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单选题在对服从正态分布的参数区间估计中,计算得置信度为0.95的置信区间为,那么我们就可以以0.95的置信度估计样本均值的观测值与参数的最大误差为( )

A. 10

B. 2.5

C. 5

D. 不确定,与观测值的大小有关

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学科：默认课程

时间：2025-12-25 00:36:04

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来自正态总体<img src="https://tihai-oss-cloud.itihey.com/img/d8cfc62eabce9fc22349afae4c96dfa6.png">,容量为400的简单随机样本,样本均值为45,则未知参数<img src="https://tihai-oss-cloud.itihey.com/img/ed1f4d3c386f168f6dd71edf78235307.png">的置信度为0.95的置信区间是<img src="https://tihai-oss-cloud.itihey.com/img/bbcf92bcc8fd13a7ef2490bc8c98df33.png"> ( )

A. [44,46]B. [44.804,45.196]C. [44.8355,45.1645]D. [44.9,45.1]

设总体<img src="https://tihai-oss-cloud.itihey.com/img/fd09698e60aab2d201fbf944514a3389.png">,<img src="https://tihai-oss-cloud.itihey.com/img/ed1f4d3c386f168f6dd71edf78235307.png">已知,通过样本<img src="https://tihai-oss-cloud.itihey.com/img/fa326f4906d7e812b00e841263e997ec.png">,求总体方差<img src="https://tihai-oss-cloud.itihey.com/img/2304db35180e3519bae5ef21b7d91262.png">的置信区间,采用的样本的函数为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/38f54fca9814ccad2fbdd2ca9d640a98.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/9a2400f338eae3c7076383bc83514227.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/d631713661254bf6cb4db0a40c1fb8d1.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/558ff453029fd8fd28b2c13b8d45f3c6.png">

设<img src="https://tihai-oss-cloud.itihey.com/img/70ad9331521c8fa20314a78b80484ca6.png">是来自区间<img src="https://tihai-oss-cloud.itihey.com/img/3649960dc92192cf34961a7cf678adb5.png">上的均匀分布总体<img src="https://tihai-oss-cloud.itihey.com/img/e22a13f7edcffe98b7a922d3fe5be3b8.png">的样本,则下列结论正确的是( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/66e40071e70d45e529df34c37d4573a0.png">是参数<img src="https://tihai-oss-cloud.itihey.com/img/142ef139a8c5575b3688ddbd70049d88.png">的无偏估计B. <img src="https://tihai-oss-cloud.itihey.com/img/2025f195b4206855c3926bcaf0bf7f9e.png">是参数<img src="https://tihai-oss-cloud.itihey.com/img/142ef139a8c5575b3688ddbd70049d88.png">的相合估计C. <img src="https://tihai-oss-cloud.itihey.com/img/142ef139a8c5575b3688ddbd70049d88.png">的极大似然估计是无偏估计D. <img src="https://tihai-oss-cloud.itihey.com/img/142ef139a8c5575b3688ddbd70049d88.png">的矩估计估计不是无偏估计

设<img src="https://tihai-oss-cloud.itihey.com/img/9a28e8682c1901865dd6bffe9444b512.png">是来自总体的样本,则下列关于总体均值的无偏估计哪一个最有效( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/6bcd3f68528db41618e7757134c91326.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/9677acc424ca37caa6cd9f92b98982d7.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/fb8ec2857f6a75896c234983c5e482c7.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/ebcf81d7c832fb67b22dd3be55ddd185.png">

关于极大似然估计法求解估计量说法正确的是( )

A. 一定可以用微积分求极值的方法求出解B. 可能用微积分求极值的方法是无解的C. 不可以先代入样本值再求极值D. 以上说法都不对

设<img src="https://tihai-oss-cloud.itihey.com/img/57c9e99f8d3e3c11df77d7f3490fbefd.png">,现从总体中抽出一个样本<img src="https://tihai-oss-cloud.itihey.com/img/4aa9d1e85463a4827c073a0adcc0f65f.png">,则<img src="https://tihai-oss-cloud.itihey.com/img/2304db35180e3519bae5ef21b7d91262.png">的极大似然估计量是( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/624849580ef767685da61bf43818c5fb.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/6fc37af15ae87066a70f1a3e48622eb2.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/1d1fcbf680eb8cb245dea770d47b7949.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/4c27a33a41e66297b094968a6e11ef33.png">

设<img src="https://tihai-oss-cloud.itihey.com/img/e9b0211d3c728768b19c60f76e78533c.png">,<img src="https://tihai-oss-cloud.itihey.com/img/69a48fefd33cd6160c31522a819600e5.png">未知,现从总体中抽出一个样本<img src="https://tihai-oss-cloud.itihey.com/img/b11a203d304d0199df1330fd8d2a43d8.png">,则<img src="https://tihai-oss-cloud.itihey.com/img/69a48fefd33cd6160c31522a819600e5.png">的矩估计量是( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/e583a331e21dbe16f3d7824fbf6516c9.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/3375ba0d30c5a0f0c0f86916d3604dd8.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/624849580ef767685da61bf43818c5fb.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/bc0caf98fb110dff0810a9343e3dc05f.png">

设总体<img src="https://tihai-oss-cloud.itihey.com/img/ed92de234b0efe6d05907a2cc6e1f1ab.png">,<img src="https://tihai-oss-cloud.itihey.com/img/78b543be91c83eab3e7b95a5bf9dd01b.png">,<img src="https://tihai-oss-cloud.itihey.com/img/bbc5a053be546d11a650ca13afee3830.png">未知,通过样本<img src="https://tihai-oss-cloud.itihey.com/img/7f1bbe1ce346b766dd86295fe73a2038.png"> <img src="https://tihai-oss-cloud.itihey.com/img/f039d7c339aa874fdd5cabc344fd0826.png">,对<img src="https://tihai-oss-cloud.itihey.com/img/78c185734d36a87a5acf982bf4b313b7.png">做置信水平为<img src="https://tihai-oss-cloud.itihey.com/img/f5d6df0e5d586fc8857e34a51c5f4dd2.png">的区间估计,采用的样本函数为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/12654910082e82257831c524bc0ae113.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/392f4280053f13106bae1d31aec3a923.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/fe9bd8b810ea376f31f49a0512e8b0ca.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/ec87e0732fa13c6c927f7dd2f8a4025b.png">

设总体<img src="https://tihai-oss-cloud.itihey.com/img/0475c2b672691a359a2a454705f2317f.png">,<img src="https://tihai-oss-cloud.itihey.com/img/952e1fa541b571d0b2a342ef533dce3d.png">,通过样本<img src="https://tihai-oss-cloud.itihey.com/img/7e1cb2faf61e40b6f5d585d09bd4e96a.png"> <img src="https://tihai-oss-cloud.itihey.com/img/005007bbba428ab286055b04e8194ca6.png">,对<img src="https://tihai-oss-cloud.itihey.com/img/a21d50a2ac34985687f367bde660eac8.png">做置信水平为<img src="https://tihai-oss-cloud.itihey.com/img/f5d6df0e5d586fc8857e34a51c5f4dd2.png">的区间估计,采用的样本函数为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/9ade972720b27017a97557f9ba4907ee.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/b2cc6544233d59d93cba6648f1e1928d.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/f0f982f1e12c3ce9241e99eca2fba4e5.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/904261b79529faec6734de3148713222.png">

在对服从正态分布<img src="https://tihai-oss-cloud.itihey.com/img/975f708a53d110b5a4297c48bf819068.png">的参数<img src="https://tihai-oss-cloud.itihey.com/img/78d0976a0e9a939d6c38a8cf700fb879.png">区间估计中,计算得置信度为0.95的置信区间为<img src="https://tihai-oss-cloud.itihey.com/img/cd907cb40c21be2f412a988c33af53ee.png">,那么我们就可以以0.95的置信度估计样本均值的观测值<img src="https://tihai-oss-cloud.itihey.com/img/fa1495e8ee3c270eea6a5f9c14688b5b.png">与参数<img src="https://tihai-oss-cloud.itihey.com/img/78d0976a0e9a939d6c38a8cf700fb879.png">的最大误差为( )

A. 10B. 2.5C. 5D. 不确定,与观测值<img src="https://tihai-oss-cloud.itihey.com/img/fa1495e8ee3c270eea6a5f9c14688b5b.png">的大小有关

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