Enviar búsqueda
Cargar
Hypothesis
•
Descargar como PPT, PDF
•
2 recomendaciones
•
1,361 vistas
Abhishek Gupta
Seguir
TBS , jammu
Leer menos
Leer más
Empresariales
Denunciar
Compartir
Denunciar
Compartir
1 de 42
Descargar ahora
Recomendados
THE NATURE AND GOALS OF ANTHROPOLOGY, SOCIOLOGY AND POLITICAL SCIENCE.pptx
THE NATURE AND GOALS OF ANTHROPOLOGY, SOCIOLOGY AND POLITICAL SCIENCE.pptx
LovellRoweAzucenas
1 Information and Communication Technology
1 Information and Communication Technology
Teodoro Llanes II
3 Financial Planning Tools and Concepts.pptx
3 Financial Planning Tools and Concepts.pptx
JessicaNalla
Information and communications technology
Information and communications technology
Zenpai Carl
Imaging and Design for Online Environment
Imaging and Design for Online Environment
Angelito Quiambao
11 Developing ICT Project for Social Change
11 Developing ICT Project for Social Change
Teodoro Llanes II
Dlp applied economics 11 2-17
Dlp applied economics 11 2-17
paul nuez
6 Advance Presentation Skill
6 Advance Presentation Skill
Teodoro Llanes II
Recomendados
THE NATURE AND GOALS OF ANTHROPOLOGY, SOCIOLOGY AND POLITICAL SCIENCE.pptx
THE NATURE AND GOALS OF ANTHROPOLOGY, SOCIOLOGY AND POLITICAL SCIENCE.pptx
LovellRoweAzucenas
1 Information and Communication Technology
1 Information and Communication Technology
Teodoro Llanes II
3 Financial Planning Tools and Concepts.pptx
3 Financial Planning Tools and Concepts.pptx
JessicaNalla
Information and communications technology
Information and communications technology
Zenpai Carl
Imaging and Design for Online Environment
Imaging and Design for Online Environment
Angelito Quiambao
11 Developing ICT Project for Social Change
11 Developing ICT Project for Social Change
Teodoro Llanes II
Dlp applied economics 11 2-17
Dlp applied economics 11 2-17
paul nuez
6 Advance Presentation Skill
6 Advance Presentation Skill
Teodoro Llanes II
Module 8: ICT Projects for Social Awareness
Module 8: ICT Projects for Social Awareness
Sherilyn Gabest
Nature of planning
Nature of planning
Kathleen Abaja
Business Statistics Chapter 1
Business Statistics Chapter 1
Lux PP
Revisiting Economics as a Social Science
Revisiting Economics as a Social Science
Leah Condina
Module 2 Entrepreneurship Development
Module 2 Entrepreneurship Development
Bibin Xavier
Business Math Chapter 6
Business Math Chapter 6
Nazrin Nazdri
ICT and Social Responsibility
ICT and Social Responsibility
DepEd-Bataan
Practical Research 1 Module 1 - REVISED.pdf
Practical Research 1 Module 1 - REVISED.pdf
AlwinSostino2
Lesson 2 - Economics as an Applied Science
Lesson 2 - Economics as an Applied Science
Hannah Enriquez
ICT as Platform for Change - Empowerment Technologies
ICT as Platform for Change - Empowerment Technologies
Mark Jhon Oxillo
Chapter 4 presentation of data
Chapter 4 presentation of data
Polytechnic University of the Philippines
RESEARCH CONTENT FOR ICT PROJECT.pptx
RESEARCH CONTENT FOR ICT PROJECT.pptx
juwe oroc
ICT as a Platform for Change
ICT as a Platform for Change
Grayzon Gonzales, LPT
Introduction to applied economics part iv
Introduction to applied economics part iv
Rabie Pasturan
Introduction to applied economics
Introduction to applied economics
mskriz
Managing and sustaining ict projects
Managing and sustaining ict projects
Aubrey Mae Antonio
Lesson 5 Contemporary Economic Issues Affecting The Filipino Entrepreneur.pptx
Lesson 5 Contemporary Economic Issues Affecting The Filipino Entrepreneur.pptx
HeronLacanlale1
TNCT PPT.pptx
TNCT PPT.pptx
MarkLouieFerrer1
Lesson 2 importance of quant r
Lesson 2 importance of quant r
mjlobetos
Trends, Networks, and Critical Thinking Module 4 -Lesson 4.pptx
Trends, Networks, and Critical Thinking Module 4 -Lesson 4.pptx
MANILYNTINGCANG1
Making of Blue Print for Success
Making of Blue Print for Success
Mrs Rizwana A Mundewadi
52.dönem özel güvenlik sınav soru ve cevapları
52.dönem özel güvenlik sınav soru ve cevapları
gokayegitimhikmet
Más contenido relacionado
La actualidad más candente
Module 8: ICT Projects for Social Awareness
Module 8: ICT Projects for Social Awareness
Sherilyn Gabest
Nature of planning
Nature of planning
Kathleen Abaja
Business Statistics Chapter 1
Business Statistics Chapter 1
Lux PP
Revisiting Economics as a Social Science
Revisiting Economics as a Social Science
Leah Condina
Module 2 Entrepreneurship Development
Module 2 Entrepreneurship Development
Bibin Xavier
Business Math Chapter 6
Business Math Chapter 6
Nazrin Nazdri
ICT and Social Responsibility
ICT and Social Responsibility
DepEd-Bataan
Practical Research 1 Module 1 - REVISED.pdf
Practical Research 1 Module 1 - REVISED.pdf
AlwinSostino2
Lesson 2 - Economics as an Applied Science
Lesson 2 - Economics as an Applied Science
Hannah Enriquez
ICT as Platform for Change - Empowerment Technologies
ICT as Platform for Change - Empowerment Technologies
Mark Jhon Oxillo
Chapter 4 presentation of data
Chapter 4 presentation of data
Polytechnic University of the Philippines
RESEARCH CONTENT FOR ICT PROJECT.pptx
RESEARCH CONTENT FOR ICT PROJECT.pptx
juwe oroc
ICT as a Platform for Change
ICT as a Platform for Change
Grayzon Gonzales, LPT
Introduction to applied economics part iv
Introduction to applied economics part iv
Rabie Pasturan
Introduction to applied economics
Introduction to applied economics
mskriz
Managing and sustaining ict projects
Managing and sustaining ict projects
Aubrey Mae Antonio
Lesson 5 Contemporary Economic Issues Affecting The Filipino Entrepreneur.pptx
Lesson 5 Contemporary Economic Issues Affecting The Filipino Entrepreneur.pptx
HeronLacanlale1
TNCT PPT.pptx
TNCT PPT.pptx
MarkLouieFerrer1
Lesson 2 importance of quant r
Lesson 2 importance of quant r
mjlobetos
Trends, Networks, and Critical Thinking Module 4 -Lesson 4.pptx
Trends, Networks, and Critical Thinking Module 4 -Lesson 4.pptx
MANILYNTINGCANG1
La actualidad más candente
(20)
Module 8: ICT Projects for Social Awareness
Module 8: ICT Projects for Social Awareness
Nature of planning
Nature of planning
Business Statistics Chapter 1
Business Statistics Chapter 1
Revisiting Economics as a Social Science
Revisiting Economics as a Social Science
Module 2 Entrepreneurship Development
Module 2 Entrepreneurship Development
Business Math Chapter 6
Business Math Chapter 6
ICT and Social Responsibility
ICT and Social Responsibility
Practical Research 1 Module 1 - REVISED.pdf
Practical Research 1 Module 1 - REVISED.pdf
Lesson 2 - Economics as an Applied Science
Lesson 2 - Economics as an Applied Science
ICT as Platform for Change - Empowerment Technologies
ICT as Platform for Change - Empowerment Technologies
Chapter 4 presentation of data
Chapter 4 presentation of data
RESEARCH CONTENT FOR ICT PROJECT.pptx
RESEARCH CONTENT FOR ICT PROJECT.pptx
ICT as a Platform for Change
ICT as a Platform for Change
Introduction to applied economics part iv
Introduction to applied economics part iv
Introduction to applied economics
Introduction to applied economics
Managing and sustaining ict projects
Managing and sustaining ict projects
Lesson 5 Contemporary Economic Issues Affecting The Filipino Entrepreneur.pptx
Lesson 5 Contemporary Economic Issues Affecting The Filipino Entrepreneur.pptx
TNCT PPT.pptx
TNCT PPT.pptx
Lesson 2 importance of quant r
Lesson 2 importance of quant r
Trends, Networks, and Critical Thinking Module 4 -Lesson 4.pptx
Trends, Networks, and Critical Thinking Module 4 -Lesson 4.pptx
Destacado
Making of Blue Print for Success
Making of Blue Print for Success
Mrs Rizwana A Mundewadi
52.dönem özel güvenlik sınav soru ve cevapları
52.dönem özel güvenlik sınav soru ve cevapları
gokayegitimhikmet
It pres en
It pres en
Abhishek Gupta
Making of my Awakened Heart a Contemporary Modern Reiki Healing Painting
Making of my Awakened Heart a Contemporary Modern Reiki Healing Painting
Mrs Rizwana A Mundewadi
45. donem ozel guvenlik sınavı soru ve cevaplari a grubu
45. donem ozel guvenlik sınavı soru ve cevaplari a grubu
gokayegitimhikmet
Important Tips While Displaying Choosing Aum Paintings Aum the spiritual soun...
Important Tips While Displaying Choosing Aum Paintings Aum the spiritual soun...
Mrs Rizwana A Mundewadi
MY Spiritual Symbolic Water Color Abstracts on Paper
MY Spiritual Symbolic Water Color Abstracts on Paper
Mrs Rizwana A Mundewadi
Crayons of Happiness by Rizwana Abstracts year 2001
Crayons of Happiness by Rizwana Abstracts year 2001
Mrs Rizwana A Mundewadi
53.dönem özel güvenlik sınav soru ve cevapları
53.dönem özel güvenlik sınav soru ve cevapları
gokayegitimhikmet
Crayons of Happiness Spiritual Abstracts by Rizwana A.Mundewadi year 2001
Crayons of Happiness Spiritual Abstracts by Rizwana A.Mundewadi year 2001
Mrs Rizwana A Mundewadi
Modern Dancing Flowing Lines Abstract Symbolic Water Color Paintings
Modern Dancing Flowing Lines Abstract Symbolic Water Color Paintings
Mrs Rizwana A Mundewadi
A Tribute with lots of love to my love bird Boku who passed away this Friday ...
A Tribute with lots of love to my love bird Boku who passed away this Friday ...
Mrs Rizwana A Mundewadi
48.dönem özel güvenlik sınav soru ve cevapları kopya
48.dönem özel güvenlik sınav soru ve cevapları kopya
gokayegitimhikmet
49.dönem özel güvenlik sınav soru ve cevapları
49.dönem özel güvenlik sınav soru ve cevapları
gokayegitimhikmet
Making of Embracing the Chaos till july 2014 Abstract Symbolic Healing Painting
Making of Embracing the Chaos till july 2014 Abstract Symbolic Healing Painting
Mrs Rizwana A Mundewadi
Pet finch bird who was a part of my spiritual journey We lost her ...
Pet finch bird who was a part of my spiritual journey We lost her ...
Mrs Rizwana A Mundewadi
52.dönem özel güvenlik sınav soru ve cevapları burada masal okumuyoruz millet...
52.dönem özel güvenlik sınav soru ve cevapları burada masal okumuyoruz millet...
gokayegitimhikmet
Destacado
(17)
Making of Blue Print for Success
Making of Blue Print for Success
52.dönem özel güvenlik sınav soru ve cevapları
52.dönem özel güvenlik sınav soru ve cevapları
It pres en
It pres en
Making of my Awakened Heart a Contemporary Modern Reiki Healing Painting
Making of my Awakened Heart a Contemporary Modern Reiki Healing Painting
45. donem ozel guvenlik sınavı soru ve cevaplari a grubu
45. donem ozel guvenlik sınavı soru ve cevaplari a grubu
Important Tips While Displaying Choosing Aum Paintings Aum the spiritual soun...
Important Tips While Displaying Choosing Aum Paintings Aum the spiritual soun...
MY Spiritual Symbolic Water Color Abstracts on Paper
MY Spiritual Symbolic Water Color Abstracts on Paper
Crayons of Happiness by Rizwana Abstracts year 2001
Crayons of Happiness by Rizwana Abstracts year 2001
53.dönem özel güvenlik sınav soru ve cevapları
53.dönem özel güvenlik sınav soru ve cevapları
Crayons of Happiness Spiritual Abstracts by Rizwana A.Mundewadi year 2001
Crayons of Happiness Spiritual Abstracts by Rizwana A.Mundewadi year 2001
Modern Dancing Flowing Lines Abstract Symbolic Water Color Paintings
Modern Dancing Flowing Lines Abstract Symbolic Water Color Paintings
A Tribute with lots of love to my love bird Boku who passed away this Friday ...
A Tribute with lots of love to my love bird Boku who passed away this Friday ...
48.dönem özel güvenlik sınav soru ve cevapları kopya
48.dönem özel güvenlik sınav soru ve cevapları kopya
49.dönem özel güvenlik sınav soru ve cevapları
49.dönem özel güvenlik sınav soru ve cevapları
Making of Embracing the Chaos till july 2014 Abstract Symbolic Healing Painting
Making of Embracing the Chaos till july 2014 Abstract Symbolic Healing Painting
Pet finch bird who was a part of my spiritual journey We lost her ...
Pet finch bird who was a part of my spiritual journey We lost her ...
52.dönem özel güvenlik sınav soru ve cevapları burada masal okumuyoruz millet...
52.dönem özel güvenlik sınav soru ve cevapları burada masal okumuyoruz millet...
Similar a Hypothesis
chapter11.ppt
chapter11.ppt
HasanGilani3
Chapter11 (1)
Chapter11 (1)
anthonytoan
eMba i qt unit-5.1_hypothesis testing
eMba i qt unit-5.1_hypothesis testing
Rai University
Math3010 week 4
Math3010 week 4
stanbridge
11주차
11주차
Kookmin University
12주차
12주차
Kookmin University
Test of hypothesis
Test of hypothesis
Jaspreet1192
6 estimation hypothesis testing t test
6 estimation hypothesis testing t test
Penny Jiang
Chapter8 Introduction to Estimation Hypothesis Testing.pdf
Chapter8 Introduction to Estimation Hypothesis Testing.pdf
mekkimekki5
Top schools in delhi ncr
Top schools in delhi ncr
Edhole.com
B.tech admission in india
B.tech admission in india
Edhole.com
Testing of hypotheses
Testing of hypotheses
RajThakuri
lecture no.7 computation.pptx
lecture no.7 computation.pptx
ssuser378d7c
Test of hypothesis
Test of hypothesis
vikramlawand
Hypothesis 151221131534
Hypothesis 151221131534
Uvise P M
Hypothesis
Hypothesis
danpaul16
Introduction to the Logic of social inquiry
Introduction to the Logic of social inquiry
John Bradford
Hypothesis
Hypothesis
Dr. Priyanka Jain
Chapter 1 biostatistics by Dr Ahmed Hussein
Chapter 1 biostatistics by Dr Ahmed Hussein
Dr Ghaiath Hussein
Hypothesis Testing Lesson 1
Hypothesis Testing Lesson 1
yhchung
Similar a Hypothesis
(20)
chapter11.ppt
chapter11.ppt
Chapter11 (1)
Chapter11 (1)
eMba i qt unit-5.1_hypothesis testing
eMba i qt unit-5.1_hypothesis testing
Math3010 week 4
Math3010 week 4
11주차
11주차
12주차
12주차
Test of hypothesis
Test of hypothesis
6 estimation hypothesis testing t test
6 estimation hypothesis testing t test
Chapter8 Introduction to Estimation Hypothesis Testing.pdf
Chapter8 Introduction to Estimation Hypothesis Testing.pdf
Top schools in delhi ncr
Top schools in delhi ncr
B.tech admission in india
B.tech admission in india
Testing of hypotheses
Testing of hypotheses
lecture no.7 computation.pptx
lecture no.7 computation.pptx
Test of hypothesis
Test of hypothesis
Hypothesis 151221131534
Hypothesis 151221131534
Hypothesis
Hypothesis
Introduction to the Logic of social inquiry
Introduction to the Logic of social inquiry
Hypothesis
Hypothesis
Chapter 1 biostatistics by Dr Ahmed Hussein
Chapter 1 biostatistics by Dr Ahmed Hussein
Hypothesis Testing Lesson 1
Hypothesis Testing Lesson 1
Último
The Path to Product Excellence: Avoiding Common Pitfalls and Enhancing Commun...
The Path to Product Excellence: Avoiding Common Pitfalls and Enhancing Commun...
Aggregage
Chandigarh Escorts Service 📞8868886958📞 Just📲 Call Nihal Chandigarh Call Girl...
Chandigarh Escorts Service 📞8868886958📞 Just📲 Call Nihal Chandigarh Call Girl...
Sheetaleventcompany
Call Girls Hebbal Just Call 👗 7737669865 👗 Top Class Call Girl Service Bangalore
Call Girls Hebbal Just Call 👗 7737669865 👗 Top Class Call Girl Service Bangalore
amitlee9823
SEO Case Study: How I Increased SEO Traffic & Ranking by 50-60% in 6 Months
SEO Case Study: How I Increased SEO Traffic & Ranking by 50-60% in 6 Months
IndeedSEO
unwanted pregnancy Kit [+918133066128] Abortion Pills IN Dubai UAE Abudhabi
unwanted pregnancy Kit [+918133066128] Abortion Pills IN Dubai UAE Abudhabi
Abortion pills in Kuwait Cytotec pills in Kuwait
Call Girls Kengeri Satellite Town Just Call 👗 7737669865 👗 Top Class Call Gir...
Call Girls Kengeri Satellite Town Just Call 👗 7737669865 👗 Top Class Call Gir...
amitlee9823
Uneak White's Personal Brand Exploration Presentation
Uneak White's Personal Brand Exploration Presentation
uneakwhite
Organizational Transformation Lead with Culture
Organizational Transformation Lead with Culture
Seta Wicaksana
Call Girls From Pari Chowk Greater Noida ❤️8448577510 ⊹Best Escorts Service I...
Call Girls From Pari Chowk Greater Noida ❤️8448577510 ⊹Best Escorts Service I...
lizamodels9
Business Model Canvas (BMC)- A new venture concept
Business Model Canvas (BMC)- A new venture concept
P&CO
Falcon Invoice Discounting: Unlock Your Business Potential
Falcon Invoice Discounting: Unlock Your Business Potential
Falcon investment
Whitefield CALL GIRL IN 98274*61493 ❤CALL GIRLS IN ESCORT SERVICE❤CALL GIRL
Whitefield CALL GIRL IN 98274*61493 ❤CALL GIRLS IN ESCORT SERVICE❤CALL GIRL
kapoorjyoti4444
Call Girls In Noida 959961⊹3876 Independent Escort Service Noida
Call Girls In Noida 959961⊹3876 Independent Escort Service Noida
dlhescort
Falcon Invoice Discounting: Empowering Your Business Growth
Falcon Invoice Discounting: Empowering Your Business Growth
Falcon investment
Phases of Negotiation .pptx
Phases of Negotiation .pptx
nandhinijagan9867
Russian Call Girls In Rajiv Chowk Gurgaon ❤️8448577510 ⊹Best Escorts Service ...
Russian Call Girls In Rajiv Chowk Gurgaon ❤️8448577510 ⊹Best Escorts Service ...
lizamodels9
Call Now ☎️🔝 9332606886🔝 Call Girls ❤ Service In Bhilwara Female Escorts Serv...
Call Now ☎️🔝 9332606886🔝 Call Girls ❤ Service In Bhilwara Female Escorts Serv...
Anamikakaur10
The Abortion pills for sale in Qatar@Doha [+27737758557] []Deira Dubai Kuwait
The Abortion pills for sale in Qatar@Doha [+27737758557] []Deira Dubai Kuwait
daisycvs
Value Proposition canvas- Customer needs and pains
Value Proposition canvas- Customer needs and pains
P&CO
Al Mizhar Dubai Escorts +971561403006 Escorts Service In Al Mizhar
Al Mizhar Dubai Escorts +971561403006 Escorts Service In Al Mizhar
allensay1
Último
(20)
The Path to Product Excellence: Avoiding Common Pitfalls and Enhancing Commun...
The Path to Product Excellence: Avoiding Common Pitfalls and Enhancing Commun...
Chandigarh Escorts Service 📞8868886958📞 Just📲 Call Nihal Chandigarh Call Girl...
Chandigarh Escorts Service 📞8868886958📞 Just📲 Call Nihal Chandigarh Call Girl...
Call Girls Hebbal Just Call 👗 7737669865 👗 Top Class Call Girl Service Bangalore
Call Girls Hebbal Just Call 👗 7737669865 👗 Top Class Call Girl Service Bangalore
SEO Case Study: How I Increased SEO Traffic & Ranking by 50-60% in 6 Months
SEO Case Study: How I Increased SEO Traffic & Ranking by 50-60% in 6 Months
unwanted pregnancy Kit [+918133066128] Abortion Pills IN Dubai UAE Abudhabi
unwanted pregnancy Kit [+918133066128] Abortion Pills IN Dubai UAE Abudhabi
Call Girls Kengeri Satellite Town Just Call 👗 7737669865 👗 Top Class Call Gir...
Call Girls Kengeri Satellite Town Just Call 👗 7737669865 👗 Top Class Call Gir...
Uneak White's Personal Brand Exploration Presentation
Uneak White's Personal Brand Exploration Presentation
Organizational Transformation Lead with Culture
Organizational Transformation Lead with Culture
Call Girls From Pari Chowk Greater Noida ❤️8448577510 ⊹Best Escorts Service I...
Call Girls From Pari Chowk Greater Noida ❤️8448577510 ⊹Best Escorts Service I...
Business Model Canvas (BMC)- A new venture concept
Business Model Canvas (BMC)- A new venture concept
Falcon Invoice Discounting: Unlock Your Business Potential
Falcon Invoice Discounting: Unlock Your Business Potential
Whitefield CALL GIRL IN 98274*61493 ❤CALL GIRLS IN ESCORT SERVICE❤CALL GIRL
Whitefield CALL GIRL IN 98274*61493 ❤CALL GIRLS IN ESCORT SERVICE❤CALL GIRL
Call Girls In Noida 959961⊹3876 Independent Escort Service Noida
Call Girls In Noida 959961⊹3876 Independent Escort Service Noida
Falcon Invoice Discounting: Empowering Your Business Growth
Falcon Invoice Discounting: Empowering Your Business Growth
Phases of Negotiation .pptx
Phases of Negotiation .pptx
Russian Call Girls In Rajiv Chowk Gurgaon ❤️8448577510 ⊹Best Escorts Service ...
Russian Call Girls In Rajiv Chowk Gurgaon ❤️8448577510 ⊹Best Escorts Service ...
Call Now ☎️🔝 9332606886🔝 Call Girls ❤ Service In Bhilwara Female Escorts Serv...
Call Now ☎️🔝 9332606886🔝 Call Girls ❤ Service In Bhilwara Female Escorts Serv...
The Abortion pills for sale in Qatar@Doha [+27737758557] []Deira Dubai Kuwait
The Abortion pills for sale in Qatar@Doha [+27737758557] []Deira Dubai Kuwait
Value Proposition canvas- Customer needs and pains
Value Proposition canvas- Customer needs and pains
Al Mizhar Dubai Escorts +971561403006 Escorts Service In Al Mizhar
Al Mizhar Dubai Escorts +971561403006 Escorts Service In Al Mizhar
Hypothesis
1.
Chapter 11
Introduction to Hypothesis Testing asures of entral ndency Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.1
2.
Nonstatistical Hypothesis Testing…
A criminal trial is an example of hypothesis testing without the statistics. In a trial a jury must decide between two hypotheses. The null hypothesis is H0: The defendant is innocent The alternative hypothesis or research hypothesis is H1: The defendant is guilty The jury does not know which hypothesis is true. They must make a decision on the basis of evidence presented. Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.2
3.
Nonstatistical Hypothesis Testing…
In the language of statistics convicting the defendant is called rejecting the null hypothesis in favor of the alternative hypothesis. That is, the jury is saying that there is enough evidence to conclude that the defendant is guilty (i.e., there is enough evidence to support the alternative hypothesis). If the jury acquits it is stating that there is not enough evidence to support the alternative hypothesis. Notice that the jury is not saying that the defendant is innocent, only that there is not enough evidence to support the alternative hypothesis. That is why we never say that we accept the null hypothesis, although most people in industry will say “We accept the null hypothesis” Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.3
4.
Nonstatistical Hypothesis Testing…
There are two possible errors. A Type I error occurs when we reject a true null hypothesis. That is, a Type I error occurs when the jury convicts an innocent person. We would want the probability of this type of error [maybe 0.001 – beyond a reasonable doubt] to be very small for a criminal trial where a conviction results in the death penalty, whereas for a civil trial, where conviction might result in someone having to “pay for damages to a wrecked auto”,we would be willing for the probability to be larger [0.49 – preponderance of the evidence ] P(Type I error) = α [usually 0.05 or 0.01] Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.4
5.
Nonstatistical Hypothesis Testing…
A Type II error occurs when we don’t reject a false null hypothesis [accept the null hypothesis]. That occurs when a guilty defendant is acquitted. In practice, this type of error is by far the most serious mistake we normally make. For example, if we test the hypothesis that the amount of medication in a heart pill is equal to a value which will cure your heart problem and “accept the hull hypothesis that the amount is ok”. Later on we find out that the average amount is WAY too large and people die from “too much medication” [I wish we had rejected the hypothesis and threw the pills in the trash can], it’s too late because we shipped the pills to the public. Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.5
6.
Nonstatistical Hypothesis Testing…
The probability of a Type I error is denoted as α (Greek letter alpha). The probability of a type II error is β (Greek letter beta). The two probabilities are inversely related. Decreasing one increases the other, for a fixed sample size. In other words, you can’t have α and β both real small for any old sample size. You may have to take a much larger sample size, or in the court example, you need much more evidence. Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.6
7.
Types of Errors…
A Type I error occurs when we reject a true null hypothesis (i.e. Reject H0 when it is TRUE) H0 T F Reject I Reject II A Type II error occurs when we don’t reject a false null hypothesis (i.e. Do NOT reject H0 when it is FALSE) Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.7
8.
Nonstatistical Hypothesis Testing…
The critical concepts are theses: 1. There are two hypotheses, the null and the alternative hypotheses. 2. The procedure begins with the assumption that the null hypothesis is true. 3. The goal is to determine whether there is enough evidence to infer that the alternative hypothesis is true, or the null is not likely to be true. 4. There are two possible decisions: Conclude that there is enough evidence to support the alternative hypothesis. Reject the null. Conclude that there is not enough evidence to support the alternative hypothesis. Fail to reject the null. Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.8
9.
Concepts of Hypothesis
Testing (1)… The two hypotheses are called the null hypothesis and the other the alternative or research hypothesis. The usual notation is: pronounced H “nought” H0: — the ‘null’ hypothesis H1: — the ‘alternative’ or ‘research’ hypothesis The null hypothesis (H0) will always state that the parameter equals the value specified in the alternative hypothesis (H1) Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.9
10.
Concepts of Hypothesis
Testing… Consider mean demand for computers during assembly lead time. Rather than estimate the mean demand, our operations manager wants to know whether the mean is different from 350 units. In other words, someone is claiming that the mean time is 350 units and we want to check this claim out to see if it appears reasonable. We can rephrase this request into a test of the hypothesis: H0: = 350 Thus, our research hypothesis becomes: H1: ≠ 350 Recall that the standard deviation [σ]was assumed to be 75, the sample size [n] was 25, and the sample mean [ ] was calculated to be 370.16 Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.10
11.
Concepts of Hypothesis
Testing… For example, if we’re trying to decide whether the mean is not equal to 350, a large value of (say, 600) would provide enough evidence. If is close to 350 (say, 355) we could not say that this provides a great deal of evidence to infer that the population mean is different than 350. Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.11
12.
Concepts of Hypothesis
Testing (4)… The two possible decisions that can be made: Conclude that there is enough evidence to support the alternative hypothesis (also stated as: reject the null hypothesis in favor of the alternative) Conclude that there is not enough evidence to support the alternative hypothesis (also stated as: failing to reject the null hypothesis in favor of the alternative) NOTE: we do not say that we accept the null hypothesis if a statistician is around… Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.12
13.
Concepts of Hypothesis
Testing (2)… The testing procedure begins with the assumption that the null hypothesis is true. Thus, until we have further statistical evidence, we will assume: H0: = 350 (assumed to be TRUE) The next step will be to determine the sampling distribution of the sample mean assuming the true mean is 350. is normal with 350 75/SQRT(25) = 15 Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.13
14.
Is the Sample
Mean in the Guts of the Sampling Distribution?? Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.14
15.
Three ways to
determine this: First way 1. Unstandardized test statistic: Is in the guts of the sampling distribution? Depends on what you define as the “guts” of the sampling distribution. If we define the guts as the center 95% of the distribution [this means α = 0.05], then the critical values that define the guts will be 1.96 standard deviations of X-Bar on either side of the mean of the sampling distribution [350], or UCV = 350 + 1.96*15 = 350 + 29.4 = 379.4 LCV = 350 – 1.96*15 = 350 – 29.4 = 320.6 Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.15
16.
1. Unstandardized Test
Statistic Approach Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.16
17.
Three ways to
determine this: Second way 2. Standardized test statistic: Since we defined the “guts” of the sampling distribution to be the center 95% [α = 0.05], If the Z-Score for the sample mean is greater than 1.96, we know that will be in the reject region on the right side or If the Z-Score for the sample mean is less than -1.97, we know that will be in the reject region on the left side. Z=( - )/ = (370.16 – 350)/15 = 1.344 Is this Z-Score in the guts of the sampling distribution??? Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.17
18.
2. Standardized Test
Statistic Approach Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.18
19.
Three ways to
determine this: Third way 3. The p-value approach (which is generally used with a computer and statistical software): Increase the “Rejection Region” until it “captures” the sample mean. For this example, since is to the right of the mean, calculate P( > 370.16) = P(Z > 1.344) = 0.0901 Since this is a two tailed test, you must double this area for the p-value. p-value = 2*(0.0901) = 0.1802 Since we defined the guts as the center 95% [α = 0.05], the reject region is the other 5%. Since our sample mean, , is in the 18.02% region, it cannot be in our 5% rejection region [α = 0.05]. Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.19
20.
3. p-value approach Copyright
© 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.20
21.
Statistical Conclusions:
Unstandardized Test Statistic: Since LCV (320.6) < (370.16) < UCV (379.4), we reject the null hypothesis at a 5% level of significance. Standardized Test Statistic: Since -Zα/2(-1.96) < Z(1.344) < Zα/2 (1.96), we fail to reject the null hypothesis at a 5% level of significance. P-value: Since p-value (0.1802) > 0.05 [α], we fail to reject the hull hypothesis at a 5% level of significance. Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.21
22.
Example 11.1…
A department store manager determines that a new billing system will be cost-effective only if the mean monthly account is more than $170. A random sample of 400 monthly accounts is drawn, for which the sample mean is $178. The accounts are approximately normally distributed with a standard deviation of $65. Can we conclude that the new system will be cost-effective? Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.22
23.
Example 11.1…
The system will be cost effective if the mean account balance for all customers is greater than $170. We express this belief as a our research hypothesis, that is: H1: > 170 (this is what we want to determine) Thus, our null hypothesis becomes: H0: = 170 (this specifies a single value for the parameter of interest) – Actually H0: μ < 170 Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.23
24.
Example 11.1…
What we want to show: H1: > 170 H0: < 170 (we’ll assume this is true) Normally we put Ho first. We know: n = 400, = 178, and = 65 = 65/SQRT(400) = 3.25 α = 0.05 Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.24
25.
Example 11.1… Rejection
Region… The rejection region is a range of values such that if the test statistic falls into that range, we decide to reject the null hypothesis in favor of the alternative hypothesis. is the critical value of to reject H0. Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.25
26.
Example 11.1…
At a 5% significance level (i.e. =0.05), we get [all α in one tail] Zα = Z0.05 = 1.645 Therefore, UCV = 170 + 1.645*3.25 = 175.35 Since our sample mean (178) is greater than the critical value we calculated (175.35), we reject the null hypothesis in favor of H1 OR (>1.645) Reject null OR p-value = P( > 178) = P(Z > 2.46) = 0.0069 < 0.05 Reject null Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.26
27.
Example 11.1… The
Big Picture… H1: > 170 =175.34 H0: = 170 =178 Reject H0 in favor of Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.27
28.
Interpreting the p-value…
The smaller the p-value, the more statistical evidence exists to support the alternative hypothesis. •If the p-value is less than 1%, there is overwhelming evidence that supports the alternative hypothesis. •If the p-value is between 1% and 5%, there is a strong evidence that supports the alternative hypothesis. •If the p-value is between 5% and 10% there is a weak evidence that supports the alternative hypothesis. •If the p-value exceeds 10%, there is no evidence that supports the alternative hypothesis. We observe a p-value of .0069, hence there is overwhelming evidence to support H1: > 170. Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.28
29.
Interpreting the p-value…
Overwhelming Evidence (Highly Significant) Strong Evidence (Significant) Weak Evidence (Not Significant) No Evidence (Not Significant) 0 .01 .05 .10 p=.0069 Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.29
30.
Conclusions of a
Test of Hypothesis… If we reject the null hypothesis, we conclude that there is enough evidence to infer that the alternative hypothesis is true. If we fail to reject the null hypothesis, we conclude that there is not enough statistical evidence to infer that the alternative hypothesis is true. This does not mean that we have proven that the null hypothesis is true! Keep in mind that committing a Type I error OR a Type II error can be VERY bad depending on the problem. Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.30
31.
One tail test
with rejection region on right The last example was a one tail test, because the rejection region is located in only one tail of the sampling distribution: More correctly, this was an example of a right tail test. H1: μ > 170 H0: μ < 170 Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.31
32.
One tail test
with rejection region on left The rejection region will be in the left tail. Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.32
33.
Two tail test
with rejection region in both tails The rejection region is split equally between the two tails. Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.33
34.
Example 11.2… Students
work AT&T’s argues that its rates are such that customers won’t see a difference in their phone bills between them and their competitors. They calculate the mean and standard deviation for all their customers at $17.09 and $3.87 (respectively). Note: Don’t know the true value for σ, so we estimate σ from the data [σ ~ s = 3.87] – large sample so don’t worry. They then sample 100 customers at random and recalculate a monthly phone bill based on competitor’s rates. Our null and alternative hypotheses are H1: ≠ 17.09. We do this by assuming that: H0: = 17.09 Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.34
35.
Example 11.2…
The rejection region is set up so we can reject the null hypothesis when the test statistic is large or when it is small. stat is “small” stat is “large” That is, we set up a two-tail rejection region. The total area in the rejection region must sum to , so we divide α by 2. Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.35
36.
Example 11.2…
At a 5% significance level (i.e. = .05), we have /2 = .025. Thus, z.025 = 1.96 and our rejection region is: z < –1.96 -or- z > 1.96 -z.025 +z.025 z 0 Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.36
37.
Example 11.2…
From the data, we calculate = 17.55 Using our standardized test statistic: We find that: Since z = 1.19 is not greater than 1.96, nor less than –1.96 we cannot reject the null hypothesis in favor of H1. That is “there is insufficient evidence to infer that there is a difference between the bills of AT&T and the competitor.” Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.37
38.
Summary of One-
and Two-Tail Tests… One-Tail Test Two-Tail Test One-Tail Test (left tail) (right tail) Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.38
39.
Probability of a
Type II Error – A Type II error occurs when a false null hypothesis is not rejected or “you accept the null when it is not true” but don’t say it this way if a statistician is around. In practice, this is by far the most serious error you can make in most cases, especially in the “quality field”. Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.39
40.
Judging the Test…
A statistical test of hypothesis is effectively defined by the significance level ( ) and the sample size (n), both of which are selected by the statistics practitioner. Therefore, if the probability of a Type II error ( ) is too large [we have insufficient power], we can reduce it by increasing , and/or increasing the sample size, n. Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.40
41.
Judging the Test…
The power of a test is defined as 1– . It represents the probability of rejecting the null hypothesis when it is false and the true mean is something other than the null value for the mean. If we are testing the hypothesis that the average amount of medication in blood pressure pills is equal to 6 mg (which is good), and we “fail to reject” the null hypothesis, ship the pills to patients worldwide, only to find out later that the “true” average amount of medication is really 8 mg and people die, we get in trouble. This occurred because the P(reject the null / true mean = 7 mg) = 0.32 which would mean that we have a 68% chance on not rejecting the null for these BAD pills and shipping to patients worldwide. Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.41
42.
Probability you ship
pills whose mean amount of medication is 7 mg approximately 67% Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc. 11.42
Notas del editor
Keller: Stats for Mgmt & Econ, 7th Ed October 13, 2012 Copyright © 2006 Brooks/Cole, a division of Thomson Learning, Inc.
Descargar ahora