c(137,189,119,63,103,107,159,63,87)y1-c(210,160,75,280,300,190)y2-c(150,200,125,60,110,100,180,75,90)N1-120X1-24500n1-6f1-n1/N1N2-180X2-21200n2-9f2-n2/N2xbar1-mean(x1)xbar2-mean(x2)ybar1-mean(y1)ybar2-mean(y2)R1-ybar1/xbar1

16、R2-ybar2/xbar2varx1-var(x1)varx2-var(x2)vary1-var(y1)vary2-var(y2)sxy1-cov(x1,y1)sxy2-cov(x2,y2)Yrs-sum(ybar1*X1/xbar1,ybar2*X2/xbar2)a-N12*(1-f1)*(vary1+R12*varx1-2*R1*sxy1)/n1b-N22*(1-f2)*(vary2+R22*varx2-2*R2*sxy2)/n2vyrs-sum(a,b)sd-sqrt(vyrs)1 751.4072得到(d do)當(dāng)年總產(chǎn)量的估計(jì)量Yrs為48206.45，估計(jì)量的標(biāo)準(zhǔn)差為751.40

17、72（2）x1-c(204,143,82,256,275,198)x2-c(137,189,119,63,103,107,159,63,87)y1-c(210,160,75,280,300,190)y2-c(150,200,125,60,110,100,180,75,90)N1-120X1-24500n1-6f1-n1/N1N2-180X2-21200n2-9f2-n2/N2X-sum(X1,X2)xbar1-mean(x1)xbar2-mean(x2)ybar1-mean(y1)ybar2-mean(y2)varx1-var(x1)varx2-var(x2)vary1-var(y1)vary2-var(y2)sxy1-cov(x1,y1)sxy2-cov(x2,y2)