经典六西格玛(6 sigma)培训内部资料A_04_Introduction To Hypothesis Testing.(7)
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Introduction To Hypothesis Testing 10
Explaining the Results 就结果进行解释
980 Girls 980个女生
The result of 980 girls out of 1000 students is very unlikely to occur by chance. 一般不会发生1000个学生中有980个女生的 情况。 Either an extremely unlikely event has occurred by chance. Or, more convincingly, the claim that girls are more likely to attend the Musical school than are boys is true. 这种情况有两种解释：一是一般不会发生的 异常事件发生了，或者是更让人信服的解释 ，报考音乐学院的女生的确比男生更多的声 明是正确的。
者否决的判定。 Î Traditional decision making is based on subjective gap
filling with high risk. Statistical testing provides an
objective solution. 传统的决策方式是基于具有高风险的主观意识，统计
Introduction To Hypothesis Testing 11
A Significant Difference 显著的区别
How significant is the difference between the sample result and what we would normally expect if there were no preferences by gender for attending the Musical School?
What would you conclude about this claim if you find the following results from your sample of 1000 students... 如果从1000个学生的抽样中得到下列结果，你会对以上声 明的正确性得出什么结论？
Introduction To Hypothesis Testing 8
Example of Reasoning in Hypothesis Testing 假设检验推论举例
Someone claims that girls are more likely to attend Musical School than are boys. 假设有人声称报考音乐学院 的女生会比男生多
Ho: μ = 40mm (The process mean
equals the target) （过程均值同目标相等）
® Must contain the condition
of equality 必须包含等号.
Introduction To Hypothesis Testing 14
Null and Alternative Hypotheses 零假设和备选假设
¾ The average time for completing an assignment is less than 30 days. 完成任务的平均时间少于30天
¾ Average gas mileage differs depending on type A or B gas. A类汽油和B类汽油的平均里程不同。
Introduction To Hypothesis Testing 4
What is a Hypothesis ?什么是假设 ?
Î When solving a problem, very often we need to decide
whether to accept or reject a statement about a parameter 在许多问题中，都需要对一个参数的陈述作出接受或
检验为我们提供了一个客观的解决方案。 Î Hypothesis testing translates a practical question into a
statistical question for decision making 。 假设检验为我们的决策将一个实际问题转换成一个统
计问题。
Introduction To Hypothesis Testing
6 Sigma路线图 – 假设检验
6 Sigma strategy 突破性改善
Characterize 特性化
Optimize 优化
define 定义
Measure 测量
Analyze 分析
To determine whether the root causes are real. 确定原因是 否真实
Alternative hypothesis is also know as Research Hypothesis 备选假设也叫研究假设
Î For example: 例子
H0 – Population mean oxide thickness IS equal to 200 angstroms. H0 – 氧化物平均厚度等于200 angstroms Ha - Population mean oxide thickness is NOT equal to 200 angstroms Ha – 氧化物平均厚度不等于200 angstroms
What is a Hypothesis?什么是假设？
A hypothesis is….A statement or claim about some unrealized true state of nature. 假设是…对于一些未知事实的陈述或声明.
A Statistical hypothesis is … A claim or statement about a characteristic of a population (such as mean, variance, proportion). 统计假设是……就对象总体特性（例如均值，方差和比例 ）的声明或陈述。
D. Compute the P-value.
计算P值
E. Compare the P-value to the level of significance, α . 比较P值和显著水平,α
F. Draw Conclusion 得出结论（统计结论和现实结论）
Introduction To Hypothesis Testing 13
Introduction To Hypothesis Testing
7
7
The Reasoning in Statistics 统计推论指导
We analyze data collected from a sample to distinguish between results that can easily occur and results that are highly unlikely. 我们对抽样中的数据进行分析，区分很容易出现的结果和 很难出现的结果。
如果报考音乐学院的学生不存 在性别上优先选择，那将与抽 样结果是否有显著的不同呢？
Introduction To Hypothesis Testing 12
抽样结果 505 out of 1000
通常的情况 500 out of 1000
A 04-2
How to Conduct Hypothesis Test 进行假设检验的步骤
Introduction To Hypothesis Testing 3
Improve 改善
Control 控制
To verify whether the solutions are effective. 验证解决方案 是否有效
To determine when significant changes take place. 确定重大改变 发生的时间
When a highly unlikely needle has occurred, our explanation may be: 如果很难出现的结果出现了，我们可以这样解释…
¾ A rare event has occurred, or 出现了罕见的结果，或者
¾ Things are not what we assumed them to be. 事物并不是我们想象的那样
Null and Alternative Hypotheses 零假设和备选假设
Null Hypothesis 零假设
Example 举例
® Is a statement about the value of a population parameter (such as the
mean) 关于一个总体参数（如均值） 的 一个陈述
完成本章节学习后，学员能够……
I. Perform hypothesis tests for population means, population variances, population proportions,
对抽样对象总体的均值，方差，比例进行假设检验
Introduction To Hypothesis Testing 2
A. State both the Ho and Ha. 建立零假设和备选假设
B. Determine the level of significance, α 决定显著性水平α
C. Take a representative sample of data randomly. 随机抽取具有代表性的样本.
www.scsway.net
Introduction To
Hypothesis Testing 假设检验简介
Hypothesis Testing - Learning Objectives 假设检验 – 学习目标
Upon completion of this chapter, you w源自文库ll be able to…
The result of 505 girls is so close to 500 that we will not support the claim that girls are more likely to attend Musical School than are boys. 505个女生跟500非常相近，我们不会支持报 考音乐学院的女生比男生多的声明
Introduction To Hypothesis Testing 6
A 04-1
Null hypothesis vs Alternative Hypothesis 零假设和备选假设
Î The actual hypotheses to be tested consist of two complementary statements, Null hypothesis (H0 ) Alternative hypothesis (Ha) 实际进行假设检验时, 假设包含两个互补的陈述, 即 零假设(H0 ) 备选假设(Ha)
5
5
Examples of Hypothesis 假设举例
¾ Factory A is running at a lower rejection rate than factory B. A工厂的不良率比B工厂的低
¾ The number of scrapped products is greater for Process A than for Process B. 过程A中次品的数量比过程B中的多
a) 505 girls? 505 个女生?
b) 980 girls? 980 个女生?
Introduction To Hypothesis Testing 9
Explaining the Results 就结果进行解释
505 girls 505 个女生
We normally expect about 500 girls out of 1000 students. 通常都是在1000个学生中有500个女生
Explaining the Results 就结果进行解释
980 Girls 980个女生
The result of 980 girls out of 1000 students is very unlikely to occur by chance. 一般不会发生1000个学生中有980个女生的 情况。 Either an extremely unlikely event has occurred by chance. Or, more convincingly, the claim that girls are more likely to attend the Musical school than are boys is true. 这种情况有两种解释：一是一般不会发生的 异常事件发生了，或者是更让人信服的解释 ，报考音乐学院的女生的确比男生更多的声 明是正确的。
者否决的判定。 Î Traditional decision making is based on subjective gap
filling with high risk. Statistical testing provides an
objective solution. 传统的决策方式是基于具有高风险的主观意识，统计
Introduction To Hypothesis Testing 11
A Significant Difference 显著的区别
How significant is the difference between the sample result and what we would normally expect if there were no preferences by gender for attending the Musical School?
What would you conclude about this claim if you find the following results from your sample of 1000 students... 如果从1000个学生的抽样中得到下列结果，你会对以上声 明的正确性得出什么结论？
Introduction To Hypothesis Testing 8
Example of Reasoning in Hypothesis Testing 假设检验推论举例
Someone claims that girls are more likely to attend Musical School than are boys. 假设有人声称报考音乐学院 的女生会比男生多
Ho: μ = 40mm (The process mean
equals the target) （过程均值同目标相等）
® Must contain the condition
of equality 必须包含等号.
Introduction To Hypothesis Testing 14
Null and Alternative Hypotheses 零假设和备选假设
¾ The average time for completing an assignment is less than 30 days. 完成任务的平均时间少于30天
¾ Average gas mileage differs depending on type A or B gas. A类汽油和B类汽油的平均里程不同。
Introduction To Hypothesis Testing 4
What is a Hypothesis ?什么是假设 ?
Î When solving a problem, very often we need to decide
whether to accept or reject a statement about a parameter 在许多问题中，都需要对一个参数的陈述作出接受或
检验为我们提供了一个客观的解决方案。 Î Hypothesis testing translates a practical question into a
statistical question for decision making 。 假设检验为我们的决策将一个实际问题转换成一个统
计问题。
Introduction To Hypothesis Testing
6 Sigma路线图 – 假设检验
6 Sigma strategy 突破性改善
Characterize 特性化
Optimize 优化
define 定义
Measure 测量
Analyze 分析
To determine whether the root causes are real. 确定原因是 否真实
Alternative hypothesis is also know as Research Hypothesis 备选假设也叫研究假设
Î For example: 例子
H0 – Population mean oxide thickness IS equal to 200 angstroms. H0 – 氧化物平均厚度等于200 angstroms Ha - Population mean oxide thickness is NOT equal to 200 angstroms Ha – 氧化物平均厚度不等于200 angstroms
What is a Hypothesis?什么是假设？
A hypothesis is….A statement or claim about some unrealized true state of nature. 假设是…对于一些未知事实的陈述或声明.
A Statistical hypothesis is … A claim or statement about a characteristic of a population (such as mean, variance, proportion). 统计假设是……就对象总体特性（例如均值，方差和比例 ）的声明或陈述。
D. Compute the P-value.
计算P值
E. Compare the P-value to the level of significance, α . 比较P值和显著水平,α
F. Draw Conclusion 得出结论（统计结论和现实结论）
Introduction To Hypothesis Testing 13
Introduction To Hypothesis Testing
7
7
The Reasoning in Statistics 统计推论指导
We analyze data collected from a sample to distinguish between results that can easily occur and results that are highly unlikely. 我们对抽样中的数据进行分析，区分很容易出现的结果和 很难出现的结果。
如果报考音乐学院的学生不存 在性别上优先选择，那将与抽 样结果是否有显著的不同呢？
Introduction To Hypothesis Testing 12
抽样结果 505 out of 1000
通常的情况 500 out of 1000
A 04-2
How to Conduct Hypothesis Test 进行假设检验的步骤
Introduction To Hypothesis Testing 3
Improve 改善
Control 控制
To verify whether the solutions are effective. 验证解决方案 是否有效
To determine when significant changes take place. 确定重大改变 发生的时间
When a highly unlikely needle has occurred, our explanation may be: 如果很难出现的结果出现了，我们可以这样解释…
¾ A rare event has occurred, or 出现了罕见的结果，或者
¾ Things are not what we assumed them to be. 事物并不是我们想象的那样
Null and Alternative Hypotheses 零假设和备选假设
Null Hypothesis 零假设
Example 举例
® Is a statement about the value of a population parameter (such as the
mean) 关于一个总体参数（如均值） 的 一个陈述
完成本章节学习后，学员能够……
I. Perform hypothesis tests for population means, population variances, population proportions,
对抽样对象总体的均值，方差，比例进行假设检验
Introduction To Hypothesis Testing 2
A. State both the Ho and Ha. 建立零假设和备选假设
B. Determine the level of significance, α 决定显著性水平α
C. Take a representative sample of data randomly. 随机抽取具有代表性的样本.
www.scsway.net
Introduction To
Hypothesis Testing 假设检验简介
Hypothesis Testing - Learning Objectives 假设检验 – 学习目标
Upon completion of this chapter, you w源自文库ll be able to…
The result of 505 girls is so close to 500 that we will not support the claim that girls are more likely to attend Musical School than are boys. 505个女生跟500非常相近，我们不会支持报 考音乐学院的女生比男生多的声明
Introduction To Hypothesis Testing 6
A 04-1
Null hypothesis vs Alternative Hypothesis 零假设和备选假设
Î The actual hypotheses to be tested consist of two complementary statements, Null hypothesis (H0 ) Alternative hypothesis (Ha) 实际进行假设检验时, 假设包含两个互补的陈述, 即 零假设(H0 ) 备选假设(Ha)
5
5
Examples of Hypothesis 假设举例
¾ Factory A is running at a lower rejection rate than factory B. A工厂的不良率比B工厂的低
¾ The number of scrapped products is greater for Process A than for Process B. 过程A中次品的数量比过程B中的多
a) 505 girls? 505 个女生?
b) 980 girls? 980 个女生?
Introduction To Hypothesis Testing 9
Explaining the Results 就结果进行解释
505 girls 505 个女生
We normally expect about 500 girls out of 1000 students. 通常都是在1000个学生中有500个女生