宝塔服务器面板，一键全能部署及管理，送你10850元礼包，点我领取

Evernote Export

body, td { font-family: 微软雅黑; font-size: 10pt }

 

参数估计与假设检验的区别

参数估计与假设检验是统计推断的两个组成部分，都是利用样本信息对总体进行推断，但是角度不同。
参数估计是样本统计量估计总体参数的方法，总体参数在估计前是未知的。
假设检验是先对总体参数提出一个假设，后用样本信息去验证这个假设是否正确。
参数估计不知道总体的信息，也不进行假定，假设不知道总体，需要验证信息。

1.假设检验的基本思想和原理
2.假设检验的步骤
3.一个总体参数的检验
4.两个总体参数的检验
5.P值的计算与应用
6.用EXCEL进行检验

假设检验的基本问题

1.假设问题的提出
2.假设的表达式
3.两类错误
4.假设检验的流程
5.利用P值进行决策

什么是假设？
对总体参数的具体数值所做的陈述
-总体参数包括总体均值、比例、方差等
-分析之前必需陈述

什么是假设检验
1.先对总体的参数(或分布形式)提出某种假设，然后利用样本信息判断假设是否成立的过程
2.有参数检验和非参数检验
3.逻辑上运用反证法，统计上依据小概率原理

原假设
1.研究者想收集证据予以反对的假设
2.又称为”0假设”
3.总是有符号=,≤或≥
4.表示为H0​
H0​:mu=某一数值
指定为符号=,≤或≥
例如 H0​:μ=10cm
一般情况下，记原假设为H0​所谓为零假设
备择假设
1.研究者想收集证据予以支持的假设
2.也称为研究假设
3.总是有符号 !=,≤或≥
4.表示为H1​
H1​:μ<某一数值，或μ>某一数值
例如：H1​:μ<10cm,或mu>10cm
原假设和备择假设是属于非此即彼的关系，一般来说，原假设是包含等于的
提出假设
1.原假设和备择假设是一个完备事件组，而且相互独立
在一项假设检验中，原假设和备择假设必有一个条件成立，而且只有一个成立
2.先确定备择假设，再确定原假设
3.等号=总是放在原假设上
4.因研究目的不同，对同一问题可能提出不同的假设(也可能得出不同的结论)
双侧检验和单侧检验
1.备择假设没有特定的方向性，并含有符号≠的假设检验，称为双侧检验或双尾检验
2.备择假设具有特定的方向性，并含有符号≤和eq的假设检验，称为单侧检验或单尾检验

备择假设的方向为<,称为左侧检验
备择假设的方向为>,称为右侧检验

双侧检验和单侧检验的假设形式

假设	双侧检验	单侧检验(左侧)	单侧检验(右侧)
原假设	H0​:μ=μ0​	H0​:μ≥μ0​	H0​:μ≤μ0​
备择假设	H1​:μ≠μ0​	H1​:μ<μ0​	H1​:μ>μ0​

假设检验中的两类错误

1.第I类错误(弃真错误)
原假设为真，拒绝原假设
第I类错误的概率记为α,被称为显著性水平
2.第II类错误(取伪错误)
原假设为假设时未拒绝原假设
第II类错误的概率记为β
两类错误时此消彼长的关系，不可能同时达到平衡，需要有所取舍

影响beta错误的因素

1.总体参数的真值
随着假设的总体参数的减少而增大
2.显著性水平α
当α减少时增大
3.总体标准差
当α增大时增大
4.样本容量n
当n减少时增大

显著性水平α
1.是一个概率值
2.原假设为真时，拒绝原假设的概率被称为抽样分布的拒绝域
表示为α

常用的α有0.01,0.05,0.1
由研究者提出

假设检验中的小概率原理
什么是小概率？
1.在一次试验中，一个几乎不可能发生的事件发生的概率
2.在一次试验中小概率事件一旦发生，就有理由拒绝原假设
3.小概率由研究者事先确定

检验统计量
1.根据样本观测结果计算得到的，并据以对原假设和备择假设作出决策的某个样本统计量
2.对样本估计量的标准化结果

原假设H0​为真
点估计量的抽样分布

3.标准化的检验统计量
标准化检验统计量 ={点估计量-假设值}/{点估计量的抽样标准差}

决策规则
1.给定显著性水平区间下，查表的出相应的临界值z或z2α​​,tm​或t2α​​
2.将检验统计量的值与显著性水平的临界值进行比较
3.做出决策

双侧检验 统计量>临界值，拒绝H0​
左侧检验 统计量<- 临界值，拒绝H0​
右侧检验 统计量>临界值，拒绝H0​

什么是P值
1.在原假设为真的条件下，检验统计量的观察值大于或等于其计算值的概率

双侧检验为分布中两侧面积的总和

2.反映实际观测到的数据与原假设H0​之间不一致的程度
3.被称为观察到的(或实测的)显著性水平
3.决策规则 若P值<α,拒绝原假设

假设检验的结论表述

1.假设检验的目的在于试图找到拒绝原假设，而不在于证明什么是正确的
2.拒绝原假设时结论是清楚的

例如 H0​:μ=10,拒绝H0​时，可以说μ≠10

3.当不拒绝原假设时，

并未给出明确的结论
不能说原假设是正确的，也不能说它不是正确的
例如，当不拒绝H0​:μ=10,并未说它就是10，但也未说它不是10.只能说样本提供的证据不足以推翻原假设。

假设检验步骤的总结

1.陈述原假设和备择假设
2.从研究的总体中抽出一个随机样本
3.确定一个适当的检验统计量，并利用样本统计依据算出具体数值
4.确定一个适当的显著性水平，并计算出其临界值，指定拒绝域
5.将统计量的值域临界值进行比较，做出决策

统计量的值落在拒绝域，拒绝H0​，否则不拒绝H0​
也可以直接利用P值做出决策

一个总体参数的检验

检验统计量的确定
总体均值的检验
总体比例的检验
总体方差的检验

总体均值的检验—大样本

1.假定条件
正态总体或非正态总体大样本n ≥ 30
2.使用z检验统计量
α2 已知 z=n​σ​x−μ0​​ N(0,1)
α2 未知 z=n​s​x−μ0​​ N(0,1)

总体均值的检验—大样本检验方法的总结

假设	双侧检验	左侧检验	右侧检验
假设形式	H0​:μ=μ0​	H0​:μ≥μ0​	H0​:μ≤μ0​
假设形式	H1​:μ≠μ0​	H1​:μ<μ0​	H1​:μ>μ0​
统计量	α已知	z=n​σ​x−μ0​​
统计量	α未知	z=n​s​x−μ0​​
拒绝域	z>z2α​​	z<−zα​	z>zα​
P值决策	P<α 拒绝H0​

总体均值的检验—小样本

1.假定条件

总体服从正态分布
小样本(n<30)

2.检验统计量
α2已知 z=n​σ​x−μ0​​~N(0,1)
α2未知 z=n​s​x−μ0​​~t(0,1)

总体均值的检验—小样本检验方法的总结

假设	双侧检验	左侧检验	右侧检验
假设形式	H0​:μ=μ0​	H0​:μ≥μ0​	H0​:μ≤μ0​
假设形式	H1​:μ≠μ0​	H1​:μ<μ0​	H1​:μ>μ0​
统计量	α已知	z=n​σ​x−μ0​​
统计量	α未知	z=n​s​x−μ0​​
拒绝域	t>t2α​​(n−1)	t<−tα​(n−1)	t>tα​(n−1)
P值决策	P<α 拒绝H0​

总体比例检验

假定条件

总体服从二项分布
可用正态分布来近似(大样本)
检验的z统计量
z=npi0​(1−π0​)​​p−π0​​
pi0​为假设的总体比例

总体比例的检验

假设	双侧检验	左侧检验	右侧检验
假设形式	H0​:μ=μ0​	H0​:μ≥μ0​	H0​:μ≤μ0​
假设形式	H1​:μ≠μ0​	H1​:μ<μ0​	H1​:μ>μ0​
统计量	z=nπ0​(1−π0​)​​p−π0​​
统计量
拒绝域	z>z2α​​	z<−aα​	z>zα​
P值决策	P<α 拒绝H0​

总体方差的检验

总体方差是服从卡方分布的，检验一个总体的方差或标准差，假设总体近似服从正态分布，使用χ2
检验统计量
χ2=σ02​(n−1)s2​~χ2(n−1)
其中s为样本方差，σ为假设总体方差

两个总体参数的检验

两个统计量的确定
两个总体均值之差的检验
两个总体比例之差的检验
两个总体方差之比的检验
检验中的匹配样本

两个总体均值之差的检验(独立大样本)

1.假定条件

两个样本是独立的随机样本
正态总体或非正态总体大样本(n_1 geq 30 n_2 eq 30)检验统计量
σ12​,σ22​已知z=n1​σ12​​+n2​σ22​​​(x1​​−x2​​)−(μ1​−μ2​)​~N(0,1)
σ12​,σ22​未知z=n1​σ12​​+n2​σ22​​​(x1​​−x2​​)−(μ1​−μ2​)​~N(0,1)

两个总体均值之差的检验(独立小样本)

1.假定条件

两个独立的小样本
两个总体都是正态分布
σ12​、σ22​已知
检验统计量
z=n1​σ12​​+n2​σ22​​​(x1​​−x2​​−(μ1​−μ2​))​~N(0,1)

两个总体均值之差的检验

sigma_1^2,sigma_2^2未知但是sigma_1^2=sigma_2^2$$
1.假定条件

两个独立的小样本
两个总体都是正态分布
σ12​、σ22​未知但是相等，即σ12​=σ22​
2.检验统计量
t=sp​n1​1​+n2​1​​(x1​​−x2​​)−(μ1​−μ2​)​
其中sp2​=n1​+n2​−2(n1​−1)s12​+(n2​−1)s22​​

两个总体均值之差的检验

σ12​,σ22​未知且不相等σ12​≠σ22​
假定条件

两个总体都是正态分布
σ22​,σ22​未知且不相等，即σ12​≠σ22​
样本容量不相等，即n1​≠n2​
检验统计量
t=n1​s12​​+n2​s22​​​(x1​​−x2​​)−(μ1​−μ2​)​
自由度 v=n1​−1n22​s12​​​+n2​−1n2​s22​​​(n1​s12​​+n2​s22​​)​

两个总体均值之差的检验(匹配样本)

假定条件
两个总体配对差值构成的总体服从配对差是由差值总体中随机抽取的数据配对或匹配(重复测量(前/后))
检验统计量
t=nd​​Sd​​d−d0​​~t(n−1)
样本差值均值d=nd​∑i=1n​di​​

两个总体比例之差的检验

假定条件
两个总体都服从二项分布
可以用正态分布来近似检验统计量
检验H0​,π1​−π2​=0,z=p(1−p)(n1​1​+n2​1​)​p1​−p2​​
检验H0​,π1​−π2​=d0​,z=n1​p1​(1−p1​)​+n2​p2​(1−p2​)​​(p1​−p2​)−d0​​

%60%60%60mermaid%0Agraph%20TD%0AA%5B%E7%BB%9F%E8%AE%A1%E6%96%B9%E6%B3%95%5D%20–%3EB(%E6%8F%8F%E8%BF%B0%E7%BB%9F%E8%AE%A1)%0AA%5B%E7%BB%9F%E8%AE%A1%E6%96%B9%E6%B3%95%5D%20–%3EC(%E6%8E%A8%E6%96%AD%E7%BB%9F%E8%AE%A1)%0AC(%E6%8E%A8%E6%96%AD%E7%BB%9F%E8%AE%A1)%20–%3ED(%E5%8F%82%E6%95%B0%E4%BC%B0%E8%AE%A1)%0AC(%E6%8E%A8%E6%96%AD%E7%BB%9F%E8%AE%A1)%20–%3EE(%E5%81%87%E8%AE%BE%E6%A3%80%E9%AA%8C)%0A%60%60%60%0A%23%23%23%23%20%E5%8F%82%E6%95%B0%E4%BC%B0%E8%AE%A1%E4%B8%8E%E5%81%87%E8%AE%BE%E6%A3%80%E9%AA%8C%E7%9A%84%E5%8C%BA%E5%88%AB%0A%0A%3E%E5%8F%82%E6%95%B0%E4%BC%B0%E8%AE%A1%E4%B8%8E%E5%81%87%E8%AE%BE%E6%A3%80%E9%AA%8C%E6%98%AF%E7%BB%9F%E8%AE%A1%E6%8E%A8%E6%96%AD%E7%9A%84%E4%B8%A4%E4%B8%AA%E7%BB%84%E6%88%90%E9%83%A8%E5%88%86%EF%BC%8C%E9%83%BD%E6%98%AF%E5%88%A9%E7%94%A8%E6%A0%B7%E6%9C%AC%E4%BF%A1%E6%81%AF%E5%AF%B9%E6%80%BB%E4%BD%93%E8%BF%9B%E8%A1%8C%E6%8E%A8%E6%96%AD%EF%BC%8C%E4%BD%86%E6%98%AF%E8%A7%92%E5%BA%A6%E4%B8%8D%E5%90%8C%E3%80%82%0A%3E%E5%8F%82%E6%95%B0%E4%BC%B0%E8%AE%A1%E6%98%AF%E6%A0%B7%E6%9C%AC%E7%BB%9F%E8%AE%A1%E9%87%8F%E4%BC%B0%E8%AE%A1%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E6%96%B9%E6%B3%95%EF%BC%8C%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E5%9C%A8%E4%BC%B0%E8%AE%A1%E5%89%8D%E6%98%AF%E6%9C%AA%E7%9F%A5%E7%9A%84%E3%80%82%0A%3E%E5%81%87%E8%AE%BE%E6%A3%80%E9%AA%8C%E6%98%AF%E5%85%88%E5%AF%B9%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E6%8F%90%E5%87%BA%E4%B8%80%E4%B8%AA%E5%81%87%E8%AE%BE%EF%BC%8C%E5%90%8E%E7%94%A8%E6%A0%B7%E6%9C%AC%E4%BF%A1%E6%81%AF%E5%8E%BB%E9%AA%8C%E8%AF%81%E8%BF%99%E4%B8%AA%E5%81%87%E8%AE%BE%E6%98%AF%E5%90%A6%E6%AD%A3%E7%A1%AE%E3%80%82%0A%3E%E5%8F%82%E6%95%B0%E4%BC%B0%E8%AE%A1%E4%B8%8D%E7%9F%A5%E9%81%93%E6%80%BB%E4%BD%93%E7%9A%84%E4%BF%A1%E6%81%AF%EF%BC%8C%E4%B9%9F%E4%B8%8D%E8%BF%9B%E8%A1%8C%E5%81%87%E5%AE%9A%EF%BC%8C%E5%81%87%E8%AE%BE%E4%B8%8D%E7%9F%A5%E9%81%93%E6%80%BB%E4%BD%93%EF%BC%8C%E9%9C%80%E8%A6%81%E9%AA%8C%E8%AF%81%E4%BF%A1%E6%81%AF%E3%80%82%0A%0A%3E1.%E5%81%87%E8%AE%BE%E6%A3%80%E9%AA%8C%E7%9A%84%E5%9F%BA%E6%9C%AC%E6%80%9D%E6%83%B3%E5%92%8C%E5%8E%9F%E7%90%86%0A%3E2.%E5%81%87%E8%AE%BE%E6%A3%80%E9%AA%8C%E7%9A%84%E6%AD%A5%E9%AA%A4%0A%3E3.%E4%B8%80%E4%B8%AA%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E6%A3%80%E9%AA%8C%0A%3E4.%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E6%A3%80%E9%AA%8C%0A%3E5.P%E5%80%BC%E7%9A%84%E8%AE%A1%E7%AE%97%E4%B8%8E%E5%BA%94%E7%94%A8%0A%3E6.%E7%94%A8EXCEL%E8%BF%9B%E8%A1%8C%E6%A3%80%E9%AA%8C%0A%0A%23%23%23%23%20%E5%81%87%E8%AE%BE%E6%A3%80%E9%AA%8C%E7%9A%84%E5%9F%BA%E6%9C%AC%E9%97%AE%E9%A2%98%0A%3E1.%E5%81%87%E8%AE%BE%E9%97%AE%E9%A2%98%E7%9A%84%E6%8F%90%E5%87%BA%0A%3E2.%E5%81%87%E8%AE%BE%E7%9A%84%E8%A1%A8%E8%BE%BE%E5%BC%8F%0A%3E3.%E4%B8%A4%E7%B1%BB%E9%94%99%E8%AF%AF%0A%3E4.%E5%81%87%E8%AE%BE%E6%A3%80%E9%AA%8C%E7%9A%84%E6%B5%81%E7%A8%8B%0A%3E5.%E5%88%A9%E7%94%A8P%E5%80%BC%E8%BF%9B%E8%A1%8C%E5%86%B3%E7%AD%96%0A%0A%3E%E4%BB%80%E4%B9%88%E6%98%AF%E5%81%87%E8%AE%BE%EF%BC%9F%0A%3E%E5%AF%B9%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E5%85%B7%E4%BD%93%E6%95%B0%E5%80%BC%E6%89%80%E5%81%9A%E7%9A%84%E9%99%88%E8%BF%B0%0A%3E%20-%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E5%8C%85%E6%8B%AC%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E3%80%81%E6%AF%94%E4%BE%8B%E3%80%81%E6%96%B9%E5%B7%AE%E7%AD%89%0A%3E%20-%E5%88%86%E6%9E%90%E4%B9%8B%E5%89%8D%E5%BF%85%E9%9C%80%E9%99%88%E8%BF%B0%0A%20%0A%20%3E%E4%BB%80%E4%B9%88%E6%98%AF%E5%81%87%E8%AE%BE%E6%A3%80%E9%AA%8C%0A%20%3E1.%E5%85%88%E5%AF%B9%E6%80%BB%E4%BD%93%E7%9A%84%E5%8F%82%E6%95%B0(%E6%88%96%E5%88%86%E5%B8%83%E5%BD%A2%E5%BC%8F)%E6%8F%90%E5%87%BA%E6%9F%90%E7%A7%8D%E5%81%87%E8%AE%BE%EF%BC%8C%E7%84%B6%E5%90%8E%E5%88%A9%E7%94%A8%E6%A0%B7%E6%9C%AC%E4%BF%A1%E6%81%AF%E5%88%A4%E6%96%AD%E5%81%87%E8%AE%BE%E6%98%AF%E5%90%A6%E6%88%90%E7%AB%8B%E7%9A%84%E8%BF%87%E7%A8%8B%0A%20%3E2.%E6%9C%89%E5%8F%82%E6%95%B0%E6%A3%80%E9%AA%8C%E5%92%8C%E9%9D%9E%E5%8F%82%E6%95%B0%E6%A3%80%E9%AA%8C%0A%20%3E3.%E9%80%BB%E8%BE%91%E4%B8%8A%E8%BF%90%E7%94%A8%E5%8F%8D%E8%AF%81%E6%B3%95%EF%BC%8C%E7%BB%9F%E8%AE%A1%E4%B8%8A%E4%BE%9D%E6%8D%AE%E5%B0%8F%E6%A6%82%E7%8E%87%E5%8E%9F%E7%90%86%0A%0A%3E%E5%8E%9F%E5%81%87%E8%AE%BE%0A%3E1.%E7%A0%94%E7%A9%B6%E8%80%85%E6%83%B3%E6%94%B6%E9%9B%86%E8%AF%81%E6%8D%AE%E4%BA%88%E4%BB%A5%E5%8F%8D%E5%AF%B9%E7%9A%84%E5%81%87%E8%AE%BE%0A%3E2.%E5%8F%88%E7%A7%B0%E4%B8%BA%220%E5%81%87%E8%AE%BE%22%0A%3E3.%E6%80%BB%E6%98%AF%E6%9C%89%E7%AC%A6%E5%8F%B7%3D%2C%24%5Cleq%24%E6%88%96%24%5Cgeq%24%0A%3E4.%E8%A1%A8%E7%A4%BA%E4%B8%BA%24H_0%24%0A%3E%24H_0%24%3A%24%5Cmu%3D%E6%9F%90%E4%B8%80%E6%95%B0%E5%80%BC%24%0A%3E%E6%8C%87%E5%AE%9A%E4%B8%BA%E7%AC%A6%E5%8F%B7%3D%2C%24%5Cleq%24%E6%88%96%24%5Cgeq%24%0A%3E%E4%BE%8B%E5%A6%82%20%24H_0%24%3A%24%5Cmu%3D10cm%24%0A%3E%E4%B8%80%E8%88%AC%E6%83%85%E5%86%B5%E4%B8%8B%EF%BC%8C%E8%AE%B0%E5%8E%9F%E5%81%87%E8%AE%BE%E4%B8%BA%24H_0%24%E6%89%80%E8%B0%93%E4%B8%BA%E9%9B%B6%E5%81%87%E8%AE%BE%0A%3E**%E5%A4%87%E6%8B%A9%E5%81%87%E8%AE%BE**%0A%3E1.%E7%A0%94%E7%A9%B6%E8%80%85%E6%83%B3%E6%94%B6%E9%9B%86%E8%AF%81%E6%8D%AE%E4%BA%88%E4%BB%A5%E6%94%AF%E6%8C%81%E7%9A%84%E5%81%87%E8%AE%BE%0A%3E2.%E4%B9%9F%E7%A7%B0%E4%B8%BA%E7%A0%94%E7%A9%B6%E5%81%87%E8%AE%BE%0A%3E3.%E6%80%BB%E6%98%AF%E6%9C%89%E7%AC%A6%E5%8F%B7%20!%3D%2C%24%5Cleq%24%E6%88%96%24%5Cgeq%24%0A%3E4.%E8%A1%A8%E7%A4%BA%E4%B8%BA%24H_1%24%0A%3E%24H_1%24%3A%24%5Cmu%24%3C%E6%9F%90%E4%B8%80%E6%95%B0%E5%80%BC%EF%BC%8C%E6%88%96%24%5Cmu%24%3E%E6%9F%90%E4%B8%80%E6%95%B0%E5%80%BC%0A%3E%E4%BE%8B%E5%A6%82%EF%BC%9A%24H_1%24%3A%24%5Cmu%3C10cm%24%2C%E6%88%96%24mu%3E10cm%24%0A%3E%E5%8E%9F%E5%81%87%E8%AE%BE%E5%92%8C%E5%A4%87%E6%8B%A9%E5%81%87%E8%AE%BE%E6%98%AF%E5%B1%9E%E4%BA%8E%E9%9D%9E%E6%AD%A4%E5%8D%B3%E5%BD%BC%E7%9A%84%E5%85%B3%E7%B3%BB%EF%BC%8C%E4%B8%80%E8%88%AC%E6%9D%A5%E8%AF%B4%EF%BC%8C%E5%8E%9F%E5%81%87%E8%AE%BE%E6%98%AF%E5%8C%85%E5%90%AB%E7%AD%89%E4%BA%8E%E7%9A%84%0A%3E**%E6%8F%90%E5%87%BA%E5%81%87%E8%AE%BE**%0A%3E1.%E5%8E%9F%E5%81%87%E8%AE%BE%E5%92%8C%E5%A4%87%E6%8B%A9%E5%81%87%E8%AE%BE%E6%98%AF%E4%B8%80%E4%B8%AA%E5%AE%8C%E5%A4%87%E4%BA%8B%E4%BB%B6%E7%BB%84%EF%BC%8C%E8%80%8C%E4%B8%94%E7%9B%B8%E4%BA%92%E7%8B%AC%E7%AB%8B%0A%3E%E5%9C%A8%E4%B8%80%E9%A1%B9%E5%81%87%E8%AE%BE%E6%A3%80%E9%AA%8C%E4%B8%AD%EF%BC%8C%E5%8E%9F%E5%81%87%E8%AE%BE%E5%92%8C%E5%A4%87%E6%8B%A9%E5%81%87%E8%AE%BE%E5%BF%85%E6%9C%89%E4%B8%80%E4%B8%AA%E6%9D%A1%E4%BB%B6%E6%88%90%E7%AB%8B%EF%BC%8C%E8%80%8C%E4%B8%94%E5%8F%AA%E6%9C%89%E4%B8%80%E4%B8%AA%E6%88%90%E7%AB%8B%0A%3E2.%E5%85%88%E7%A1%AE%E5%AE%9A%E5%A4%87%E6%8B%A9%E5%81%87%E8%AE%BE%EF%BC%8C%E5%86%8D%E7%A1%AE%E5%AE%9A%E5%8E%9F%E5%81%87%E8%AE%BE%0A%3E3.%E7%AD%89%E5%8F%B7%3D%E6%80%BB%E6%98%AF%E6%94%BE%E5%9C%A8%E5%8E%9F%E5%81%87%E8%AE%BE%E4%B8%8A%0A%3E4.%E5%9B%A0%E7%A0%94%E7%A9%B6%E7%9B%AE%E7%9A%84%E4%B8%8D%E5%90%8C%EF%BC%8C%E5%AF%B9%E5%90%8C%E4%B8%80%E9%97%AE%E9%A2%98%E5%8F%AF%E8%83%BD%E6%8F%90%E5%87%BA%E4%B8%8D%E5%90%8C%E7%9A%84%E5%81%87%E8%AE%BE(%E4%B9%9F%E5%8F%AF%E8%83%BD%E5%BE%97%E5%87%BA%E4%B8%8D%E5%90%8C%E7%9A%84%E7%BB%93%E8%AE%BA)%0A%3E**%E5%8F%8C%E4%BE%A7%E6%A3%80%E9%AA%8C%E5%92%8C%E5%8D%95%E4%BE%A7%E6%A3%80%E9%AA%8C**%0A%3E1.%E5%A4%87%E6%8B%A9%E5%81%87%E8%AE%BE%E6%B2%A1%E6%9C%89%E7%89%B9%E5%AE%9A%E7%9A%84%E6%96%B9%E5%90%91%E6%80%A7%EF%BC%8C%E5%B9%B6%E5%90%AB%E6%9C%89%E7%AC%A6%E5%8F%B7%24%5Cneq%24%E7%9A%84%E5%81%87%E8%AE%BE%E6%A3%80%E9%AA%8C%EF%BC%8C%E7%A7%B0%E4%B8%BA%E5%8F%8C%E4%BE%A7%E6%A3%80%E9%AA%8C%E6%88%96%E5%8F%8C%E5%B0%BE%E6%A3%80%E9%AA%8C%0A%3E2.%E5%A4%87%E6%8B%A9%E5%81%87%E8%AE%BE%E5%85%B7%E6%9C%89%E7%89%B9%E5%AE%9A%E7%9A%84%E6%96%B9%E5%90%91%E6%80%A7%EF%BC%8C%E5%B9%B6%E5%90%AB%E6%9C%89%E7%AC%A6%E5%8F%B7%24%5Cleq%24%E5%92%8C%24%5Creq%24%E7%9A%84%E5%81%87%E8%AE%BE%E6%A3%80%E9%AA%8C%EF%BC%8C%E7%A7%B0%E4%B8%BA%E5%8D%95%E4%BE%A7%E6%A3%80%E9%AA%8C%E6%88%96%E5%8D%95%E5%B0%BE%E6%A3%80%E9%AA%8C%0A%3E-%20%E5%A4%87%E6%8B%A9%E5%81%87%E8%AE%BE%E7%9A%84%E6%96%B9%E5%90%91%E4%B8%BA%24%3C%24%2C%E7%A7%B0%E4%B8%BA%E5%B7%A6%E4%BE%A7%E6%A3%80%E9%AA%8C%0A%3E-%20%E5%A4%87%E6%8B%A9%E5%81%87%E8%AE%BE%E7%9A%84%E6%96%B9%E5%90%91%E4%B8%BA%24%3E%24%2C%E7%A7%B0%E4%B8%BA%E5%8F%B3%E4%BE%A7%E6%A3%80%E9%AA%8C%0A%0A%23%23%23%23%20%E5%8F%8C%E4%BE%A7%E6%A3%80%E9%AA%8C%E5%92%8C%E5%8D%95%E4%BE%A7%E6%A3%80%E9%AA%8C%E7%9A%84%E5%81%87%E8%AE%BE%E5%BD%A2%E5%BC%8F%0A%0A%7C%20%E5%81%87%E8%AE%BE%20%7C%E5%8F%8C%E4%BE%A7%E6%A3%80%E9%AA%8C%20%7C%20%E5%8D%95%E4%BE%A7%E6%A3%80%E9%AA%8C(%E5%B7%A6%E4%BE%A7)%20%20%7C%20%E5%8D%95%E4%BE%A7%E6%A3%80%E9%AA%8C(%E5%8F%B3%E4%BE%A7)%20%7C%0A%7C%20—%20%7C%20—%20%7C%20—%20%7C%20—%20%7C%0A%7C%E5%8E%9F%E5%81%87%E8%AE%BE%20%7C%24H_0%3A%5Cmu%3D%5Cmu_0%24%20%20%7C%20%24H_0%20%3A%20%5Cmu%20%5Cgeq%20%5Cmu_0%24%20%7C%24H_0%20%3A%20%5Cmu%20%5Cleq%20%5Cmu_0%24%20%20%7C%0A%7C%20%E5%A4%87%E6%8B%A9%E5%81%87%E8%AE%BE%20%7C%20%24H_1%3A%5Cmu%20%5Cneq%20%5Cmu_0%24%20%7C%20%24H_1%3A%5Cmu%20%3C%20%5Cmu_0%24%20%7C%24H_1%3A%5Cmu%3E%5Cmu_0%24%20%20%7C%0A%0A%23%23%23%23%20%E5%81%87%E8%AE%BE%E6%A3%80%E9%AA%8C%E4%B8%AD%E7%9A%84%E4%B8%A4%E7%B1%BB%E9%94%99%E8%AF%AF%0A%3E-%201.%E7%AC%ACI%E7%B1%BB%E9%94%99%E8%AF%AF(%E5%BC%83%E7%9C%9F%E9%94%99%E8%AF%AF)%0A%3E-%20%E5%8E%9F%E5%81%87%E8%AE%BE%E4%B8%BA%E7%9C%9F%EF%BC%8C%E6%8B%92%E7%BB%9D%E5%8E%9F%E5%81%87%E8%AE%BE%0A%3E%E7%AC%ACI%E7%B1%BB%E9%94%99%E8%AF%AF%E7%9A%84%E6%A6%82%E7%8E%87%E8%AE%B0%E4%B8%BA%24%5Calpha%24%2C%E8%A2%AB%E7%A7%B0%E4%B8%BA%E6%98%BE%E8%91%97%E6%80%A7%E6%B0%B4%E5%B9%B3%0A%3E2.%E7%AC%ACII%E7%B1%BB%E9%94%99%E8%AF%AF(%E5%8F%96%E4%BC%AA%E9%94%99%E8%AF%AF)%0A%3E-%20%E5%8E%9F%E5%81%87%E8%AE%BE%E4%B8%BA%E5%81%87%E8%AE%BE%E6%97%B6%E6%9C%AA%E6%8B%92%E7%BB%9D%E5%8E%9F%E5%81%87%E8%AE%BE%0A%3E-%20%E7%AC%ACII%E7%B1%BB%E9%94%99%E8%AF%AF%E7%9A%84%E6%A6%82%E7%8E%87%E8%AE%B0%E4%B8%BA%24%5Cbeta%24%0A%3E%E4%B8%A4%E7%B1%BB%E9%94%99%E8%AF%AF%E6%97%B6%E6%AD%A4%E6%B6%88%E5%BD%BC%E9%95%BF%E7%9A%84%E5%85%B3%E7%B3%BB%EF%BC%8C%E4%B8%8D%E5%8F%AF%E8%83%BD%E5%90%8C%E6%97%B6%E8%BE%BE%E5%88%B0%E5%B9%B3%E8%A1%A1%EF%BC%8C%E9%9C%80%E8%A6%81%E6%9C%89%E6%89%80%E5%8F%96%E8%88%8D%0A%0A%3E**%E5%BD%B1%E5%93%8Dbeta%E9%94%99%E8%AF%AF%E7%9A%84%E5%9B%A0%E7%B4%A0**%0A%3E-%201.%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E7%9C%9F%E5%80%BC%0A%3E-%20%E9%9A%8F%E7%9D%80%E5%81%87%E8%AE%BE%E7%9A%84%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E5%87%8F%E5%B0%91%E8%80%8C%E5%A2%9E%E5%A4%A7%0A%3E2.%E6%98%BE%E8%91%97%E6%80%A7%E6%B0%B4%E5%B9%B3%24%5Calpha%24%0A%3E%E5%BD%93%24%5Calpha%24%E5%87%8F%E5%B0%91%E6%97%B6%E5%A2%9E%E5%A4%A7%0A%3E3.%E6%80%BB%E4%BD%93%E6%A0%87%E5%87%86%E5%B7%AE%0A%3E%E5%BD%93%24%5Calpha%24%E5%A2%9E%E5%A4%A7%E6%97%B6%E5%A2%9E%E5%A4%A7%0A%3E4.%E6%A0%B7%E6%9C%AC%E5%AE%B9%E9%87%8Fn%0A%3E%E5%BD%93n%E5%87%8F%E5%B0%91%E6%97%B6%E5%A2%9E%E5%A4%A7%0A%0A%3E**%E6%98%BE%E8%91%97%E6%80%A7%E6%B0%B4%E5%B9%B3**%24%5Calpha%24%0A%3E1.%E6%98%AF%E4%B8%80%E4%B8%AA%E6%A6%82%E7%8E%87%E5%80%BC%0A%3E2.%E5%8E%9F%E5%81%87%E8%AE%BE%E4%B8%BA%E7%9C%9F%E6%97%B6%EF%BC%8C%E6%8B%92%E7%BB%9D%E5%8E%9F%E5%81%87%E8%AE%BE%E7%9A%84%E6%A6%82%E7%8E%87%E8%A2%AB%E7%A7%B0%E4%B8%BA%E6%8A%BD%E6%A0%B7%E5%88%86%E5%B8%83%E7%9A%84%E6%8B%92%E7%BB%9D%E5%9F%9F%0A%3E%E8%A1%A8%E7%A4%BA%E4%B8%BA%24%5Calpha%24%0A%3E-%20%E5%B8%B8%E7%94%A8%E7%9A%84%24%5Calpha%24%E6%9C%890.01%2C0.05%2C0.1%0A%3E%E7%94%B1%E7%A0%94%E7%A9%B6%E8%80%85%E6%8F%90%E5%87%BA%0A%0A%3E%E5%81%87%E8%AE%BE%E6%A3%80%E9%AA%8C%E4%B8%AD%E7%9A%84%E5%B0%8F%E6%A6%82%E7%8E%87%E5%8E%9F%E7%90%86%0A%3E%E4%BB%80%E4%B9%88%E6%98%AF%E5%B0%8F%E6%A6%82%E7%8E%87%EF%BC%9F%0A%3E1.%E5%9C%A8%E4%B8%80%E6%AC%A1%E8%AF%95%E9%AA%8C%E4%B8%AD%EF%BC%8C%E4%B8%80%E4%B8%AA%E5%87%A0%E4%B9%8E%E4%B8%8D%E5%8F%AF%E8%83%BD%E5%8F%91%E7%94%9F%E7%9A%84%E4%BA%8B%E4%BB%B6%E5%8F%91%E7%94%9F%E7%9A%84%E6%A6%82%E7%8E%87%0A%3E2.%E5%9C%A8%E4%B8%80%E6%AC%A1%E8%AF%95%E9%AA%8C%E4%B8%AD%E5%B0%8F%E6%A6%82%E7%8E%87%E4%BA%8B%E4%BB%B6%E4%B8%80%E6%97%A6%E5%8F%91%E7%94%9F%EF%BC%8C%E5%B0%B1%E6%9C%89%E7%90%86%E7%94%B1%E6%8B%92%E7%BB%9D%E5%8E%9F%E5%81%87%E8%AE%BE%0A%3E3.%E5%B0%8F%E6%A6%82%E7%8E%87%E7%94%B1%E7%A0%94%E7%A9%B6%E8%80%85%E4%BA%8B%E5%85%88%E7%A1%AE%E5%AE%9A%0A%0A%3E%E6%A3%80%E9%AA%8C%E7%BB%9F%E8%AE%A1%E9%87%8F%0A%3E1.%E6%A0%B9%E6%8D%AE%E6%A0%B7%E6%9C%AC%E8%A7%82%E6%B5%8B%E7%BB%93%E6%9E%9C%E8%AE%A1%E7%AE%97%E5%BE%97%E5%88%B0%E7%9A%84%EF%BC%8C%E5%B9%B6%E6%8D%AE%E4%BB%A5%E5%AF%B9%E5%8E%9F%E5%81%87%E8%AE%BE%E5%92%8C%E5%A4%87%E6%8B%A9%E5%81%87%E8%AE%BE%E4%BD%9C%E5%87%BA%E5%86%B3%E7%AD%96%E7%9A%84%E6%9F%90%E4%B8%AA%E6%A0%B7%E6%9C%AC%E7%BB%9F%E8%AE%A1%E9%87%8F%0A%3E2.%E5%AF%B9%E6%A0%B7%E6%9C%AC%E4%BC%B0%E8%AE%A1%E9%87%8F%E7%9A%84%E6%A0%87%E5%87%86%E5%8C%96%E7%BB%93%E6%9E%9C%0A%3E-%20%E5%8E%9F%E5%81%87%E8%AE%BE%24H_0%24%E4%B8%BA%E7%9C%9F%0A%3E-%20%E7%82%B9%E4%BC%B0%E8%AE%A1%E9%87%8F%E7%9A%84%E6%8A%BD%E6%A0%B7%E5%88%86%E5%B8%83%0A%0A%3E3.%E6%A0%87%E5%87%86%E5%8C%96%E7%9A%84%E6%A3%80%E9%AA%8C%E7%BB%9F%E8%AE%A1%E9%87%8F%0A%3E%E6%A0%87%E5%87%86%E5%8C%96%E6%A3%80%E9%AA%8C%E7%BB%9F%E8%AE%A1%E9%87%8F%20%3D%7B%E7%82%B9%E4%BC%B0%E8%AE%A1%E9%87%8F-%E5%81%87%E8%AE%BE%E5%80%BC%7D%2F%7B%E7%82%B9%E4%BC%B0%E8%AE%A1%E9%87%8F%E7%9A%84%E6%8A%BD%E6%A0%B7%E6%A0%87%E5%87%86%E5%B7%AE%7D%0A%0A%3E**%E5%86%B3%E7%AD%96%E8%A7%84%E5%88%99**%0A%3E1.%E7%BB%99%E5%AE%9A%E6%98%BE%E8%91%97%E6%80%A7%E6%B0%B4%E5%B9%B3%E5%8C%BA%E9%97%B4%E4%B8%8B%EF%BC%8C%E6%9F%A5%E8%A1%A8%E7%9A%84%E5%87%BA%E7%9B%B8%E5%BA%94%E7%9A%84%E4%B8%B4%E7%95%8C%E5%80%BCz%E6%88%96%24z_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%24%2C%24t_m%24%E6%88%96%24t_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%24%0A%3E2.%E5%B0%86%E6%A3%80%E9%AA%8C%E7%BB%9F%E8%AE%A1%E9%87%8F%E7%9A%84%E5%80%BC%E4%B8%8E%E6%98%BE%E8%91%97%E6%80%A7%E6%B0%B4%E5%B9%B3%E7%9A%84%E4%B8%B4%E7%95%8C%E5%80%BC%E8%BF%9B%E8%A1%8C%E6%AF%94%E8%BE%83%0A%3E3.%E5%81%9A%E5%87%BA%E5%86%B3%E7%AD%96%0A%3E-%20%E5%8F%8C%E4%BE%A7%E6%A3%80%E9%AA%8C%20%E7%BB%9F%E8%AE%A1%E9%87%8F%3E%E4%B8%B4%E7%95%8C%E5%80%BC%EF%BC%8C%E6%8B%92%E7%BB%9D%24H_0%24%0A%3E-%20%E5%B7%A6%E4%BE%A7%E6%A3%80%E9%AA%8C%20%E7%BB%9F%E8%AE%A1%E9%87%8F%3C-%20%E4%B8%B4%E7%95%8C%E5%80%BC%EF%BC%8C%E6%8B%92%E7%BB%9D%24H_0%24%0A%3E-%20%E5%8F%B3%E4%BE%A7%E6%A3%80%E9%AA%8C%20%E7%BB%9F%E8%AE%A1%E9%87%8F%3E%E4%B8%B4%E7%95%8C%E5%80%BC%EF%BC%8C%E6%8B%92%E7%BB%9D%24H_0%24%0A%0A%3E**%E4%BB%80%E4%B9%88%E6%98%AFP%E5%80%BC**%0A%3E1.%E5%9C%A8%E5%8E%9F%E5%81%87%E8%AE%BE%E4%B8%BA%E7%9C%9F%E7%9A%84%E6%9D%A1%E4%BB%B6%E4%B8%8B%EF%BC%8C%E6%A3%80%E9%AA%8C%E7%BB%9F%E8%AE%A1%E9%87%8F%E7%9A%84%E8%A7%82%E5%AF%9F%E5%80%BC%E5%A4%A7%E4%BA%8E%E6%88%96%E7%AD%89%E4%BA%8E%E5%85%B6%E8%AE%A1%E7%AE%97%E5%80%BC%E7%9A%84%E6%A6%82%E7%8E%87%0A%3E-%20%E5%8F%8C%E4%BE%A7%E6%A3%80%E9%AA%8C%E4%B8%BA%E5%88%86%E5%B8%83%E4%B8%AD%E4%B8%A4%E4%BE%A7%E9%9D%A2%E7%A7%AF%E7%9A%84%E6%80%BB%E5%92%8C%0A%0A%3E2.%E5%8F%8D%E6%98%A0%E5%AE%9E%E9%99%85%E8%A7%82%E6%B5%8B%E5%88%B0%E7%9A%84%E6%95%B0%E6%8D%AE%E4%B8%8E%E5%8E%9F%E5%81%87%E8%AE%BE%24H_0%24%E4%B9%8B%E9%97%B4%E4%B8%8D%E4%B8%80%E8%87%B4%E7%9A%84%E7%A8%8B%E5%BA%A6%0A%3E3.%E8%A2%AB%E7%A7%B0%E4%B8%BA%E8%A7%82%E5%AF%9F%E5%88%B0%E7%9A%84(%E6%88%96%E5%AE%9E%E6%B5%8B%E7%9A%84)%E6%98%BE%E8%91%97%E6%80%A7%E6%B0%B4%E5%B9%B3%0A%3E3.%E5%86%B3%E7%AD%96%E8%A7%84%E5%88%99%20%E8%8B%A5P%E5%80%BC%3C%24%5Calpha%24%2C%E6%8B%92%E7%BB%9D%E5%8E%9F%E5%81%87%E8%AE%BE%0A%0A%23%23%23%23%20%E5%81%87%E8%AE%BE%E6%A3%80%E9%AA%8C%E7%9A%84%E7%BB%93%E8%AE%BA%E8%A1%A8%E8%BF%B0%0A%3E1.%E5%81%87%E8%AE%BE%E6%A3%80%E9%AA%8C%E7%9A%84%E7%9B%AE%E7%9A%84%E5%9C%A8%E4%BA%8E%E8%AF%95%E5%9B%BE%E6%89%BE%E5%88%B0%E6%8B%92%E7%BB%9D%E5%8E%9F%E5%81%87%E8%AE%BE%EF%BC%8C%E8%80%8C%E4%B8%8D%E5%9C%A8%E4%BA%8E%E8%AF%81%E6%98%8E%E4%BB%80%E4%B9%88%E6%98%AF%E6%AD%A3%E7%A1%AE%E7%9A%84%0A%3E2.%E6%8B%92%E7%BB%9D%E5%8E%9F%E5%81%87%E8%AE%BE%E6%97%B6%E7%BB%93%E8%AE%BA%E6%98%AF%E6%B8%85%E6%A5%9A%E7%9A%84%0A%3E-%20%E4%BE%8B%E5%A6%82%20%24H_0%3A%20%5Cmu%3D10%24%2C%E6%8B%92%E7%BB%9D%24H_0%24%E6%97%B6%EF%BC%8C%E5%8F%AF%E4%BB%A5%E8%AF%B4%24%5Cmu%20%5Cneq10%24%0A%0A%3E3.%E5%BD%93%E4%B8%8D%E6%8B%92%E7%BB%9D%E5%8E%9F%E5%81%87%E8%AE%BE%E6%97%B6%EF%BC%8C%0A%3E-%20%E5%B9%B6%E6%9C%AA%E7%BB%99%E5%87%BA%E6%98%8E%E7%A1%AE%E7%9A%84%E7%BB%93%E8%AE%BA%0A%3E-%20%E4%B8%8D%E8%83%BD%E8%AF%B4%E5%8E%9F%E5%81%87%E8%AE%BE%E6%98%AF%E6%AD%A3%E7%A1%AE%E7%9A%84%EF%BC%8C%E4%B9%9F%E4%B8%8D%E8%83%BD%E8%AF%B4%E5%AE%83%E4%B8%8D%E6%98%AF%E6%AD%A3%E7%A1%AE%E7%9A%84%0A%3E-%20%E4%BE%8B%E5%A6%82%EF%BC%8C%E5%BD%93%E4%B8%8D%E6%8B%92%E7%BB%9D%24H_0%3A%5Cmu%3D10%24%2C%E5%B9%B6%E6%9C%AA%E8%AF%B4%E5%AE%83%E5%B0%B1%E6%98%AF10%EF%BC%8C%E4%BD%86%E4%B9%9F%E6%9C%AA%E8%AF%B4%E5%AE%83%E4%B8%8D%E6%98%AF10.%E5%8F%AA%E8%83%BD%E8%AF%B4%E6%A0%B7%E6%9C%AC%E6%8F%90%E4%BE%9B%E7%9A%84%E8%AF%81%E6%8D%AE%E4%B8%8D%E8%B6%B3%E4%BB%A5%E6%8E%A8%E7%BF%BB%E5%8E%9F%E5%81%87%E8%AE%BE%E3%80%82%0A%0A%23%23%23%23%20%E5%81%87%E8%AE%BE%E6%A3%80%E9%AA%8C%E6%AD%A5%E9%AA%A4%E7%9A%84%E6%80%BB%E7%BB%93%0A%3E1.%E9%99%88%E8%BF%B0%E5%8E%9F%E5%81%87%E8%AE%BE%E5%92%8C%E5%A4%87%E6%8B%A9%E5%81%87%E8%AE%BE%0A%3E2.%E4%BB%8E%E7%A0%94%E7%A9%B6%E7%9A%84%E6%80%BB%E4%BD%93%E4%B8%AD%E6%8A%BD%E5%87%BA%E4%B8%80%E4%B8%AA%E9%9A%8F%E6%9C%BA%E6%A0%B7%E6%9C%AC%0A%3E3.%E7%A1%AE%E5%AE%9A%E4%B8%80%E4%B8%AA%E9%80%82%E5%BD%93%E7%9A%84%E6%A3%80%E9%AA%8C%E7%BB%9F%E8%AE%A1%E9%87%8F%EF%BC%8C%E5%B9%B6%E5%88%A9%E7%94%A8%E6%A0%B7%E6%9C%AC%E7%BB%9F%E8%AE%A1%E4%BE%9D%E6%8D%AE%E7%AE%97%E5%87%BA%E5%85%B7%E4%BD%93%E6%95%B0%E5%80%BC%0A%3E4.%E7%A1%AE%E5%AE%9A%E4%B8%80%E4%B8%AA%E9%80%82%E5%BD%93%E7%9A%84%E6%98%BE%E8%91%97%E6%80%A7%E6%B0%B4%E5%B9%B3%EF%BC%8C%E5%B9%B6%E8%AE%A1%E7%AE%97%E5%87%BA%E5%85%B6%E4%B8%B4%E7%95%8C%E5%80%BC%EF%BC%8C%E6%8C%87%E5%AE%9A%E6%8B%92%E7%BB%9D%E5%9F%9F%0A%3E5.%E5%B0%86%E7%BB%9F%E8%AE%A1%E9%87%8F%E7%9A%84%E5%80%BC%E5%9F%9F%E4%B8%B4%E7%95%8C%E5%80%BC%E8%BF%9B%E8%A1%8C%E6%AF%94%E8%BE%83%EF%BC%8C%E5%81%9A%E5%87%BA%E5%86%B3%E7%AD%96%0A%3E-%20%E7%BB%9F%E8%AE%A1%E9%87%8F%E7%9A%84%E5%80%BC%E8%90%BD%E5%9C%A8%E6%8B%92%E7%BB%9D%E5%9F%9F%EF%BC%8C%E6%8B%92%E7%BB%9D%24H_0%24%EF%BC%8C%E5%90%A6%E5%88%99%E4%B8%8D%E6%8B%92%E7%BB%9D%24H_0%24%0A%3E-%20%E4%B9%9F%E5%8F%AF%E4%BB%A5%E7%9B%B4%E6%8E%A5%E5%88%A9%E7%94%A8P%E5%80%BC%E5%81%9A%E5%87%BA%E5%86%B3%E7%AD%96%0A%0A%23%23%23%23%20%E4%B8%80%E4%B8%AA%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E6%A3%80%E9%AA%8C%0A%E6%A3%80%E9%AA%8C%E7%BB%9F%E8%AE%A1%E9%87%8F%E7%9A%84%E7%A1%AE%E5%AE%9A%0A%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E7%9A%84%E6%A3%80%E9%AA%8C%0A%E6%80%BB%E4%BD%93%E6%AF%94%E4%BE%8B%E7%9A%84%E6%A3%80%E9%AA%8C%0A%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%E7%9A%84%E6%A3%80%E9%AA%8C%0A%0A%23%23%23%23%20%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E7%9A%84%E6%A3%80%E9%AA%8C—%E5%A4%A7%E6%A0%B7%E6%9C%AC%0A%3E1.%E5%81%87%E5%AE%9A%E6%9D%A1%E4%BB%B6%0A%20%20%20%20%3E%E6%AD%A3%E6%80%81%E6%80%BB%E4%BD%93%E6%88%96%E9%9D%9E%E6%AD%A3%E6%80%81%E6%80%BB%E4%BD%93%E5%A4%A7%E6%A0%B7%E6%9C%ACn%20%24%5Cgeq%24%2030%0A%3E2.%E4%BD%BF%E7%94%A8z%E6%A3%80%E9%AA%8C%E7%BB%9F%E8%AE%A1%E9%87%8F%0A%3E%24%5Calpha%5E2%24%20%E5%B7%B2%E7%9F%A5%20%24z%3D%5Cfrac%7B%5Coverline%7Bx%7D-%5Cmu_0%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D~N(0%2C1)%24%0A%3E%24%5Calpha%5E2%24%20%E6%9C%AA%E7%9F%A5%20%24z%3D%5Cfrac%7B%5Coverline%7Bx%7D-%5Cmu_0%7D%7B%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%7D~N(0%2C1)%24%0A%0A%0A%23%23%23%23%20%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E7%9A%84%E6%A3%80%E9%AA%8C—%E5%A4%A7%E6%A0%B7%E6%9C%AC%E6%A3%80%E9%AA%8C%E6%96%B9%E6%B3%95%E7%9A%84%E6%80%BB%E7%BB%93%0A%0A%7C%20%E5%81%87%E8%AE%BE%20%7C%20%E5%8F%8C%E4%BE%A7%E6%A3%80%E9%AA%8C%20%7C%20%E5%B7%A6%E4%BE%A7%E6%A3%80%E9%AA%8C%20%7C%20%E5%8F%B3%E4%BE%A7%E6%A3%80%E9%AA%8C%20%7C%0A%7C%20%3A—%3A%20%7C%20%3A—%3A%20%7C%20%3A—%3A%20%7C%20%3A—%3A%20%7C%0A%7C%20%E5%81%87%E8%AE%BE%E5%BD%A2%E5%BC%8F%20%7C%20%24H_0%3A%5Cmu%3D%5Cmu_0%24%20%7C%20%24H_0%3A%5Cmu%20%5Cgeq%20%5Cmu_0%24%20%7C%20%24H_0%3A%5Cmu%20%5Cleq%20%5Cmu_0%24%20%7C%0A%7C%20%E5%81%87%E8%AE%BE%E5%BD%A2%E5%BC%8F%20%7C%20%24H_1%3A%20%5Cmu%20%5Cneq%20%5Cmu_0%24%20%7C%20%24H_1%3A%5Cmu%20%3C%20%5Cmu_0%24%20%7C%20%24H_1%3A%20%5Cmu%20%3E%20%5Cmu_0%24%20%7C%0A%7C%20%E7%BB%9F%E8%AE%A1%E9%87%8F%20%7C%20%24%5Calpha%24%E5%B7%B2%E7%9F%A5%20%7C%20%24z%3D%5Cfrac%7B%5Coverline%7Bx%7D-%5Cmu_0%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D%24%20%7C%20%20%7C%0A%7C%20%E7%BB%9F%E8%AE%A1%E9%87%8F%20%7C%20%24%5Calpha%24%E6%9C%AA%E7%9F%A5%20%20%7C%20%24z%3D%5Cfrac%7B%5Coverline%7Bx%7D-%5Cmu_0%7D%7B%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%7D%24%20%7C%20%20%7C%0A%7C%20%E6%8B%92%E7%BB%9D%E5%9F%9F%20%7C%20%24z%3Ez_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%24%20%7C%20%24z%3C-z_%7B%5Calpha%7D%24%20%7C%20%24z%3Ez_%7B%5Calpha%7D%24%20%7C%0A%7C%20P%E5%80%BC%E5%86%B3%E7%AD%96%20%7C%20%24P%3C%5Calpha%24%20%E6%8B%92%E7%BB%9D%24H_0%24%7C%20%20%7C%20%20%7C%0A%0A%23%23%23%23%20%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E7%9A%84%E6%A3%80%E9%AA%8C—%E5%B0%8F%E6%A0%B7%E6%9C%AC%0A%3E1.%E5%81%87%E5%AE%9A%E6%9D%A1%E4%BB%B6%0A%3E-%20%E6%80%BB%E4%BD%93%E6%9C%8D%E4%BB%8E%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%0A%3E-%20%E5%B0%8F%E6%A0%B7%E6%9C%AC(n%3C30)%0A%0A%3E2.%E6%A3%80%E9%AA%8C%E7%BB%9F%E8%AE%A1%E9%87%8F%0A%3E%24%5Calpha%5E2%24%E5%B7%B2%E7%9F%A5%20%24z%3D%5Cfrac%7B%5Coverline%7Bx%7D-%5Cmu_0%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D%24~%24N(0%2C1)%24%0A%3E%24%5Calpha%5E2%24%E6%9C%AA%E7%9F%A5%20%24z%3D%5Cfrac%7B%5Coverline%7Bx%7D-%5Cmu_0%7D%7B%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%7D%24~%24t(0%2C1)%24%0A%0A%0A%23%23%23%23%20%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E7%9A%84%E6%A3%80%E9%AA%8C—%E5%B0%8F%E6%A0%B7%E6%9C%AC%E6%A3%80%E9%AA%8C%E6%96%B9%E6%B3%95%E7%9A%84%E6%80%BB%E7%BB%93%0A%0A%7C%20%E5%81%87%E8%AE%BE%20%7C%20%E5%8F%8C%E4%BE%A7%E6%A3%80%E9%AA%8C%20%7C%20%E5%B7%A6%E4%BE%A7%E6%A3%80%E9%AA%8C%20%7C%20%E5%8F%B3%E4%BE%A7%E6%A3%80%E9%AA%8C%20%7C%0A%7C%20%3A—%3A%20%7C%20%3A—%3A%20%7C%20%3A—%3A%20%7C%20%3A—%3A%20%7C%0A%7C%20%E5%81%87%E8%AE%BE%E5%BD%A2%E5%BC%8F%20%7C%20%24H_0%3A%5Cmu%3D%5Cmu_0%24%20%7C%20%24H_0%3A%5Cmu%20%5Cgeq%20%5Cmu_0%24%20%7C%20%24H_0%3A%5Cmu%20%5Cleq%20%5Cmu_0%24%20%7C%0A%7C%20%E5%81%87%E8%AE%BE%E5%BD%A2%E5%BC%8F%20%7C%20%24H_1%3A%20%5Cmu%20%5Cneq%20%5Cmu_0%24%20%7C%20%24H_1%3A%5Cmu%20%3C%20%5Cmu_0%24%20%7C%20%24H_1%3A%20%5Cmu%20%3E%20%5Cmu_0%24%20%7C%0A%7C%20%E7%BB%9F%E8%AE%A1%E9%87%8F%20%7C%20%24%5Calpha%24%E5%B7%B2%E7%9F%A5%20%7C%20%24z%3D%5Cfrac%7B%5Coverline%7Bx%7D-%5Cmu_0%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D%24%20%7C%20%20%7C%0A%7C%20%E7%BB%9F%E8%AE%A1%E9%87%8F%20%7C%20%24%5Calpha%24%E6%9C%AA%E7%9F%A5%20%20%7C%20%24z%3D%5Cfrac%7B%5Coverline%7Bx%7D-%5Cmu_0%7D%7B%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%7D%24%20%7C%20%20%7C%0A%7C%20%E6%8B%92%E7%BB%9D%E5%9F%9F%20%7C%24t%3Et_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D(n-1)%24%20%7C%20%24t%3C-t_%7B%5Calpha%7D(n-1)%24%20%7C%20%24t%3Et_%7B%5Calpha%7D(n-1)%24%20%7C%0A%7C%20P%E5%80%BC%E5%86%B3%E7%AD%96%20%7C%20%24P%3C%5Calpha%24%20%E6%8B%92%E7%BB%9D%24H_0%24%7C%20%20%7C%20%20%7C%0A%0A%23%23%23%23%20%E6%80%BB%E4%BD%93%E6%AF%94%E4%BE%8B%E6%A3%80%E9%AA%8C%0A%3E%E5%81%87%E5%AE%9A%E6%9D%A1%E4%BB%B6%0A%3E-%20%E6%80%BB%E4%BD%93%E6%9C%8D%E4%BB%8E%E4%BA%8C%E9%A1%B9%E5%88%86%E5%B8%83%0A%3E-%20%E5%8F%AF%E7%94%A8%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%E6%9D%A5%E8%BF%91%E4%BC%BC(%E5%A4%A7%E6%A0%B7%E6%9C%AC)%0A%3E%E6%A3%80%E9%AA%8C%E7%9A%84z%E7%BB%9F%E8%AE%A1%E9%87%8F%0A%3E%24z%3D%5Cfrac%7Bp-%5Cpi_0%7D%7B%5Csqrt%7B%5Cfrac%7Bpi_0(1-%5Cpi_0)%7D%7Bn%7D%7D%7D%24%0A%3E%24pi_0%24%E4%B8%BA%E5%81%87%E8%AE%BE%E7%9A%84%E6%80%BB%E4%BD%93%E6%AF%94%E4%BE%8B%0A%0A%23%23%23%23%20%E6%80%BB%E4%BD%93%E6%AF%94%E4%BE%8B%E7%9A%84%E6%A3%80%E9%AA%8C%0A%0A%7C%20%E5%81%87%E8%AE%BE%20%7C%20%E5%8F%8C%E4%BE%A7%E6%A3%80%E9%AA%8C%20%7C%20%E5%B7%A6%E4%BE%A7%E6%A3%80%E9%AA%8C%20%7C%20%E5%8F%B3%E4%BE%A7%E6%A3%80%E9%AA%8C%20%7C%0A%7C%20%3A—%3A%20%7C%20%3A—%3A%20%7C%20%3A—%3A%20%7C%20%3A—%3A%20%7C%0A%7C%20%E5%81%87%E8%AE%BE%E5%BD%A2%E5%BC%8F%20%7C%20%24H_0%3A%5Cmu%3D%5Cmu_0%24%20%7C%20%24H_0%3A%5Cmu%20%5Cgeq%20%5Cmu_0%24%20%7C%20%24H_0%3A%5Cmu%20%5Cleq%20%5Cmu_0%24%20%7C%0A%7C%20%E5%81%87%E8%AE%BE%E5%BD%A2%E5%BC%8F%20%7C%20%24H_1%3A%20%5Cmu%20%5Cneq%20%5Cmu_0%24%20%7C%20%24H_1%3A%5Cmu%20%3C%20%5Cmu_0%24%20%7C%20%24H_1%3A%20%5Cmu%20%3E%20%5Cmu_0%24%20%7C%0A%7C%20%E7%BB%9F%E8%AE%A1%E9%87%8F%20%7C%24z%3D%5Cfrac%7Bp-%5Cpi_0%7D%7B%5Csqrt%7B%5Cfrac%7B%5Cpi_0(1-%5Cpi_0)%7D%7Bn%7D%7D%7D%24%20%20%7C%20%20%7C%0A%7C%20%E7%BB%9F%E8%AE%A1%E9%87%8F%20%7C%20%7C%20%20%7C%0A%7C%20%E6%8B%92%E7%BB%9D%E5%9F%9F%20%7C%24z%3Ez_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%24%20%7C%20%24z%3C-a_%7B%5Calpha%7D%24%20%7C%20%24z%3Ez_%7B%5Calpha%7D%24%20%7C%0A%7C%20P%E5%80%BC%E5%86%B3%E7%AD%96%20%7C%20%24P%3C%5Calpha%24%20%E6%8B%92%E7%BB%9D%24H_0%24%7C%20%20%7C%20%20%7C%0A%0A%0A%23%23%23%23%20%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%E7%9A%84%E6%A3%80%E9%AA%8C%0A%3E%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%E6%98%AF%E6%9C%8D%E4%BB%8E%E5%8D%A1%E6%96%B9%E5%88%86%E5%B8%83%E7%9A%84%EF%BC%8C%E6%A3%80%E9%AA%8C%E4%B8%80%E4%B8%AA%E6%80%BB%E4%BD%93%E7%9A%84%E6%96%B9%E5%B7%AE%E6%88%96%E6%A0%87%E5%87%86%E5%B7%AE%EF%BC%8C%E5%81%87%E8%AE%BE%E6%80%BB%E4%BD%93%E8%BF%91%E4%BC%BC%E6%9C%8D%E4%BB%8E%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%EF%BC%8C%E4%BD%BF%E7%94%A8%24%5Cchi%5E2%24%0A%3E%E6%A3%80%E9%AA%8C%E7%BB%9F%E8%AE%A1%E9%87%8F%0A%3E%24%5Cchi%5E2%3D%5Cfrac%7B(n-1)s%5E2%7D%7B%5Csigma_0%5E2%7D%24~%24%5Cchi%5E2(n-1)%24%0A%3E%E5%85%B6%E4%B8%ADs%E4%B8%BA%E6%A0%B7%E6%9C%AC%E6%96%B9%E5%B7%AE%EF%BC%8C%24%5Csigma%24%E4%B8%BA%E5%81%87%E8%AE%BE%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%0A%0A%23%23%23%23%20%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%8F%82%E6%95%B0%E7%9A%84%E6%A3%80%E9%AA%8C%0A%3E%E4%B8%A4%E4%B8%AA%E7%BB%9F%E8%AE%A1%E9%87%8F%E7%9A%84%E7%A1%AE%E5%AE%9A%0A%3E%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E4%B9%8B%E5%B7%AE%E7%9A%84%E6%A3%80%E9%AA%8C%0A%3E%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E6%AF%94%E4%BE%8B%E4%B9%8B%E5%B7%AE%E7%9A%84%E6%A3%80%E9%AA%8C%0A%3E%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E6%96%B9%E5%B7%AE%E4%B9%8B%E6%AF%94%E7%9A%84%E6%A3%80%E9%AA%8C%0A%3E%E6%A3%80%E9%AA%8C%E4%B8%AD%E7%9A%84%E5%8C%B9%E9%85%8D%E6%A0%B7%E6%9C%AC%0A%0A%23%23%23%23%20%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E4%B9%8B%E5%B7%AE%E7%9A%84%E6%A3%80%E9%AA%8C(%E7%8B%AC%E7%AB%8B%E5%A4%A7%E6%A0%B7%E6%9C%AC)%0A%3E1.%E5%81%87%E5%AE%9A%E6%9D%A1%E4%BB%B6%0A%3E*%20%E4%B8%A4%E4%B8%AA%E6%A0%B7%E6%9C%AC%E6%98%AF%E7%8B%AC%E7%AB%8B%E7%9A%84%E9%9A%8F%E6%9C%BA%E6%A0%B7%E6%9C%AC%0A%3E*%20%E6%AD%A3%E6%80%81%E6%80%BB%E4%BD%93%E6%88%96%E9%9D%9E%E6%AD%A3%E6%80%81%E6%80%BB%E4%BD%93%E5%A4%A7%E6%A0%B7%E6%9C%AC(%24n_1%20%5Cgeq%2030%20n_2%20%5Creq%2030%24)%E6%A3%80%E9%AA%8C%E7%BB%9F%E8%AE%A1%E9%87%8F%0A%3E%24%5Csigma_1%5E2%24%2C%24%5Csigma_2%5E2%24%E5%B7%B2%E7%9F%A5%24z%3D%5Cfrac%7B(%5Coverline%7Bx_1%7D-%5Coverline%7Bx_2%7D)-(%5Cmu_1-%5Cmu_2)%7D%7B%5Csqrt%7B%5Cfrac%7B%5Csigma_1%5E2%7D%7Bn_1%7D%2B%5Cfrac%7B%5Csigma_2%5E2%7D%7Bn_2%7D%7D%7D%24~%24N(0%2C1)%24%0A%3E%24%5Csigma_1%5E2%24%2C%24%5Csigma_2%5E2%24%E6%9C%AA%E7%9F%A5%24z%3D%5Cfrac%7B(%5Coverline%7Bx_1%7D-%5Coverline%7Bx_2%7D)-(%5Cmu_1-%5Cmu_2)%7D%7B%5Csqrt%7B%5Cfrac%7B%5Csigma_1%5E2%7D%7Bn_1%7D%2B%5Cfrac%7B%5Csigma_2%5E2%7D%7Bn_2%7D%7D%7D%24~%24N(0%2C1)%24%0A%0A%23%23%23%23%20%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E4%B9%8B%E5%B7%AE%E7%9A%84%E6%A3%80%E9%AA%8C(%E7%8B%AC%E7%AB%8B%E5%B0%8F%E6%A0%B7%E6%9C%AC)%0A%3E1.%E5%81%87%E5%AE%9A%E6%9D%A1%E4%BB%B6%0A%3E*%20%E4%B8%A4%E4%B8%AA%E7%8B%AC%E7%AB%8B%E7%9A%84%E5%B0%8F%E6%A0%B7%E6%9C%AC%0A%3E*%20%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E9%83%BD%E6%98%AF%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%0A%3E%20%24%5Csigma_1%5E2%24%E3%80%81%24%5Csigma_2%5E2%24%E5%B7%B2%E7%9F%A5%0A%3E%20%E6%A3%80%E9%AA%8C%E7%BB%9F%E8%AE%A1%E9%87%8F%0A%3E%20%24z%3D%5Cfrac%7B(%5Coverline%7Bx_1%7D-%5Coverline%7Bx_2%7D-(%5Cmu_1-%5Cmu_2))%7D%7B%5Csqrt%7B%5Cfrac%7B%5Csigma_1%5E2%7D%7Bn_1%7D%2B%5Cfrac%7B%5Csigma_2%5E2%7D%7Bn_2%7D%7D%7D%24~%24N(0%2C1)%24%0A%0A%0A%23%23%23%23%20%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E4%B9%8B%E5%B7%AE%E7%9A%84%E6%A3%80%E9%AA%8C%0A%3E%24%5Csigma_1%5E2%2C%5Csigma_2%5E2%E6%9C%AA%E7%9F%A5%E4%BD%86%E6%98%AF%24%5Csigma_1%5E2%3D%5Csigma_2%5E2%24%24%0A%3E1.%E5%81%87%E5%AE%9A%E6%9D%A1%E4%BB%B6%0A%3E*%20%E4%B8%A4%E4%B8%AA%E7%8B%AC%E7%AB%8B%E7%9A%84%E5%B0%8F%E6%A0%B7%E6%9C%AC%0A%3E*%20%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E9%83%BD%E6%98%AF%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%0A%3E*%20%24%5Csigma_1%5E2%24%E3%80%81%24%5Csigma_2%5E2%24%E6%9C%AA%E7%9F%A5%E4%BD%86%E6%98%AF%E7%9B%B8%E7%AD%89%EF%BC%8C%E5%8D%B3%24%5Csigma_1%5E2%3D%5Csigma_2%5E2%24%0A%3E2.%E6%A3%80%E9%AA%8C%E7%BB%9F%E8%AE%A1%E9%87%8F%0A%3E%24t%3D%5Cfrac%7B(%5Coverline%7Bx_1%7D-%5Coverline%7Bx_2%7D)-(%5Cmu_1-%5Cmu_2)%7D%7Bs_p%5Csqrt%7B%5Cfrac%7B1%7D%7Bn_1%7D%2B%5Cfrac%7B1%7D%7Bn_2%7D%7D%7D%24%0A%3E%E5%85%B6%E4%B8%AD%24s_p%5E2%3D%5Cfrac%7B(n_1-1)s_1%5E2%2B(n_2-1)s_2%5E2%7D%7Bn_1%2Bn_2-2%7D%24%0A%0A%23%23%23%23%20%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E4%B9%8B%E5%B7%AE%E7%9A%84%E6%A3%80%E9%AA%8C%0A%3E%24%5Csigma_1%5E2%2C%5Csigma_2%5E2%24%E6%9C%AA%E7%9F%A5%E4%B8%94%E4%B8%8D%E7%9B%B8%E7%AD%89%24%5Csigma_1%5E2%20%5Cneq%20%5Csigma_2%5E2%24%0A%3E%E5%81%87%E5%AE%9A%E6%9D%A1%E4%BB%B6%0A%3E*%20%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E9%83%BD%E6%98%AF%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%0A%3E*%20%24%5Csigma_2%5E2%2C%5Csigma_2%5E2%24%E6%9C%AA%E7%9F%A5%E4%B8%94%E4%B8%8D%E7%9B%B8%E7%AD%89%EF%BC%8C%E5%8D%B3%24%5Csigma_1%5E2%20%5Cneq%20%5Csigma_2%5E2%24%0A%3E*%20%E6%A0%B7%E6%9C%AC%E5%AE%B9%E9%87%8F%E4%B8%8D%E7%9B%B8%E7%AD%89%EF%BC%8C%E5%8D%B3%24n_1%20%5Cneq%20n_2%24%0A%3E%E6%A3%80%E9%AA%8C%E7%BB%9F%E8%AE%A1%E9%87%8F%0A%3E%24t%3D%5Cfrac%7B(%5Coverline%7Bx_1%7D-%5Coverline%7Bx_2%7D)-(%5Cmu_1-%5Cmu_2)%7D%7B%5Csqrt%7B%5Cfrac%7Bs_1%5E2%7D%7Bn_1%7D%2B%5Cfrac%7Bs_2%5E2%7D%7Bn_2%7D%7D%7D%24%0A%3E%E8%87%AA%E7%94%B1%E5%BA%A6%20%24v%3D%5Cfrac%7B(%5Cfrac%7Bs_1%5E2%7D%7Bn_1%7D%2B%5Cfrac%7Bs_2%5E2%7D%7Bn_2%7D)%7D%7B%5Cfrac%7B%5Cfrac%7Bs_1%5E2%7D%7Bn_2%5E2%7D%7D%7Bn_1-1%7D%2B%5Cfrac%7B%5Cfrac%7Bs_2%5E2%7D%7Bn_2%7D%7D%7Bn_2-1%7D%7D%24%0A%0A%23%23%23%23%20%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E5%9D%87%E5%80%BC%E4%B9%8B%E5%B7%AE%E7%9A%84%E6%A3%80%E9%AA%8C(%E5%8C%B9%E9%85%8D%E6%A0%B7%E6%9C%AC)%0A%3E%E5%81%87%E5%AE%9A%E6%9D%A1%E4%BB%B6%0A%3E%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E9%85%8D%E5%AF%B9%E5%B7%AE%E5%80%BC%E6%9E%84%E6%88%90%E7%9A%84%E6%80%BB%E4%BD%93%E6%9C%8D%E4%BB%8E%E9%85%8D%E5%AF%B9%E5%B7%AE%E6%98%AF%E7%94%B1%E5%B7%AE%E5%80%BC%E6%80%BB%E4%BD%93%E4%B8%AD%E9%9A%8F%E6%9C%BA%E6%8A%BD%E5%8F%96%E7%9A%84%E6%95%B0%E6%8D%AE%E9%85%8D%E5%AF%B9%E6%88%96%E5%8C%B9%E9%85%8D(%E9%87%8D%E5%A4%8D%E6%B5%8B%E9%87%8F(%E5%89%8D%2F%E5%90%8E))%0A%3E%E6%A3%80%E9%AA%8C%E7%BB%9F%E8%AE%A1%E9%87%8F%0A%3E%24t%3D%5Cfrac%7B%5Coverline%7Bd%7D-d_0%7D%7B%5Cfrac%7BS_d%7D%7B%5Csqrt%7Bn_d%7D%7D%7D%24~%24t(n-1)%24%0A%3E%E6%A0%B7%E6%9C%AC%E5%B7%AE%E5%80%BC%E5%9D%87%E5%80%BC%24%5Coverline%7Bd%7D%3D%5Cfrac%7B%5Csum%5En_%7Bi%3D1%7Dd_i%7D%7Bn_d%7D%24%0A%0A%23%23%23%23%20%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E6%AF%94%E4%BE%8B%E4%B9%8B%E5%B7%AE%E7%9A%84%E6%A3%80%E9%AA%8C%0A%3E%E5%81%87%E5%AE%9A%E6%9D%A1%E4%BB%B6%0A%3E%E4%B8%A4%E4%B8%AA%E6%80%BB%E4%BD%93%E9%83%BD%E6%9C%8D%E4%BB%8E%E4%BA%8C%E9%A1%B9%E5%88%86%E5%B8%83%0A%3E%E5%8F%AF%E4%BB%A5%E7%94%A8%E6%AD%A3%E6%80%81%E5%88%86%E5%B8%83%E6%9D%A5%E8%BF%91%E4%BC%BC%E6%A3%80%E9%AA%8C%E7%BB%9F%E8%AE%A1%E9%87%8F%0A%3E%E6%A3%80%E9%AA%8C%24H_0%24%2C%24%5Cpi_1-%5Cpi_2%3D0%24%2C%24z%3D%5Cfrac%7Bp_1-p_2%7D%7B%5Csqrt%7Bp(1-p)(%5Cfrac%7B1%7D%7Bn_1%7D%2B%5Cfrac%7B1%7D%7Bn_2%7D)%7D%7D%24%0A%3E%E6%A3%80%E9%AA%8C%24H_0%24%2C%24%5Cpi_1-%5Cpi_2%3Dd_0%24%2C%24z%3D%5Cfrac%7B(p_1-p_2)-d_0%7D%7B%5Csqrt%7B%5Cfrac%7Bp_1(1-p_1)%7D%7Bn_1%7D%2B%5Cfrac%7Bp_2(1-p_2)%7D%7Bn_2%7D%7D%7D%24

Win a contest, win a challenge