（完整版）假设检验习题及答案

relationship, established equivalent relationship 14, and subject: application problem (4)--scores and percentage application problem review content overview answers scores, and percentage application problem of key is: according to meaning, (1) determine standard volume (units \hen in-line solution. Category fraction multiplication word problem score Division applications engineering problem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurement of common units of measurement and their significance in rate 1, currency, length, area, volume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units and their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and tool measurement 2, and estimates 16, and subject: geometry preliminary knowledge (1)--line and angle review content line, and segment, and Ray, and vertical, and parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)--plane graphics review content triangle, and edges shaped, and round, and fan axisymmetric graphics perimeter and area combination graphics of area subject : Preliminary knowledge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided into: cuboid, square 3, cone cone of the features of cuboids and cubes relationship between characteristics of circular cone is slightly solid surface area and volume 1, size 2, table ...和2?12?（（5）=11.071?k-1）=?0.95由于 ?2??12?（?k-1） 所以接受H0 即认为这个是均匀的。 3.11 某电话站在一小时内接到电话用户的呼唤次数按每分钟记录的如下表： 呼吸次数 频数 0 8 1 16 2 17 3 10 4 6 5 2 6 1 >=7 0 试问这个分布能看作为泊松分布吗？ （?=0.05）解：

检验问题为： H0:P(x?k)??ke??k! 参数为?已知?的最大似然估计 ??X?np?0???81610?1*?L?6*?7*?L?26060606020e?2P?e?2?0.13531?P?X?0??0!21e?2P2?P?X?1???2*e?2?0.27071!22e?2P3?P?X?2???2*e?2?0.27072!23e?2P4?P?X?3???1.5*e?2?0.20303!24e?22?2P5?P?X?4???*e?0.09024!325e?24?2P6?P?X?5???*e? 0.03615!1526e?24P7?P?X?6???*e?2? 0.01206!45P8?P?X?7??1?P?X?6??0(ni?npi)2(8?60*0.1353)2(16?60*0.2707)2(1?60*0.0120)2??????L?npi60*0.135360*0.270760*0.0120i?12k

=0.61452由于?12?（（5）=11.071?k-1）=?0.95Q?2??12?（?k-1）

?接受H0,即分布可以看作为泊松分布。3.13从一批滚珠中随机抽取了50个，测得他们的直径为（单位：mm）:

relationship, established equivalent relationship 14, and subject: application problem (4)--scores and percentage application problem review content overview answers scores, and percentage application problem of key is: according to meaning, (1) determine standard volume (units \hen in-line solution. Category fraction multiplication word problem score Division applications engineering problem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurement of common units of measurement and their significance in rate 1, currency, length, area, volume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units and their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and tool measurement 2, and estimates 16, and subject: geometry preliminary knowledge (1)--line and angle review content line, and segment, and Ray, and vertical, and parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)--plane graphics review content triangle, and edges shaped, and round, and fan axisymmetric graphics perimeter and area combination graphics of area subject : Preliminary knowledge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided into: cuboid, square 3, cone cone of the features of cuboids and cubes relationship between characteristics of circular cone is slightly solid surface area and volume 1, size 2, table ...和15.0 15.8 15.2 15.1 15.9 14.7 14.8 15.5 15.6 15.3 15.1 15.3 15.0 15.6 15.7 14.8 14.5 14.2 14.9 14.9 15.2 15.0 15.3 15.6 15.1 14.9 14.2 14.6 15.8 15.2 15.9 15.2 15.0 14.9 14.8 14.5 15.1 15.5 15.5 15.1 15.1 15.0 15.3 14.7 14.5 15.5 15.0 14.7 14.6 14.2 是否可认为这批滚珠直径服从正态分布？(??0.05) 解：

设X为滚球的直径，其分布函数为F(x),则检验问题为x?? H0:F(x)??()?在H0成立的条件下，参数?，?2的最大似然估计为?=15.078，?2?0.183314.6-15.078)??(-1.1163)?0.1321 0.428214.8?15.078p2??()??(-1.1163)??(-0.6492)??(-1.1163)?0.12600.428215.1?15.078p3??()??(-0.6492)??(0.0514)??(-0.6492)?0.26240.428215.4?15.078p4??()??(-0.6492)??(0.7520)??(0.0514)?0.25350.4282p5?1?p1?p2?p3?p4?0.2260p1??(22?1-（（2）=5.991?k-m-1）=?0.95

2Q?2??1-（?k-m-1）=5.991?接受H0,认为滚珠直径服从正态分布。 3-13表

i 1 2 3 4 5 (ai?1,ai) ni pi npi (ni?npi)2npi (0,14.6) [14.6,14.8) [14.8,15.1) [15.1,15.4) [15.4,??) 6 5 13 14 12 0.1321 0.1260 0.2624 0.2535 0.2260 6.6061 6.2976 13.1209 12.6752 11.3003 0.0556 0.2674 0.0011 0.1385 0.0433 0.5059 ?relationship, established equivalent relationship 14, and subject: application problem (4)--scores and percentage application problem review content overview answers scores, and percentage application problem of key is: according to meaning, (1) determine standard volume (units \hen in-line solution. Category fraction multiplication word problem score Division applications engineering problem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurement of common units of measurement and their significance in rate 1, currency, length, area, volume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units and their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and tool measurement 2, and estimates 16, and subject: geometry preliminary knowledge (1)--line and angle review content line, and segment, and Ray, and vertical, and parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)--plane graphics review content triangle, and edges shaped, and round, and fan axisymmetric graphics perimeter and area combination graphics of area subject : Preliminary knowledge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided into: cuboid, square 3, cone cone of the features of cuboids and cubes relationship between characteristics of circular cone is slightly solid surface area and volume 1, size 2, table ...和3.15下列为某种药治疗感冒效果的3*3列联表。

疗效 年龄 儿童 成年 老年 ? 显著 一般 较差 58 38 32 28 44 45 23 18 14 109 100 91 128 117 55 300 ?解：

试问疗效与年龄是否有关(??0.05)？

设X为年龄 X1?儿童 X2?成年 X3?老年 Y为疗效 Y1?显著 Y2?一般 Y3?较差H0： pij?pi??p?j i=1,2,3 j=1,2,3 即X与Y独立本题选择的统计量为

ni?n?j????n?2rs?nij?npi?p?j?rs?ijrsnijn?????2 ?????n???n(???1)??ni?n?ji?1j?1i?1j?1i?1j?1ni?n?jnpi?p?j??22代入数据得： ??n(??2i?1j?1rs2nijni?n?j?1)582382322282442452 =300(+++++109*128100*12891*128109*117100*11791*117232182142 +++-1)109*55100*5591*55 =13.586222?1-((r?1)(s?1))???0.95(4)?9.48822Q?2??1-?((r?1)(s?1))??0.95(4)

?拒绝H0,认为疗效与年龄有关。3.16自动机床加工轴，从成品中抽取11根，并测得它们直径（单位：

relationship, established equivalent relationship 14, and subject: application problem (4)--scores and percentage application problem review content overview answers scores, and percentage application problem of key is: according to meaning, (1) determine standard volume (units \hen in-line solution. Category fraction multiplication word problem score Division applications engineering problem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurement of common units of measurement and their significance in rate 1, currency, length, area, volume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units and their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and tool measurement 2, and estimates 16, and subject: geometry preliminary knowledge (1)--line and angle review content line, and segment, and Ray, and vertical, and parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)--plane graphics review content triangle, and edges shaped, and round, and fan axisymmetric graphics perimeter and area combination graphics of area subject : Preliminary knowledge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided into: cuboid, square 3, cone cone of the features of cuboids and cubes relationship between characteristics of circular cone is slightly solid surface area and volume 1, size 2, table ...和mm）如下：10.52 10.41 10.32 10.18 10.64 10.77 10.82 10.67 10.59 10.38 10.49

试检验这批零件的直径是否服从正态分布？(??0.05,用W检验) 解： 为了便于计算，列表如下：这里n=11。表3-16

k 1 2 3 4 5 6 X(k) 10.18 10.32 10.38 10.41 10.49 10.52 X(n?1?k) X(n?1?k)?X(k) ak(W) 10.82 10.77 10.67 10.64 10.59 10.52 0.64 0.45 0.29 0.23 0.1 0 0.5601 0.3315 0.2260 0.1429 0.0695 H0:总体服从正态分布 H1:总体不服从正态分布将观察值按非降次序排列成： X(1)?X(2)?L?X(n)本题采用的统计量为：]?[n?2??X?X???ak(W)??(n+1-k)(k)???k=1??? W=2?(Xk?1n(k)?X)2?(Xi?1511(k)?X)2?0.3821X?10.5264 ?ak(W)[X(12?k)?X(k)]i=1

=0.5601*0.64+0.3315*0.45+0.2260*0.29+0.1429*0.23+0.0695*0.1=0.6130所以0.61302 W=?0.98340.3821W0.05?0.85QW?W0.05?接受H0,认为这批零件的直径服从正态分布。3.18用两种材料的灯丝制造灯泡，今分别随机抽取若干个进行寿命试验，其结果如下：