湖师数理统计题库习题六.doc

out city created, and care masses life, focus work, in-depth investigation, more out boutique masterpiece, makes we of research results more to into led of decision vision, more to in national some has effect of newspaper Shang published, for advance work, and publicity changde play due of role. Third, information submitted to be pragmatic. Quick and timely. The ancients said: for the time system; statement back for the time being, nothing. Therefore, the submission of information to do four, that is, find the problem faster, editorial writing, send and read faster approval and feedback to implement quickly. To be true and accurate. True mainly reflect the full picture of events, one is one, two, this is the life of the information. Accuracy is primarily qualitative and quantitative questions, quantitative objective of publicQualitative logic. To be reliable and useful. We submit information to have access to decision-making, to guide and promote the work and solve practical problems. Mixed cum. On the negative information and emergency information, rapid escalation in strict accordance with the procedures, firm, newspaper, newspapers, never late, fail to report, false claim and skimming. Investee 2. supervision and insist on, around and protecting their interests to touch the truth, seek practical results. Adhere to people-oriented, the most important thing is to realize, safeguard and develop the fundamental interests of the overwhelming majority of the people. We carry out inspection, so must go deep among the masses, go deep into the realities, always pay attention to the peoples livelihood, to grasp the public sentiment, and earnestly safeguard the benefit, addressing the masses are most concerned about and reflecting the strongest issues, efforts to solve the problem of decisions implemented and not implemented. One is to stick to principles. Right of inspection is one of the most important powers of the Office, should not only dare to use, but also with caution. So-called dared to use, is to hold a number of important issues, bold supervision over supervision, track inspection, problems are not solved do not pass, the blame does not hold did not miss, dissatisfaction of the masses did not miss, the real right of supervision authority, with the benefits. Call with caution, is supervising departments should strengthen the consciousness of authorized strictly according to procedure, preventing the supervision and excessive to prevent adding burden to grass-roots. To this end, the supervision Department of the Party Committee of supervision must be under city and County party Committee Secretary-General (Office). Second, we should focus on. Is the Governor, those related to the globalEvent, Governor the protracted difficult, strong Governor during emergency urgent. Not having special departments in charge of the General Governor, under the normal procedure can do good things not Governor, not authorized by County leaders, not the Governor. Third is to solve the problem. The purpose of supervision, to resolve the problem. To adhere to and further improve the假设检验 1设取自正态母体其中为未知参数,为子样均值，对检验问题取检验的拒绝域:,试决定常数c使检验的显著性水平为0.05.解:因为所以 在成立下, , 所以 C=1.176.2设子样取自正态母体已知，对检验假设的问题，取临界域.（i）求此检验犯第一类错误的概率,犯第二类错误的概率,并讨论它们之间的关系.（ii）设,求时不犯第二类错误的概率. 解: (i).在成立下, ,其中是N（0，1）分布的分位点。在H1成立下, =当增加时，减少，从而减少；反之当减少时，将导致增加。（ii）不犯第二类错误的概率为1-。 =4，设某产品指标服从正态分布，它的根方差已知为150小时，今由一批产品中随机地抽查了26个，测得指标的平均值为1637小时，问在5%的显著性水平下，能否认为这批产品的指标为1600小时？解：母体， 对假设采用U检验法，在H0为真下，检验统计量观察值为时临界值。 由于， 所以接受，即不能否定这批产品指标为1600小时5某电器零件的平均电阻一直保持在2.64均方差保持在0.06.改变加工工艺后测的100个零件,其平均电阻为2.62,均方差不变.问新工艺对此零件的电阻有无显著差异?取显著性水平 。解：设改变工艺后，电器零件电阻为随机变量，则未知，。 检验假设。 从母体中取了容量为100子样，近似服从正态分布，即：。因而对假设可采用u检验计算检验统计量观察值， 。 由于。所以拒绝原假设即改革工艺后零件的电阻一有显著差异。6. 有一种新安眠剂,据说在一定剂量下能比某种就旧暗昧安眠剂平均增加睡眠时间3小时,根据资料用某种旧安眠剂时平均睡眠时间为20.8小时,均方差为1.8小时,为了检验新安眠剂的这种说法是否正确,收集到一种使用新安眠剂的睡眠时间(以小时为单位)为: 26.7, 22.0, 24.1, 21.0, 27.2, 25.0, 23.4试问这组数据能否说明新安眠剂已达到新的疗效? 解：设新安眠剂疗效为随机变量，则未知，。 检验假设， 从母体中取了容量为7子样，近似服从正态分布，即：。因而对假设可采用u检验计算检验统计量观察值， 。 由于。所以接收原假设，即新安眠剂未达到新的疗效。15设 X1,X2,- ,Xn为取自总体X 的简单随机样本，其中0为已知常数，选择统计量U = ，求的1-的置信区间。解：由于U = 服从(n)， 于是故 的1-的置信区间 。16在某校的一个班体检记录中，随意抄录 25 名男生的身高数据，测得平均高为170厘米，（修正）标准差为12厘米，试求该班男生的平均身高和身高标准差的 0 .95置信区间（假设身高近似服从正态分布）。解：由题设 身高XN（），n=25，。（1） 先求的置信区间（未知）取故置信区间为：(170)=(170-4.94, 170+4.94)=(165.06, 174.94) (2). 的置信区间（未知）取故的0.95置信区间为 的0.95置信区间为 .14在测量反应时间中，一心理学家估计的标准差为 0.05 秒，为了以 95% 的置信度使他对平均反应时间的估计误差不超过0.01秒，应取多大的样本容量n?解：以X表示反应时间，则为平均反应时间，由条件知，样本标准差S=0.05, 用样本均值估计 当n充分大时，统计量近似服从标准正态分布N（0，1），根据条件，要求样本容量满足. 即即应取样本容量n为96或97。8在某年级学生中抽测9名跳远年成绩，得样本均值= 4.38 m . 假设跳远绩X服从正态分布，且= 03, 问是否可认为该年级学生跳远平均成绩为= 4.40 m ( = 0.10).解：(1) (2) 选统计量 （3）查标准正态分布表，得出临界值拒绝域(4)算得,显然0.2不在拒绝域内，因此H0被接收，即可认为该年级学生跳远平均成绩为4.40米。9设某次考试的考生成绩服从正态分布，从中随机地抽取 36位考生的成绩，算得平均成绩为66.5分，标准差 S*为15分，问在显著水平0.05下，是否可认为这次考试全体考生的平均成绩为 70 分？并给出检验过程。解：（1）待检假设备择假设 （2）在H0成立条件下选择统计量 （3）在显著性水平0.05下，查t分布表，找出临界值 拒绝域 （4）计算，故接受H0,，因此可以认为这次考试全体考生的平均成绩为70分。11某厂生产的电子仪表的寿命服从正态分布，其标准差为= 1.6, 改进新工艺后，从新的产品抽出9件，测得平均寿命= 52.8, S*n2 = 1.19 ，问用新工艺后仪表的寿命方差是否发生了变化？（取显著性水平 = 0.05）解：（！）待检假设，备择假设 （2）选取统计量 （3）查分布表，找出临界值 拒绝域为（4）计算，接受H0，即改进工艺后仪表寿命的方差没有显著变化。12电工器材厂生产一批保险丝，抽取10根试验其熔断时间，结果为 ： 42, 65, 75, 78, 71, 59, 57, 68, 54, 55. 问是否可认为整批保险丝的熔断时间的方差不大于 80 ？（熔断时间服从正态分布，显著性水平 = 0.05）.解：（1）待检假设备择假设 （2）选取统计量 （3）由查分布表 (4)。故接受假设H0，即在下，可认为整批保险丝的熔断时间的方差不大于80.10某校从经常参加体育锻炼的男生中随机地选出50名,测得平均身高174.34 厘米从不经常参加体育锻炼的男生中随机地选50名，测得平均身172.42 厘米，统计资料表明两种男生的身高都服从正态分布，其标准差分别为5.35和6.11厘米，问该校经常参加锻炼的男生是否比不常参加体育锻炼的男生平均身高些？ 解： X, Y分别表常锻炼和不常锻炼男生的身高，由题设(1) 待检假设，备择假设(2) 选取统计量(3) 对于 查正态分布表，(4) 计算故否定假设即表明经常体育锻炼的男生平均身高比不经常体育锻炼的男生平均身高高些。7.14 假设六个整数1，2，3，4，5，6被随机地选择，重复60次独立实验中出现1，2，3，4，5，6的次数分别为13，19，11，8，5，4。问在5%的显著性水平下是否可以认为下列假设成立：。解：用拟合优度检验，如果成立 列表计算的观察值：组数i频数123456131911854101010101010391-2-5-， =11.07由于，所以拒绝。即等概率的假设不成立。7.15 对某型号电缆进行耐压测试实验，记录43根电缆的最低击穿电压，数据列表如下：测试电压 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8击穿频数 1 1 1 2 7 8 8 4 6 4 1试对电缆耐压数据作分析检验（用概率图纸法和拟合优度检验）。解：用正态概率纸检验出数据基本上服从正态分布，下面拟合优度检验假设其中为和的极大似然估计，其观察值 所以要检验的假设 分组列表计算统计量的观察值。组 距 频数标准化区间 4.14.1 4.24.2 4.34.3 4.54.5 4.64.6 5781265 -1.25-1.25 -0.79-0.79 -0.34-0.34 0.570.57 1.030.31 0.10560.10870.15260.34880.13280.15154.54084.67416.561814.99845.71046.51450.04641.15740.21520.59940.01470.3521 用查表由于，所以不能否定正态分布的假设。7.16 用手枪对100个靶各打10发，只记录命中或不命中，射击结果列表如下 命中数：0 1 2 3 4 5 6 7 8 9 10 频 数： 0 2 4 10 22 26 18 12 4 2 0在显著水平下用拟合优度检验法检验射击结果所服从的分布。解 对每一靶打一发，只记录命中或不命中可用二点分布描述，而对一个靶打十发，其射击结果可用二项分布来描述，其中未知，可求其极大似然估计为设是十发射击中射中靶的个数，建立假设用拟合优度检验法列表如下：01234567891002410222618124...0980.9764.39511.71920.52124.60920.52111.7194.3950.9760.0980.0981.0740.0360.2520.1070.0790.3100.0070.0361.0740.098 取 ，=由于，所以接受。7.17 在某细纱机上进行断头率测定，试验锭子总数为440，测得断头总次数为292次只锭子的断头次数纪律于下表。问每只锭子的纺纱条件是否相同？每锭断头数 0 1 2 3 4 5 6 7 9锭数（实测） 263 112 38 19 3 1 1 0 3 解：如果各个锭子的纺纱条件元差异，则所有锭子断头次数服从同一个普哇松分布，所以问题是要检验每只锭子的断头数。其中未知，求其极大似然估计为，建立假设，由拟合优度检验。列表断头数1234501234-8268112381980.51690.34110.11260.02470.0047227.41150.0949.5310.8972.0685.5689.6682.6846.02617.016取，=，取 ，=由于，所以拒绝。即认为每只锭子纺纱条件不相同。整个外脚手架工程涉及到搭设、维护及拆除三个阶段，根据各个阶段的不同工作内容，劳动力的需用情况不同。本工程主体施工进度要求较快，外脚手架工作量较大，需投入较多劳动力，外脚手架将根据现场分栋搭设。外脚手架维护阶段主要是配合外装单位进行施工，因此需用劳动力较少feelings survey, by looking up public sentiments to find problems. Problems will increase its special supervision, set up accounts, hold on to it. We should conscientiously implement the leading contracting matters, secured, had an answer to everything, then settles rate of 100%. Have an impact on some of the outstanding issues, supervision departments and information components together, play the supervisory role of the news media to promote problem solving. Investee 3. insist on a daily run, around the practice of truth catching efficiency, focus specification. To give full play to the party Office around connecting, coordinating internal and external features, contact, rally at all levels, to motivate every aspect, adhere to the truth, strengthening standardized management to achieve coherent, efficient and effective functioning of the daily work of the Party Committee. Is processing messages should strive to streamline, standardize and quality. Streamlining is to control the number of messages, compress messages, reducing procedures, improve message handling efficiency. Specifications, is to strictly enforce the ban issued by the Communist party authorities in document handling regulations and provincial and municipal regulations, conscientiously strengthen and improve communications management to ensure that party documents orderly. High quality, is to improve the quality of message processing, it is necessary to accurately implementing the intention of the Party Committee, clearance, good communications, policy program closed, ensuring that there is no error. Second meeting scheduled to ensure thorough, safe and efficient. Any arrangements for the meetings and events, carefully arranged, item-by-item interface implemented, sure. To vigorously streamline meetings, activities, number of pressure reduction, scale to ensure that leadership emerged from the General Conference and entertainment services, focus on big things, matters. Third, reception services should lay stress on humane, personal, cultural and human. Reception and work directly with people, re