统计学考点

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1、统计学考点（统计推断）一、选择正确的统计方法二、软件操作1、一台自动包装奶粉的包装机，其额定标准为每袋净重0.5 kg。某天开工时，随机抽取了 10 袋产品，称得其净重为：0.497, 0.506, 0.509, 0.508, 0.497, 0.510，0.506, 0.495, 0.502, 0.507。在显著水平a = 0.05下，检验该天包装机的重量设定是否正确？H :日=0.5 H :日卫 0.5 a = 0.05-1双侧检验，否定区，%05/2,9zN/MeanStd.DeviationStd. Error Mean净重10/ .50370| .005539.001752One-Sa

2、mple Statistics样本标准差-一样本标准误样备容量样*平均数Test Value = 0.5AdfSig. (2-tailed)Mean Difference95% ConfidenceInterval of the DifferenceLowerUpper逢重2.1129.064/.003700-.00026.00766区间One-Sample Test总体平均数与Q. S 差数的此%的置信自由度喜春哮席营口样本平均数应的两尾面初与Q. S的差数2、新车的平均首次故障里程数是汽车的一个主要可靠性指标。现测得甲、乙两种品牌轿车的首次故障里程数数据如下：甲品牌 XI： 1200, 1

3、400, 1580, 1700, 1900乙品牌 X2： 1100, 1300, 1800, 1800, 2000, 2400问：能否据此判定乙品牌轿车的平均首次故障里程高于甲品牌?H :日一日2 0 H :日一日 0012112a = 0.05t = （土一如 一 ,u= ndSs_1X1一 X2:11sJ+, s 2 =eV nn e12x 一 x122（n 一 1）s2 + （n 一 1）s21122-n + n 2左侧检验，否定区t t0.05,9样本不均数l/leanStcl.DeviationStd. Error MenPair 甲2.330/ 102.0022一321乙.7501

4、01.7890.5胡7Paired Samples StatisticsPaired Samples TestNCorrelationSig.Pairl 中&乙10.795.006ciuO nsPaired Differences/ tdfSig. (2-tailed)MeanStd.DeviationStcl. Error Mearx.95% Confidence Interval of the DifferenceLowerUpperPairl中-乙/1.58001.23003890 .7001245994.0629.003差数革均数差数平均数标准差差数为数标准误4、某大型连锁超市为研究各

5、种促销方式的效果，每种促销方式选择4个门店对包装食品进 行了4个月的试验。试验结果如下：促销方式与上年同期相比（）* （广告宣传）104.895.5104.2103.0a2（有奖销售）112.3107.1109.299.2A3 （特价销售）143.2150.3184.7154.5A4（买送一）145.6111.0139.8122.7超市管理部门希望了解：不同促销方式对销售量是否有显著影响?哪种促销方式的效果最好？单个方向方差分析的原理:H :目=目=目=目 H :日、目、目、目不全相等0123411234a = 0.05SS（总变异平方和）=SS（组间平方和）+ SSE（组内平方和） 总变异自

6、由度=组间自由度+组内自由度 总变异自由度=16 -1 = 15 组间自由度=4 -1 = 3 组内自由度=（4 -1）04 = 12SSA 组间自由度（3）组内均方MSE二SSE组内自由度（12）MSAF= mse，1=组间自由度（3），口2=组内自由度（12）F 孔05。）,否定,否则接受。多重比较的方法：最小显著差数法国法）第i个平均数与第j个平均数的显著性水平为0.05的最小显著差数浇2.05 =2,组内自由度景七_ = Mse（1+1）,第i个平均数与个平均数差数标准误i j LSD 时，无与无.在0.05下差异显著,否则不显著。(li促W式(J：促丰肪式Uan Difference

7、 (l-Ji/Std ErrorSig-95% Confidence IntervalLower BoundUpper Bound厂告宣传有奖销售-5 07508.9127.580-24 49414 344恃街肖售-56 3OOI0&9127.0001-75.719-3S.S81亲f-27 9Oo/*8.9127.009-47.319-S 481有奖销售广告宣传5 0708.9127.580-14 34424 494持价销售-51 N如*8.9127.0-70 644-31 SOE买-22也S护8.9127.025-42.244-3.406恃价销售广告宣传畔加*8.9127.00036.881

8、75.719有奖销售5t.2250ft8.9127.00031.80670.344亲f名 4000fr8.9127.0088 9S147.S19买一送一厂告宣传121 9000*8.9127cog8.48147 319有奖销售22 8250*8.9127.0253.40642.244恃佛肖售/-28 4000*8.9127.008-47.819-8.981e mean difference is significant at the 05 lew数此%置信区间总体平均数如总体平均却9旅置信区间Descriptives/MeanStd.DeviationError95% Confidetice

9、I literal for MeanMinimumFvlaimumLower BoundUpper Bound广告宣传4101.875 4.31642 157795.008108.742l 95.5/104.8有奖销售4106.9506.59082.796498.054116.84699.2112.3特价销售4158.17518.28809 1440129.075187.275/143.2184.7买T4129.77515.84817.9241104.557154.993 /111.0145.6Total124 1941 25.601916.4005110 561137 8395.61 184

10、.7销售量同比样本标准误Sum of SquaresdfMean SquareFSig.Between GroupsWithin GroupsTotals/7925.3971906.4739831.8691 3)2G41.799158.873/ 6 一 628.000销售量同比Multiple Comparison;均数差数样本平均数差数标准误5、有四个品牌的彩电在五个地区销售，为分析彩电的品牌因素A）和销售地区（因素B）对销 售量是否有影响，对每个品牌在各地区的销售量取得以下数据，见下表。试分析品牌和销售 地区对彩电的销售量是否有显著影响？不同品牌的彩电在各地区的销售量数据品牌（因素B1b2

11、b3b4B5365350343340323345368363330333358323353343308288280298260298销售地区（因素B ）平2和Tests of Betwee n-Subjects Effects _自由度 、方实际H值对应甲右边的面积Dependent Variabfe;品牌间变毕地区间变4随机误差一Sourceype III Sum of SquaresMea?i SquareFSiq.Corrected ModelInterceptTP-DQ-ErrorTotalCorrected Total15016.2503215758805013004.5502011

12、.7002872.7002175477.00017888.95020192145.17921575880504334.850502.925239.392/89619012.79518.1082.101.001.000.000.144/ a- R Squared = .839 (Adjusted R Squared = .746) pj !总变异1.品牌总体平均数9盛的置信区间Dependent Variable:品牌ManStq Error95% Confidence IntervalLower BoundUpper BoundA131.200J 6.919329.124359.276A234

13、7.8006.919332.724362.876A3337.0006.919321.924352.076A4/284.800/ 6.919269.724299.876样本车均数样未标准误Dependent Variabl销售量销售地区MeanStd. Error95% Confidence IntervalLower BoundUpper BoundB1339.0007.736322.144355.856B2330.2507.736313.394347.106B3339.2507.736322.394356.106B4318.2507.736301.394335.106B5315.5007.7

14、36298.644332.356Multiple ComparisonsDependent VariablehSLSD(I) 品牌(J) 品牌Mean Difference (I-J)Std. ErrorSig.95% Confidence InteavLower BoundUpper BoundA1A2-3.609.786.719-24.9217.72A37.209.786.476-14.1228.52A459.40*9.786.00038.0880.72A2A13.609.786.719-17.7224.92A310.809.786.291-10.5232.12A463.00*9.786.

15、00041.6884.32A3A1-7.209.786.476-28.5214.12A2-10.809.786.291-32.1210.52A452.20*9.786.00030.8873.52A4A1-59.40*9.786.000-80.72-38.08A2-63.00*9.786.000-84.32-41.68A3-52.20*9.786.000-73.52-30.88Based on observedeans.*. The mean difference is significant at the .05 level.Multiple ComparisonsDependent Vari

16、ables售S LSD(I) h售地区(J) h售地区Mean Difference (I-J)Std. ErrorSig.95% Confidence Interv1 ower BoundUpper BoundB1B28.7510.941.439-15.0932.59B3-.2510.941.982-24.0923.59B420.7510.941.082-3.0944.59B523.5010.941.053-.3447.34B2B1-8.7510.941.439-32.5915.09B3-9.0010.941.427-32.8414.84B412.0010.941.294-11.8435.8

17、4B514.7510.941.202-9.0938.59B3B1.2510.941.982-23.5924.09B29.0010.941.427-14.8432.84B421.0010.941.079-2.8444.84B523.7510.941.051-.0947.59B4B1-20.7510.941.082-44.593.09B2-12.0010.941.294-35.8411.84B3-21.0010.941.079-44.842.84B52.7510.941.806-21.0926.59B5B1-23.5010.941.053-47.34.34B2-14.7510.941.202-38

18、.599.09B3-23.7510.941.051-47.59.09B4-2.7510.941.806-26.5921.09Based on observedeans.Estimated Marginal Means of 销售量Estimated Marginal Means of 销售量603- - - - 00 4 2 0 83 3 3 2sna&m LsnbEAmEstimated Marginal Means of 销售量603如3203003sna&m LHnbLAm decm-LLSE6、在研究我国人均消费水平的问题中，把全国人均消费额记为y ,把人均国民收入记为x。直我国人均国

19、1民收入与人均消费金额数据单位：元我们收集到19811993年的样本数据（土, y,）,i 1,2,.,13，数据见下表，试作分析。年份I民 收入消费金额1981393.82491982419.142671983460.862891984544.113291985668.294061986737.734511987859.975131200.00一1000.00一年份人均I民收入人均消费金额人均消费额800.00600.00400.00200.00 一1988198919901991199219931068.81169.21250.71429.51725.92099.5643690713803

20、9471148300.00600.00900.001200.001500.001800.002100.00人均国民收入Model 、Sum of SquaresMean SquareSiq.1Regression944762.61944762.58854.954_000a离回 esidual2004.33611182.212/总变一otal946766.912/a. rredidors: (Constail)r 人均国民收入b. Dependent Vari able: A 均消费额Descriptive StatisticstleanStd.DeviationN人均国民收入 人均消费额/0.

21、7308572.92315315443528,886531313样本伞均数样本蠕准差人均国 民收入人均消河天均国民收人 Pearson Correlation1Sig. (2-tailed).000N1313人均消费额Pearson Correlation.999fc)1Sig. (2-tailed)J&dON/ 1313Correlationsorrelation is significant at the 0.01 level (2-tails相关系数Coefficients3ModelUnstandardizedCoefficientsStandardized Coefficientst

22、Siq._a_Std. ErrorBeta1(Constant)8.1210.650.000人均国民收入C52.007.99972.007.000回归截距a. Dependentvariable: A均消费额 回归系数7、某高尔夫球场在过去几个月里高尔夫运动者有20%是女性，为增加女性运动者比率，球 场以特价方式吸引女性运动者，一周以后，一个400名运动者所组成的样本中，300名为男 性，100名为女性。能否得出结论认为球场的女性运动者比率上升了（ a =0.05）。8、对两个大型企业青年工人参加技术培训的情况进行调查，调查结果如下：甲厂：调查50 人，18人参加技术培训。乙厂：调查查40人，14人参加技术培训。能否根据以上调查结果认 为乙厂工人参加技术培训的人数比例高于甲厂（a =0.05）。