大学【统计】- 搜题酱免费题库

设总体 X 的数学期望 mu 和方差 sigma^2 存在，X_1, X_2, ..., X_n 是 X 的样本，则下面的统计量中可作为 sigma^2 的无偏估计的是:A. 当 mu 已知时，统计量 (1)/(n) sum_(i=1)^n (X_i - mu)^2；B. 当 mu 已知时，统计量 (1)/(n-1) sum_(i=1)^n (X_i - mu)^2；C. 当 mu 未知时，统计量 (1)/(n) sum_(i=1)^n (X_i - mu)^2；D. 当 mu 未知时，统计量 (1)/(n-1) sum_(i=1)^n (X_i - mu)^2。

待并侧与系统侧频率相等时，无法实现快速准同期并列。A. 正确B. 错误

两变量关联性分析，对于相关系数说法正确的是（）A. r的取值范围[0，1]B. r的绝对值越接近0，关联程度越高C. r为总体相关系数D. r的符号代表了两变量关联的方向

某医生为了解甲、乙两法治疗抑郁症的情况，将100名随机分组，一组47人，采用甲法治疗，无效21例；一组53人，采用乙法治疗，无效23例。本题对应的四格表，a,b,c,d的值可能为（）A. 21-47-23-53B. 21-26-30-23C. 26-47-30-53D. 26-21-23-30E. 26-21-30-23

[判断题](10分)同度量因素在综合指数的编制中只起过渡或媒介作用。()A. 对B. 错

某研究欲了解某市新入学医学生专业认知现状，已知该市共有8所医学院校，现随机抽取其中3所学校，经学校校长同意后选取其中1所学校，对该校医学院新入学新生按照临床、医技、护理、康复4个专业随机抽取专业人数的20%组成研究样本，该研究运用了了哪些抽样方法？简单随机抽样分层抽样

用样本均数估计总体均数的可靠性大小时所用指标是A. σB. SC. RD. CVE. SX

[例7]在电源电压不超过200V,在 sim 240V 和超过240V三种情况下,-|||-某种电子元件损坏的概率分别为0.1,0.001和0.2.假设电源电压X服从正态分布-|||-N(220,25^2),试求:-|||-(1)该电子元件损坏的概率α;-|||-(2)该电子元件损坏时,电源电压在 sim 240V 的概率β.

一、为了了解中国税收增长的全貌,选择了Y(税收收入,亿元)作为因变量,以反映国家税收的增长,X1(国内生产总值)作为经济整体增长水平的代表,X2(财政支出,亿元)作为公共财政需求的代表,选择X3(商品零售物价指数,%)作为物价水平的代表。搜集了1978-2001统计数据见下表一。假设因变量Y与自变量X1—X3之间满足线性回归关系:._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ,._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon 其中._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon 且独立,拟合线性回归模型,研究相应的统计推断问题。要求(1)写出程序及运行结果;(2)写出方差分析表,说明Y与X1—X3之间的线性关系是否显著?(3)写出参数估计表,并说明回归参数是否显著?(4)写出回归方程,并简单解释回归系数的含义。已知2002年X1—X3观测数据为._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ,预测其税收收入._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon 的值._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ,及._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon 置信度0.95的置信区间。表一中国税收收入及相关数据年份 Y X1 X2 X31978 519.28 3624.1 1122.09 100.71979 537.82 4038.2 1281.79 102.01980 571.70 4517.8 1228.83 106.01981 629.89 4862.4 1138.41 102.41982 700.02 5294.7 1229.98 101.91983 775.59 5934.5 1409.52 101.5北京华业 0.40 34.91 20.80 6.68 374.21 0.32 65.09 0.08天地源 0.11 69.23 6.94 1.88 9.41 0.27 30.77 2.40上海实业 0.25 55.93 13.19 5.60 78.73 0.42 44.07 0.39上海多伦 0.02 50.05 5.28 0.84 20.99 0.16 49.95 0.86上海世茂 0.14 50.05 11.26 4.64 11.66 0.41 49.95 3.31上海万业 1.07 32.48 54.28 10.86 184.72 0.2 67.52 0.12外高桥 0.01 73.62 1.40 0.26 1.26 0.19 26.38 12.5黄浦置业 0.31 31.58 31.68 5.11 53.43 0.16 68.42 0.36中华企业 0.67 65.02 34.08 9.40 13.21 0.28 34.98 1.82运盛上海 0.05 14.46 46.03 3.31 4.13 0.07 85.54 2.27陆家嘴 0.40 35.34 42.03 6.37 49.63 0.15 64.66 0.26上海金丰 0.42 39.51 13.62 6.00 66.3 0.44 60.49 0.61天津地产 0.06 51.89 2.92 0.89 12.81 0.3 48.11 1.91北京天鸿 0.39 82.75 4.67 1.52 7.40 0.33 17.25 4.33北京万通 0.37 67.26 12.64 4.34 165.50 0.34 32.74 0.14浙江广厦 0.23 88.42 6.51 1.93 3.06 0.3 11.58 7.65金地集团 1.31 63.65 17.67 7.32 96.03 0.41 36.35 0.31广州东华 0.32 76.40 8.07 4.35 42.26 0.54 23.6 1.15天创置业 0.48 45.51 11.32 9.28 34.49 0.82 54.49 2.70美都控股 0.34 67.40 3.88 4.19 11.27 1.08 32.6 9.311984 947.35 7171.0 1701.02 102.81985 2040.79 8964.4 2004.25 108.81986 2090.73 10202.2 2204.91 106.01987 2140.36 11962.5 2262.18 107.31988 2390.47 14928.3 2491.21 118.51989 2727.40 16909.2 2823.78 117.81990 2821.86 18547.9 3083.59 102.11991 2990.17 21617.8 3386.63 102.91992 3296.91 26638.1 3742.20 105.41993 4255.30 36634.4 4642.30 113.21994 5126.88 46759.4 5792.62 121.71995 6038.04 58478.1 6823.72 114.81996 6909.82 67884.6 7937.55 106.11997 8234.04 74462.6 9233.56 100.81998 9262.80 78345.2 10798.18 97.41999 10682.58 82067.5 13187.67 97.02000 12581.51 89468.1 15886.50 98.52001 15301.38 97314.8 18902.58 99.2(1)代码如下:data examp1;input y x1-x3;cards;519.28 3624.1 1122.09 100.7537.82 4038.2 1281.79 102.0571.70 4517.8 1228.83 106.0629.89 4862.4 1138.41 102.4700.02 5294.7 1229.98 101.9775.59 5934.5 1409.52 101.5947.35 7171.0 1701.02 102.82040.79 8964.4 2004.25 108.82090.73 10202.2 2204.91 106.02140.36 11962.5 2262.18 107.32390.47 14928.3 2491.21 118.52727.40 16909.2 2823.78 117.82821.86 18547.9 3083.59 102.12990.17 21617.8 3386.63 102.93296.91 26638.1 3742.20 105.44255.30 36634.4 4642.30 113.25126.88 46759.4 5792.62 121.76038.04 58478.1 6823.72 114.86909.82 67884.6 7937.55 106.18234.04 74462.6 9233.56 100.89262.80 78345.2 10798.18 97.410682.58 82067.5 13187.67 97.012581.51 89468.1 15886.50 98.515301.38 97314.8 18902.58 99.2;run;proc reg data=examp1;model y=x1-x3/i;run;运行结果:(2)由方差分析表进行统计推断A. nalysis of Variance 方差分析表 B. ._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon C. 从方差分析表得出._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ; D. 线性回归关系显著性检验: ._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon E. 统计量._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ,其观测值._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon F. ._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ,拒绝._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ,认为._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon 与._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon 的线性回归关系是高度显著的. G. 另外,由方差分析表给出._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon , 也表明线性回归关系高度显著。SAS输出结果Parameter Estimates参数估计表._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon 由程序结果给出参数估计值._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ,检验假设._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ,._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon 对给出显著性水平._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ,由参数估计表最后一列检验._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon 值看出,._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ,拒绝._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ,认为._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon (._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon )对._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon 均有显著影响.(4)进一步,取置信水平._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ,由于._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ,利用表中的参数估计值和相应的标准差估计式._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ,求得._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon 的置信度95%的置信区间分别为关于._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon 的预测The REG Procedure._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon 由上表1-4行,2-5列构成的矩阵为._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ,._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ,代入得._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon --------经验回归方程对于给定._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon 的值._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ,由经验回归方程可得._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon 预测值._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon 17513令._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ,由._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon 直接计算可得tlab求._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon ._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon 结果为:827.8588._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon 的置信度为95%的置信区间._(i)=(P)_(0)+(P)_(1)(x)_(i)+(P)_(2)(X)_(12)+(P)_(3)(X)_(13)+varepsilon

1.设x1,x2,···,x1是是自参数为λ的治松分布的样本,下列统计量中,哪个不是-|||-λ的无偏估计量? ()-|||-A. X B.S C. overrightarrow (x)+(1-k)(S)^2 lt klt 1 D. (sum )_(n=1)^n(x)_(1), 其中 (sum )_(n=1)^n=1

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