西南交通大学：《管理统计学》（双语版） 第9章 参数假设检验

第9章参数假设检验 Hypotheses Test with Parametrics

第9章 参数假设检验 Hypotheses Test with Parametrics

开篇案例] 北京地区大学教授与合资企业职工收入比较 统计量大学教授 合资企业职工 样本含量n=150 n=150 平均收入￥1000 ￥1000 标准差 ￥200 ￥800 标准误 ￥16.33 ￥65.32 95%的C|(968,1032) (872,1128) 问题 两人群收入的离散(“贫富”分化)程度如何?

[开篇案例] 北京地区大学教授与合资企业职工收入比较 统计量 大学教授 合资企业职工 样本含量 n=150 n=150 平均收入 ￥1000 ￥1000 标准差 ￥ 200 ￥ 800 标准误 ￥16.33 ￥65.32 95%的CI （968，1032） （872，1128） 问题： 两人群收入的离散（“贫富”分化）程度如何？

假设检验的基本概念 某项市场调研想分析一次特定的广告大战之后 是否明显提高了某彩电在消费者中的知名度 ?是否显著激发了消费兴趣?--显著性检验 1、零假设与备择假设 零假设( null hypothesis,H)又称无差异假设 备择假设( alternative hypothesis,H1):单双侧 2、假设检验的分类 参数检验( parametric tests)要求明确的总体分布 非参数检验(non- parametric tests)无须总体分布 3、显著性水平:样本参数偏离总体参数的概率

一、假设检验的基本概念 某项市场调研想分析一次特定的广告大战之后 是否明显提高了某彩电在消费者中的知名度 ？是否显著激发了消费兴趣？----显著性检验 1、零假设与备择假设 零假设（null hypothesis, H0）又称无差异假设 备择假设（alternative hypothesis, H1）：单双侧 2、假设检验的分类 参数检验(parametric tests)要求明确的总体分布 非参数检验(non-parametric tests)无须总体分布 3、显著性水平：样本参数偏离总体参数的概率

4、假设检验的基本步骤 正确给出两类假设及检验水平; 正确选择并计算样本统计量的值: 将样本统让量与由样本含量、检验水平及统计量 的理论分布决定的临界值比较,获得样本统 计量大(小)于临界值的概率P; 将P与检验水平比较,并做出是否拒绝或不拒绝 零假设的决策 5、两类错误: 接受Ho 拒绝H H0.为真 型错误 H0为假 型错误

4、假设检验的基本步骤 正确给出两类假设及检验水平； 正确选择并计算样本统计量的值； 将样本统计量与由样本含量、检验水平及统计量 的理论分布决定的临界值比较，获得样本统 计量大（小）于临界值的概率P； 将P与检验水平比较，并做出是否拒绝或不拒绝 零假设的决策。 5、两类错误： 接受H0 拒绝H0 H0为真 --- I型错误 H0为假 II型错误 ---

二、One- Sample tests(单样本检验) Hypothesis Testing Methodology Z Test for the mean( o Known总体方差已知) p-Value Approach to Hypothesis Testing Connection to Confidence Interval Estimation One Tail Test(单侧检验) t Test of Hypothesis for the mean Z Test of Hypothesis for the Proportion

二、One-Sample Tests （单样本检验） •Hypothesis Testing Methodology •Z Test for the Mean (s Known总体方差已知) • p-Value Approach to Hypothesis Testing •Connection to Confidence Interval Estimation •One Tail Test（单侧检验） • t Test of Hypothesis for the Mean •Z Test of Hypothesis for the Proportion

What is a Hypothesis? 关于总体参数的假设 A hypothesis is an I assume the mean gpa assumption about the of this class is 3.5! population parameter. 口 A parameter is a Population mean or proportion 口 The parameter must be identified before analysis ?1984-1994 TMaker Co

A hypothesis is an assumption about the population parameter.  A parameter is a Population mean or proportion  The parameter must be identified before analysis. I assume the mean GPA of this class is 3.5! ?1984-1994 T/Maker Co. What is a Hypothesis? 关于总体参数的假设

The Null Hypothesis, Ho 无效假设 States the Assumption (numerical) to be tested e.g. The average TV sets in US homes is at least 3(H0:u>3) Begin with the assumption that the null hypothesis iS TRUE. (Similar to the notion of innocent until proven guilty o Refers to the Status Quo .Always contains the ?=?sign The Null Hypothesis may or may not be rejected

• States the Assumption (numerical) to be tested e.g. The average # TV sets in US homes is at least 3 (H0 : m >3) • Begin with the assumption that the null hypothesis is TRUE. (Similar to the notion of innocent until proven guilty) The Null Hypothesis, H0 无效假设 •Refers to the Status Quo •Always contains the ?= ?sign •The Null Hypothesis may or may not be rejected

The Alternative Hypothesis, HI 被择假设 Is the opposite of the null hypothesis e.g. The average TV sets in US homes is less than3(H1:μ<3) Challenges the status Quo Never contains the ??sign The Alternative Hypothesis may or may not be accepted

• Is the opposite of the null hypothesis e.g. The average # TV sets in US homes is less than 3 (H1 : m < 3) • Challenges the Status Quo • Never contains the ??sign • The Alternative Hypothesis may or may not be accepted The Alternative Hypothesis, H1 被择假设

Identify the problem 解决问题的步骤 Steps: a State the Null Hypothesis (Ho: u=3) a State its opposite, the Alternative Hypothesis(H1:μ<3) o Hypotheses are mutually exclusive exhaustive e Sometimes it is easier to form the alternative hypothesis first

Steps:  State the Null Hypothesis (H0 : m = 3)  State its opposite, the Alternative Hypothesis (H1 : m < 3) ⚫ Hypotheses are mutually exclusive & exhaustive ⚫ Sometimes it is easier to form the alternative hypothesis first. Identify the Problem 解决问题的步骤

Hypothesis Testing process 假设检验过程 Assume the population mean age is 50 (Null Hypothesis) Population lsX=20=50? The Sample Mean Is 20 No, not likely ■■■■I ■■■ Null Hypothesis 回■ Sample

Population Assume the population mean age is 50. (Null Hypothesis) REJECT The Sample Mean Is 20 Null Hypothesis Sample Is X = 20  m = 50? Hypothesis Testing Process 假设检验过程 No, not likely!