一、簡(jiǎn)答題(3*3=9分)1、試舉例說明總體和總體單位之間的關(guān)系。2、舉例說明標(biāo)志和指標(biāo)之間的關(guān)系。3、抽樣調(diào)查、重點(diǎn)調(diào)查和典型調(diào)查這3種非全面調(diào)查的區(qū)分是什么4、季節(jié)變動(dòng)的測(cè)定常用什么方法？簡(jiǎn)述其根本步驟。5、影響抽樣誤差的因素有哪些？二、宏發(fā)電腦公司在全國(guó)各地有36家銷售分公司，為了分析各公司的銷售狀況，宏發(fā)公司36家公司上個(gè)月的銷售額，所得數(shù)據(jù)如表3-4所示。(6分)表3-4 分公司銷售額數(shù)據(jù)表 〔單位：萬(wàn)元〕606062656566677071727374757676767677787879798082838484868788898990919292依據(jù)上面的資料進(jìn)展適當(dāng)分組，并編制頻數(shù)分布表。R926032K13.3lg367d32/7560為最小組的下限，其他組限利用組距依次確定。3-8所示。按銷售額分組〔萬(wàn)元〕公司數(shù)〔個(gè)〕頻率〔%〕按銷售額分組〔萬(wàn)元〕公司數(shù)〔個(gè)〕頻率〔%〕60～6538.3365～70411.1170～75513.8975～801027.7880～85513.8985～90513.8990～95411.11合計(jì)36100.0031季度生產(chǎn)狀況分析如下：119095%2250100%；3609105%3個(gè)車間產(chǎn)品產(chǎn)量的平均打算完成程度為：95%100%105%100%。另外，118元/件，2車間產(chǎn)品單位成3本為12元/件，3車間產(chǎn)品單位本錢為 15元/件，則3個(gè)車間平均單位本錢為：18121515元/件。以上平均指標(biāo)的計(jì)算是否正確？如不正確請(qǐng)說明理由并改正。(63分)答：兩種計(jì)算均不正確。打算完成程度指標(biāo)的特定含義。正確的計(jì)算方法是：m平均打算完成程度x

190250609

101.84%m 190x 0.95

2501.0

6091.05直接的影響。所以正確的計(jì)算方法為：xf

181901225015609 15555x

f

609

1049

14.83〔元/件〕四、某高校某系學(xué)生的體重資料如表4-6所示。試依據(jù)所給資料計(jì)算學(xué)生體重的算術(shù)平均數(shù)、中位數(shù)和眾數(shù)。(6分)4-6學(xué)生體重資料表按體重分組〔公斤〕學(xué)生人數(shù)〔人〕52以下2852～553955～586858～615361以上24合計(jì)212解:4-8表4-8 學(xué)生體重計(jì)算表〔公斤〕組中值(x)〔f〕xf向上累積頻數(shù)52以下50.5281414.02852～5553.5392086.56755～5856.5683842.013558～6159.5533153.518861以上62.5241500.0212合計(jì)_21211996.0_〔1〕學(xué)生平均體重：

xfxf

11996212

56.58〔公斤〕學(xué)生體重中位數(shù)：Me學(xué)生體重眾數(shù)：

fL 2

S 21267m1d55 2 356.72〔公斤〕f 68mMoLf

f f m

m1 df )(fm m1 m

m155

6839 (6839)(6853)五、假定總體為5000個(gè)單位，被爭(zhēng)論標(biāo)志的方差不小于4003，當(dāng)概率保證程度為95%時(shí)，問〔1〕承受重復(fù)抽樣需抽多少單位？〔2〕假設(shè)要求抽樣允許誤差削減50%，又需抽多少單位？(6解：n5000,

400, d3, 195%, Z/21.96

(Z/2

)221.962400170.74171個(gè)單位。d2 32

(Z/2

)221.962400682.95683個(gè)單位。d2 1.52斷裂強(qiáng)度聽從正態(tài)分布，標(biāo)準(zhǔn)差為10千克。依據(jù)標(biāo)準(zhǔn)，要求該金屬線的平均斷裂強(qiáng)度高于50055040.01性水平推斷該廠產(chǎn)品是否符合標(biāo)準(zhǔn)。(6分)解：由題意可知，這是關(guān)于總體均值的假設(shè)檢驗(yàn)問題，其檢驗(yàn)過程如下：〔1〕建立假設(shè)：H :500, H:5000 1選擇并計(jì)算統(tǒng)計(jì)量：由于總體方差，所以用Z統(tǒng)計(jì)量進(jìn)展檢驗(yàn)。x 504500/ n10/ 5Z / n10/ 5確定臨界值：由于顯著性水平0.01，所以左單側(cè)臨界值Z2.33。進(jìn)展統(tǒng)計(jì)決策：因Z0.892.33，所以不能拒絕原假設(shè)，即承受該廠產(chǎn)品符合標(biāo)準(zhǔn)。310-6(6出廠價(jià)格〔元〕產(chǎn)量產(chǎn)品計(jì)量單位表10-6 某廠出廠價(jià)格〔元〕產(chǎn)量產(chǎn)品計(jì)量單位基期報(bào)告期基期報(bào)告期A件88.51350015000B個(gè)10111100010200C公斤6540004800試分析出廠價(jià)格和產(chǎn)量變動(dòng)對(duì)總產(chǎn)值的影響。解：10-9所示的計(jì)算表。表10-9 某廠3種產(chǎn)品的價(jià)格指數(shù)和產(chǎn)量指數(shù)計(jì)算表計(jì)量 出廠價(jià)格〔元〕 產(chǎn)量 產(chǎn)值〔元〕產(chǎn)品單位

報(bào)告期q pq pq pq0 1 0 1 00 01 11A件88.51350015000108000120230127500B個(gè)10111100010200110000102023112200C公斤6540004800240002880024000合計(jì)-----242023250800263700pq

263700總產(chǎn)值指數(shù)

11pq00

242023

108.97%pqpq

26370024202321700元11 00即：該廠總產(chǎn)值報(bào)告期比基期上升了8.97%21700元。pq

250800產(chǎn)量指數(shù)

01pq00

242023

103.64%pqpq

2508002420238800元01 003.64%8800元。pq

263700出廠價(jià)格指數(shù) 11pq01

105.14%pqpq11 01

263700250800012900元即：該廠出廠價(jià)格報(bào)告期比基期上升了5.14%12900元。八、方差分析計(jì)算輸出結(jié)果如下界面解釋上表中第56行每項(xiàng)的含義，并用表達(dá)式表示；對(duì)原假設(shè)H0做出承受或拒絕的打算。(6分)或者類似于方差分析的結(jié)果中，填上缺掉的局部?jī)r(jià)值和當(dāng)年紅利：公司賬面價(jià)值 紅利 公司 賬面價(jià)值序號(hào)〔元〕序號(hào)〔元〕〔元〕序號(hào)〔元〕122.442.4912.140.80220.892.981023.311.94322.092.061116.233.00414.481.09120.560.28520.731.96130.840.84619.251.551418.051.80720.372.161512.451.21826.431.601611.331.07依據(jù)上表資料，利用Excel得到下面的回歸結(jié)果： 〔15分〕判定系數(shù)R2為多少？建立每股賬面價(jià)值和當(dāng)年紅利的回歸方程；解釋回歸系數(shù)的經(jīng)濟(jì)意義；1元，估量當(dāng)年紅利可能為多少？回歸統(tǒng)計(jì)表參數(shù)估量表 CoefficientsIntercept 參數(shù)估量表 CoefficientsIntercept 0.479775XVariable1 0.072876分析表MultipleR0.707947RSquare0.501189AdjustedRSquare0.465559標(biāo)準(zhǔn)誤差0.562775觀測(cè)值16自由度平方和方差F來(lái)自回歸14.455152DE來(lái)自殘差A(yù)C0.316716----------總計(jì)B8.889175---------------------A=14 B=15 C=4.434023 D=4.455152 E=14.06672一個(gè)電視節(jié)目主持人想了解觀眾對(duì)某個(gè)電視專題的寵愛程度，他選取了500個(gè)觀眾作樣本概率度t1.962.58概率F(t)0.950.99〔重復(fù)抽樣，結(jié)果覺察寵愛該節(jié)目的有175〔〕試以95概率度t1.962.58概率F(t)0.950.99某超市想要估量每個(gè)顧客平均每次購(gòu)物花費(fèi)的金額。依據(jù)過去的閱歷，標(biāo)準(zhǔn)差大約為12095%20元，應(yīng)抽取多少個(gè)顧客作為樣本？九、供給統(tǒng)計(jì)軟件計(jì)算結(jié)果，進(jìn)展統(tǒng)計(jì)分析。(20分)1、依據(jù)我國(guó)常用的消費(fèi)支出分類方法,人均消費(fèi)性支出分為食品、衣著、居住、家庭設(shè)備8個(gè)局部,這8個(gè)X1,X2,…,X8。31個(gè)省(市)數(shù)據(jù)如下(只列出局部樣本)地區(qū)生活消費(fèi)支出食品衣著居住家庭設(shè)備及效勞健交通和通訊教育文化消遣效勞其他商品及效勞北京7228.442420.86577.811156.6402.56709.44950.53883.35127.29天津3746.061489.65292.52699.21153.54301.06402.87324.4782.75CorrelationCorrelationMatrixCommunalitiesExtractionMethod:PrincipalComponentAnalysis.x1x2x3x4x5x6x7x8Correlationx11.000.775.913.923.815.922.866.905x2.7751.000.771.801.893.894.861.734x3.913.7711.000.900.837.889.827.812x4.923.801.9001.000.812.892.858.818x5.815.893.837.8121.000.896.862.724x6.922.894.889.892.8961.000.942.854x7.866.861.827.858.862.9421.000.798x8.905.734.812.818.724.854.7981.000KMOKMOandBartlett”sTestKaiser-Meyer-OlkinMeasureofSamplingAdequacy.Bartlett”sTestofSphericityApprox.Chi-SquaredfSig..912361.01828.000InitialExtractionx11.000.967x21.000.934x31.000.889x41.000.900x51.000.927x61.000.960x71.000.900x81.000.891Total%ofVari.Cumu.%Total%ofVari.Cumul.%Total%ofVari.Cumul.%16.95486.92486.9246.95486.92486.9243.85948.23348.2332.4145.18092.104.4145.18092.1043.51043.87192.1043.2162.70094.8034.1431.79296.5955.1161.45398.0486.075.93998.9877.050.62299.6098.031.391100.000Comp-onentInitialComp-onentInitialEigenvaluesTotalVarianceExplainedExtractionSumsofSquaredLoadingsRotationSumsofSquaredLoadingsExtractionMethod:PrincipalComponentAnalysis.ComponentMatrixaComponentExtractionMethod:PrincipalComponentAnalysis.a.2componentsextracted.12x6.978.058x1.955-.232x7.941.120x4.940-.130x3.932-.140x5.917.295x2.902.348x8.891-.313RotatedRotatedComponentMatrixaComponent12x1.853.488x2.415.873x3.773.540x4.772.552x5.463.845x6.670.715x7.600.735x8.861.386正態(tài)性檢驗(yàn)Kolmogorov-Smirnov正態(tài)性檢驗(yàn)Kolmogorov-SmirnovaShapiro-Wilk*.這是真實(shí)顯著水平的下限。多變量檢驗(yàn)c效應(yīng)值F假設(shè)df誤差dfSig.ExtractionMethod:PrincipalComponentAnalysis.RotationMethod:VarimaxwithKaiserNormalization.a.Rotationconvergedin3iterations.公司簡(jiǎn)股票代凈資產(chǎn)總資產(chǎn)資產(chǎn)負(fù)總資產(chǎn)流淌資產(chǎn)已獲利銷售增資本積行業(yè)21999酬率、總資產(chǎn)周轉(zhuǎn)率、流淌資產(chǎn)周轉(zhuǎn)率、資產(chǎn)負(fù)債率、已獲利息倍數(shù)、銷售增長(zhǎng)率和資本積存率。依據(jù)這一指標(biāo)體系對(duì)我國(guó)上市公司的運(yùn)營(yíng)狀況進(jìn)展分析，以下數(shù)據(jù)為35家上市公司202335公司簡(jiǎn)股票代凈資產(chǎn)總資產(chǎn)資產(chǎn)負(fù)總資產(chǎn)流淌資產(chǎn)已獲利銷售增資本積行業(yè)稱碼收益率酬勞率債率周轉(zhuǎn)率周轉(zhuǎn)率息倍數(shù)長(zhǎng)率累率電力、煤氣及水的生產(chǎn)和供給業(yè)深圳能源0000279.174.9253.45.391.573.562.7633.00統(tǒng)計(jì)量dfSig.統(tǒng)計(jì)量dfSig.凈資產(chǎn)收益率.15235.039.94435.077總資產(chǎn)酬勞率.13735.095.94235.064資產(chǎn)負(fù)債率.14435.065.93935.052總資產(chǎn)周轉(zhuǎn)率.23535.000.68335.000流淌資產(chǎn)周轉(zhuǎn)率.15935.026.85035.000已獲利息倍數(shù).17235.011.88035.001銷售增長(zhǎng)率.11635.200*.98235.836資本積存率.25235.000.69535.000a.Lilliefors顯著水平修正截距Pillai的跟蹤.947130.278a4.00029.000.000Wilks的Lambda.053130.278a4.00029.000.000Hotelling的跟蹤17.969130.278a4.00029.000.000Roy的最大根17.969130.278a4.00029.000.000行業(yè)Pillai的跟蹤.7124.1498.00060.000.001Wilks的Lambda.3884.387a8.00058.000.000準(zhǔn)確統(tǒng)計(jì)量該統(tǒng)計(jì)量是F準(zhǔn)確統(tǒng)計(jì)量該統(tǒng)計(jì)量是F主體間效應(yīng)的檢驗(yàn)Hotelling的跟蹤1.3174.6118.00056.000.000Roy的最大根1.0778.079b4.00030.000.000源因變量III型平方和df均方FSig.校正模型凈資產(chǎn)收益率458.258a2229.1296.841.003總資產(chǎn)酬勞率250.101b2125.05010.034.000資產(chǎn)負(fù)債率1728.665c2864.3334.515.019銷售增長(zhǎng)率9467.268d24733.6343.814.033截距凈資產(chǎn)收益率3633.32913633.329108.483.000總資產(chǎn)酬勞率1987.13211987.132159.453.000資產(chǎn)負(fù)債率71640.788171640.788374.189.000銷售增長(zhǎng)率15289.807115289.80712.321.001行業(yè)凈資產(chǎn)收益率458.2582229.1296.841.003總資產(chǎn)酬勞率250.1012125.05010.034.000資產(chǎn)負(fù)債率1728.6652864.3334.515.019銷售增長(zhǎng)率9467.26824733.6343.814.033誤差凈資產(chǎn)收益率1071.7453233.492總資產(chǎn)酬勞率398.7903212.462資產(chǎn)負(fù)債率6126.59632191.456銷售增長(zhǎng)率39711.458321240.983總計(jì)凈資產(chǎn)收益率4814.44835總資產(chǎn)酬勞率2483.79735資產(chǎn)負(fù)債率85553.31435銷售增長(zhǎng)率60514.04635校正的總計(jì)凈資產(chǎn)收益率1530.00334總資產(chǎn)酬勞率648.89134資產(chǎn)負(fù)債率7855.26134銷售增長(zhǎng)率49178.72634a.R方=.300〔調(diào)整R方=.256〕b.R方=.385〔調(diào)整R方=.347〕c.R方=.220〔調(diào)整R方=.171〕d.R方=.193〔調(diào)整R方=.142〕比照結(jié)果〔K比照結(jié)果〔K〕行業(yè)簡(jiǎn)潔比照a因變量表表3Correlation Matrix表4KMOandBartlet t”sTestKaiser-Meyer-OlkinMeasureoAdequacy.fSampling.735Bartlett”sT SphericityApprox.Chi-SquaredfSig.21.000級(jí)別1和級(jí)別 比照估算值-1.0701.317-9.215-27.8503假設(shè)值0000差分〔估量〕-1.0701.317-9.215-27.850標(biāo)準(zhǔn)誤差2.6011.5876.21915.834Sig..684.413.148.088差分的95%置信區(qū)間下限-6.368-1.915-21.883-60.102上限4.2294.5493.4534.402級(jí)別2和級(jí)別比照估算值-7.855-4.5847.286-40.9423假設(shè)值0000差分〔估量〕-7.855-4.5847.286-40.942標(biāo)準(zhǔn)誤差2.4401.4885.83414.853Sig..003.004.221.010差分的95%置信區(qū)間下限-12.825-7.616-4.598-71.197上限-2.885-1.55219.170-10.686a.參考類別=3凈資產(chǎn)收益率總資產(chǎn)酬勞率資產(chǎn)負(fù)債率銷售增長(zhǎng)率3、選取7個(gè)指標(biāo)，即固定資產(chǎn)產(chǎn)值率(X1)、固定資產(chǎn)利稅率(X2)、資金利潤(rùn)率(X3)、資金凈資產(chǎn)收益率總資產(chǎn)酬勞率資產(chǎn)負(fù)債率銷售增長(zhǎng)率利稅率(X4)、流淌資金周轉(zhuǎn)天數(shù)(X5)、銷售收入利稅率(X6)和全員勞動(dòng)生產(chǎn)率(X7)對(duì)某市15個(gè)大中型企業(yè)進(jìn)展經(jīng)濟(jì)效益分析。在SPSS中進(jìn)展因子分析得出如下結(jié)果，請(qǐng)結(jié)合表3-8答復(fù)以下問題：(20分)固定資固定資產(chǎn)資金利資金利流淌資金周銷售收入利全員勞動(dòng)產(chǎn)率(X1)利稅率(X2)潤(rùn)率(X3)稅率(X4)轉(zhuǎn)天數(shù)(X5)稅率(X6)生產(chǎn)率(X7)固定資產(chǎn)率(X1)1.000.849.865.870-.009.593.464固定資產(chǎn)利稅率(X2).8491.000.904.851-.247.908.601資金利潤(rùn)率(X3).865.9041.000.988-.099.767.337資金利稅率(X4).870.851.9881.000-.098.682.271流淌資金周轉(zhuǎn)天數(shù)(X5)-.009-.247-.099-.0981.000-.331-.384銷售收入利稅率(X6).593.908.767.682-.3311.000.530全員勞動(dòng)生產(chǎn)率(X7).464.601.337.271-.384.5301.000因子Total%ofVariancCumulative%Total%ofVariance Cumulative%Total%ofVarianceCumulative%14.64466.3e3966.3394.64466.339 66.3394.21560.21060.21021.276(a)(b)1.276(a) (b)1.70524.35884.5683.6158.78993.3564.3605.14298.4995.0901.28699.7856.013.18599.9697.002.031100.0001212固定資產(chǎn)利稅率(X2).985-.036資金利潤(rùn)率(X3).975.098資金利潤(rùn)率(X3).946.256資金利稅率(X4).959.044資金利稅率(X4).911.301固定資產(chǎn)率(X1).921.075固定資產(chǎn)率(X1).888.259固定資產(chǎn)利稅率(X2).907.385銷售收入利稅率(X6).868-.190銷售收入利稅率(X6).743.488全員勞動(dòng)生產(chǎn)率(X7) .584-.563流淌資金周轉(zhuǎn)天數(shù)(X5).05