SlideShare ist ein Scribd-Unternehmen logo
1 von 51
Downloaden Sie, um offline zu lesen
HYPOTHESIS TESTING
 We develop a procedure to test the
validity of a statement about a population
parameter.
Examples:
 The mean starting salary for graduates of
four year business schools is Rs. 32,000
per month.
 Eighty percent of those who play the state
lottery regularly never win more than $
100 in any one play.
What is Hypothesis?
 Is a statement about a population
developed for the purpose of testing.
 In most cases the population is too
large that it is not feasible to study
all items in the population.
 We can, therefore, test a statement
to determine whether the sample
does or does not support the
statement concerning the population.
HYPOTHESIS TESTING
 A procedure based on sample
evidence and probability theory to
determine whether the hypothesis is
a reasonable statement.
Five-Step Procedure for Testing a
Hypothesis
 State the Null Hypothesis (Ho) and
the Alternate Hypothesis (Hı)
 Select a level of significance.
 Identify the test statistic.
 Formulate a decision rule.
 Make a decision
Step 1: State the Null Hypothesis (Ho)
and the Alternate Hypothesis (Hı)
 The first step is to state the
hypothesis being tested. It is called
the null hypothesis, designated (Ho).
 The capital H stands for hypothesis,
and the subscript zero implies “no
difference”.
 There is usually a “not” or a “no”
term in the null hypothesis, meaning
that there is “no change”.
 For example, the null hypothesis is that
the number of miles driven on the steel-
belted tire is not different from 60,000.
 Therefore, Ho: μ = 60,000.
 We either reject or fail to reject the null
hypothesis.
 The null hypothesis is a statement that is
not rejected unless our sample data provide
convincing evidence that it is false.
ALTERNATE HYPOTHESIS
 The alternate hypothesis describes
what you will conclude if you reject
the null hypothesis. It is written as
Hı.
 It is also called the research
hypothesis.
 The alternate hypothesis is accepted
if the sample data provide us with
enough statistical evidence that the
null hypothesis is false.
Example:
 A recent article indicated that the
mean age of U.S. commercial
aircraft is 15 years.
 The null hypothesis represents the
current or reported condition.
 Ho: μ = 15.
 The alternate hypothesis is that the
statement is not true: H1: μ ≠15.
Select a level of significance
 The level of significance is designated
α , the Greek letter alpha. It is also
sometimes called level of risk.
 There is no one level of significance that it
is applied to all tests.
 The common choices for α are .05, .01 and
.10.
LEVEL OF SIGNIFICANCE The probability of making a
Type 1 error when the null hypothesis is true as an equality.
 Traditionally, .05 level is selected
for consumer research projects, .01
for quality assurance, and .10 for
political polling.
Type I and Type II Errors
Population Condition
Ho True Hı True
Accept Ho Correct Type II
Conclusion Error
Conclusion
Reject Ho Type I Correct
Error Conclusion
Type I Error from Indian Epic
It may be recalled that in “Abhigyan
Shakuntalam” , king Dushyanta had married
shakuntala when he met her in her village, while
wandering in a jungle. He gave her his royal ring
as a gift which could also serve as her identity
when she would come to meet him, in future.
However, while going to meet him, she lost the
ring in the river. When she reached Dushayant’s
place and met him, he failed to recognize her
especially since she did not have the ring. Thus
Dushayant committed Type I error as he
rejected Shankutla as his wife when, in fact, she
was his true wife.
Type II Error from Indian Epic
In Mahabharta epic, Dronacharya – the
‘guru’ of both Pandavas and Kauravas –
was fighting from the Kaurav’s side.
However, he had taken a vow that he
would stop fighting if and when his son
Aswathama was killed in the war. It so
happened that during the war, one
elephant named Aswathama was killed.
Lord - Krishna the mentor of Pandavas –
thought of a strategy to make
Dronacharya lay down his arms.
Yudhishter on advice of lord Krishna, went
to Dronacharya and pronounced
Aswathama was dead-but was it a human
or an elephant? Dronacharya, on listening
the first part of Yudhishtir’s sentence,
presumed that his son was dead, and he
left for his heavenly abode without
waiting to listen to the second part of
Yudhishter’s sentence. Thus, Droncharya
could be said to have committed Type II
error i.e. accepting a statement when it
was not true.
Select a Test Statistic
 A value, determined from sample
information, used to determine
whether to reject the null
hypothesis.
 The test criteria that are frequently
used in hypothesis testing are Z, t,
F, Χ test.
Formulate the Decision Rule
 A decision rule is a statement of the
specific conditions under which the
null hypothesis is rejected and the
conditions under which it is not
rejected .
Step 5: Make a Decision
 Make a decision regarding the null
hypothesis on the sample
information .
 Interpret the results of the test.
Population Mean: known
One - tailed Test
Lower Tail Test Upper Tail Test
Ho: μ ≥ μo Ho: μ ≤ μo
H1: μ < μo H1: μ > μo
σ
Example:
 The Federal trade Commission (FTC)
periodically conducts statistical studies
designed to tests the claims that
manufacturers make about their products.
 For example, the label on a large can of
Hilltop Coffee States that the can contains
3 pounds of coffee.
 The FTC knows that Hilltop production
process cannot place exactly 3 pounds of
coffee, even if the mean filling weight is
for the population of all cans filled is 3
pounds per can.
 However, as long as the population mean
filing weight is at least 3 pounds per can,
the rights of consumers can be protected.
 Thus, the FTC interprets the label
information on a large can of coffee as a
claim by Hilltop that the population mean
is at least 3 pounds per can.
 We will show how the FTC can check the
hilltops claim by conducting the lower tail
hypothesis test?
Develop Null and Alternative
Hypothesis
If the population mean filling weight
is at least 3 pounds per can,
Hilltop’s claim is correct.
Ho: μ ≥ 3
Hı: μ < 3
The hypothesized value of population
mean is μo = 3
 Suppose a sample of 36 cans of coffee is
selected.
 Sample mean is computed as an estimate of
population mean μ.
 If < 3 pounds, the sample results will cast a
doubt on null hypothesis.
 We want to know how much less than 3 pounds
must be before we would be willing to declare
the difference significant and risk making a Type
I error by falsely accusing Hilltop of a label
violation.
x
x
x
The director of FTC’s program made
the following statement:
If the company is meeting its weights
specifications at µ = 3, I would like 99%
chance of not taking any action against the
company. Although I do not want to accuse
the company wrongly of under filling its
product, I am willing to risk a 1% chance of
making such an error.”
Therefore from the director’s statement we
would set a = .01
Thus we must design the hypothesis test so
that probability of making a type I error when
µ = 3 is .01
Test Statistic
 For the Hilltop Coffee study,
previous FTC test show that the
population standard deviation can
be assumed known with the value
of σ = .18
 In addition these tests also show
the population of filling weights can
be assumed to have a normal
distribution.
Sampling distribution of x
36n
03.018. ===σσx
TEST STATISTIC FOR HYPOTHESIS TESTS ABOUT A POPULATION
MEAN: σ KNOWN
n/
0
σ
µ−=xz
Suppose the sample of 36 Hilltop coffee
cans provides a sample mean of =
2.92 small enough to cause us to reject
Ho ?
= 2.92; σ = .18 and n = 36
x
x
36.18/n/
67.2392.20
σ
µ −=−=−= xz
Critical Value Approach
 The critical value is the value of the
test statistic that corresponds to the
area of α = .01 in the lower tail of
the standard normal distribution.
 Using standard normal distribution
table, we find that z = -2.33 provides
an area of .01 in the lower tail.
For Hilltop Coffee Study Critical Value
Rejection Rule for a level of significance of .
01 is
Reject Ho if Z ≤ -2.33
Hypothesis
0
z
Z=-2.33
01.=α
 = 2.92
 z = -2.67
 Since z = -2.67 < -2.33, we can
reject Ho and conclude that Hilltop
coffee is under filling cans.
x
Two – Tailed Test
Ho: μ = μo
H1: μ ≠ μo
Example:
 The U.S. Golf Association (USGA)
establishes rules that manufacturers of golf
equipment must meet if their products are
to be acceptable for use in USGA events.
 MaxFlight uses a high technology
manufacturing process to produce golf balls
with average distances from 295 yards.
 When the average distance passes 295
yards, MaxFlight’s golf balls may be
rejected by the USGA for exceeding the
overall distance standard concerning carry
and roll.
 MaxFlights’s quality control program
involves taking periodic samples of
50 golf balls to monitor the
manufacturing process.
 For each sample, a hypothesis test
is conducted to determine whether
the process has fallen out of
adjustment.
 We assume that the process is functioning
correctly; i.e. the golf balls produced have
a mean distance of 295 yards.
H0: μ = 295
H1: μ ≠ 295
 If the sample mean is less than is
significantly less than 295 yards or
significantly greater than 295 yards, we will
reject H0.
 The quality control team selected = .05 as
the level of significance for the test. Data
from previous tests conducted when the
process was known to be in adjustment
show that the population standard deviation
can be assumed known with a value of =
12. Thus, with a sample size of n = 50, the
standard error of is
x
x
50n
7.112 ===σσx
 Because the sample size is large, the
central limit theorem allows us to conclude
that the sampling distribution of can be
approximated by a normal distribution.
Suppose that a sample of 50 golf balls is
selected and that the sample mean is =
297.6 yards. This sample mean provides
support for the conclusion that the
population mean is larger than 295 yards.
Computing z - statistic
5012//
53.12956.2970
n
xz
σ
µ =−=−=
Critical Value Approach
 With a level of significance of = .05
 The area in each tail beyond the
critical values is
 Using the table of of areas of
standard normal distribution.
025.2/05.2/ ==α
Hypothesis
0
z
-1.96 1.96
Reject H0Reject H0
96.1and96.1 025.025. =−=− zz
Reject H0 if z ≤ 1.96 or if z ≥ 1.96
Because the value of the test for the MaxFlight study is z = 1.53,
The statistical evidence will not permit us to reject the null
hypothesis at the .05 level of significance.
Example:
• The Jamestown Steel Company
manufactures and assembles desks
and other office equipment at several
plants in Western New York State. The
weekly production of Model A325 desk
at the Fredonia Plant follows a normal
distribution, with a mean of 200 and a
standard deviation of 16. recently
because of market expansion, new
production methods have been
introduced and new employees hired.
 The vice president of manufacturing
would like to investigate whether
there has been a change in the
weekly production of the model
A325 desk. To put it another way, is
the mean number of desk produced
at the Florida plant different from
200 at the .01 significance level?
Solution
 State the null hypothesis and
alternate hypothesis:
 This is a two-tailed test because the
alternative hypothesis does not
state a direction.
200:
200:
1
0
≠
=
µ
µ
H
H
 As noted, the .01 level of
significance is used.
 It is the probability of committing a
Type I error, and it is the probability
of rejecting a true null hypothesis.
Select the test statistic
n/σ
µ−=xz
Formulate the decision Rule
 The decision rule is formulated by
finding the critical values of z.
 Since it is a two tailed test, half of .
01, or .005, is placed in each tail.
 The area where H0 is not rejected,
located between the two tails, is
therefore .99.
Make a decision and interpret the
result
50/16n/
55.12005.203
σ
µ =−=−= xz
Because H0 does not fall in the rejection region, H0 is not
rejected
We conclude that population mean is not different from 200.

Weitere ähnliche Inhalte

Was ist angesagt?

Lecture 7 Hypothesis Testing Two Sample
Lecture 7 Hypothesis Testing Two SampleLecture 7 Hypothesis Testing Two Sample
Lecture 7 Hypothesis Testing Two SampleAhmadullah
 
Pre-commitment Strategies in Behavioral Economics
Pre-commitment Strategies in Behavioral EconomicsPre-commitment Strategies in Behavioral Economics
Pre-commitment Strategies in Behavioral EconomicsRussell James
 
How do Geopolitical Events impact Business
How do Geopolitical Events impact BusinessHow do Geopolitical Events impact Business
How do Geopolitical Events impact Businesspaul young cpa, cga
 
Multiplier cocepts & effects
Multiplier cocepts & effectsMultiplier cocepts & effects
Multiplier cocepts & effectsAtindya K Ghosh
 
Probability Case Study Rheam, Smith, Gandhotra
Probability Case Study Rheam, Smith, GandhotraProbability Case Study Rheam, Smith, Gandhotra
Probability Case Study Rheam, Smith, Gandhotraguest3c11a5
 
Steps in formulating research problem
Steps in formulating research problem   Steps in formulating research problem
Steps in formulating research problem Rijitha R
 
Public provision of social goods
Public provision of social goodsPublic provision of social goods
Public provision of social goodsEjaz Dilshad
 
Fixed income tutorial question
Fixed income tutorial questionFixed income tutorial question
Fixed income tutorial questionTinku Kumar
 
Prisoner's Dilemma
Prisoner's DilemmaPrisoner's Dilemma
Prisoner's DilemmaAcquate
 
Test of hypothesis
Test of hypothesisTest of hypothesis
Test of hypothesisJaspreet1192
 
Short hedge and Long hedge
Short hedge and Long hedgeShort hedge and Long hedge
Short hedge and Long hedgeabisek123
 
Externalities
ExternalitiesExternalities
ExternalitiesKevin A
 
POVERTY & DEPRIVATION123.pptx
POVERTY & DEPRIVATION123.pptxPOVERTY & DEPRIVATION123.pptx
POVERTY & DEPRIVATION123.pptxintisar24
 
Unit principles of option pricing call
Unit  principles of option pricing callUnit  principles of option pricing call
Unit principles of option pricing callSudarshan Kadariya
 

Was ist angesagt? (20)

Lecture 7 Hypothesis Testing Two Sample
Lecture 7 Hypothesis Testing Two SampleLecture 7 Hypothesis Testing Two Sample
Lecture 7 Hypothesis Testing Two Sample
 
Pre-commitment Strategies in Behavioral Economics
Pre-commitment Strategies in Behavioral EconomicsPre-commitment Strategies in Behavioral Economics
Pre-commitment Strategies in Behavioral Economics
 
How do Geopolitical Events impact Business
How do Geopolitical Events impact BusinessHow do Geopolitical Events impact Business
How do Geopolitical Events impact Business
 
Game Theory
Game TheoryGame Theory
Game Theory
 
Multiplier cocepts & effects
Multiplier cocepts & effectsMultiplier cocepts & effects
Multiplier cocepts & effects
 
Probability Case Study Rheam, Smith, Gandhotra
Probability Case Study Rheam, Smith, GandhotraProbability Case Study Rheam, Smith, Gandhotra
Probability Case Study Rheam, Smith, Gandhotra
 
Steps in formulating research problem
Steps in formulating research problem   Steps in formulating research problem
Steps in formulating research problem
 
Public provision of social goods
Public provision of social goodsPublic provision of social goods
Public provision of social goods
 
Fixed income tutorial question
Fixed income tutorial questionFixed income tutorial question
Fixed income tutorial question
 
Prisoner's Dilemma
Prisoner's DilemmaPrisoner's Dilemma
Prisoner's Dilemma
 
Test of hypothesis
Test of hypothesisTest of hypothesis
Test of hypothesis
 
Ch12
Ch12Ch12
Ch12
 
Secondary data
Secondary dataSecondary data
Secondary data
 
Ie 03 (2)
Ie 03 (2)Ie 03 (2)
Ie 03 (2)
 
Formulatinghypotheses
Formulatinghypotheses Formulatinghypotheses
Formulatinghypotheses
 
Short hedge and Long hedge
Short hedge and Long hedgeShort hedge and Long hedge
Short hedge and Long hedge
 
Addition rule and multiplication rule
Addition rule and multiplication rule  Addition rule and multiplication rule
Addition rule and multiplication rule
 
Externalities
ExternalitiesExternalities
Externalities
 
POVERTY & DEPRIVATION123.pptx
POVERTY & DEPRIVATION123.pptxPOVERTY & DEPRIVATION123.pptx
POVERTY & DEPRIVATION123.pptx
 
Unit principles of option pricing call
Unit  principles of option pricing callUnit  principles of option pricing call
Unit principles of option pricing call
 

Andere mochten auch

Andere mochten auch (15)

Testing of Hypothesis
Testing of Hypothesis Testing of Hypothesis
Testing of Hypothesis
 
Hypothesis 2 - copy
Hypothesis 2 - copyHypothesis 2 - copy
Hypothesis 2 - copy
 
Indusrial policy
Indusrial policyIndusrial policy
Indusrial policy
 
import policy &licensing procedure
import policy &licensing procedureimport policy &licensing procedure
import policy &licensing procedure
 
Industrial Policy
Industrial PolicyIndustrial Policy
Industrial Policy
 
Regulatory Barriers to Micro, Small and Medium Enterprises
Regulatory Barriers to Micro, Small and Medium EnterprisesRegulatory Barriers to Micro, Small and Medium Enterprises
Regulatory Barriers to Micro, Small and Medium Enterprises
 
Hypothesis Testing
Hypothesis TestingHypothesis Testing
Hypothesis Testing
 
Design of Experiment
Design of ExperimentDesign of Experiment
Design of Experiment
 
Industrial Policy, Fiscal Policy and Licensing Policy
Industrial Policy, Fiscal Policy and Licensing PolicyIndustrial Policy, Fiscal Policy and Licensing Policy
Industrial Policy, Fiscal Policy and Licensing Policy
 
Chapter 11
Chapter 11 Chapter 11
Chapter 11
 
Z test, f-test,etc
Z test, f-test,etcZ test, f-test,etc
Z test, f-test,etc
 
Chapter 10
Chapter 10Chapter 10
Chapter 10
 
Industrial policy.ppt
Industrial policy.pptIndustrial policy.ppt
Industrial policy.ppt
 
Industrial development in india
Industrial development in indiaIndustrial development in india
Industrial development in india
 
Hypothesis testing examples on z test
Hypothesis testing examples on z testHypothesis testing examples on z test
Hypothesis testing examples on z test
 

Ähnlich wie Hypothesis

Hypothesis Testing Lesson 1
Hypothesis Testing Lesson 1Hypothesis Testing Lesson 1
Hypothesis Testing Lesson 1yhchung
 
hypothesis test
 hypothesis test hypothesis test
hypothesis testUnsa Shakir
 
Ch 7. HYPOTHESIS TESTING.doc
Ch 7. HYPOTHESIS TESTING.docCh 7. HYPOTHESIS TESTING.doc
Ch 7. HYPOTHESIS TESTING.docbiruktessema1
 
Chapter 8-hypothesis-testing-1211425712197151-9
Chapter 8-hypothesis-testing-1211425712197151-9Chapter 8-hypothesis-testing-1211425712197151-9
Chapter 8-hypothesis-testing-1211425712197151-9stone66
 
Chapter 8 – Hypothesis Testing
Chapter 8 – Hypothesis TestingChapter 8 – Hypothesis Testing
Chapter 8 – Hypothesis Testingguest3720ca
 
Chapter 8 – Hypothesis Testing
Chapter 8 – Hypothesis TestingChapter 8 – Hypothesis Testing
Chapter 8 – Hypothesis TestingRose Jenkins
 
Hypothesis testing
Hypothesis testingHypothesis testing
Hypothesis testingNirajan Bam
 
Top schools in delhi ncr
Top schools in delhi ncrTop schools in delhi ncr
Top schools in delhi ncrEdhole.com
 
Testing of hypothesis and tests of significance
Testing of hypothesis and tests of significanceTesting of hypothesis and tests of significance
Testing of hypothesis and tests of significanceSudha Rameshwari
 
Ch5 Hypothesis Testing
Ch5 Hypothesis TestingCh5 Hypothesis Testing
Ch5 Hypothesis TestingFarhan Alfin
 
STA101 presentations.pdf
STA101 presentations.pdfSTA101 presentations.pdf
STA101 presentations.pdfLabibHossain6
 
Hypothesis, Types of errors - Parametric and Non-Parametric tests - Critical ...
Hypothesis, Types of errors - Parametric and Non-Parametric tests - Critical ...Hypothesis, Types of errors - Parametric and Non-Parametric tests - Critical ...
Hypothesis, Types of errors - Parametric and Non-Parametric tests - Critical ...Sundar B N
 
Research methodology module 3
Research methodology module 3Research methodology module 3
Research methodology module 3Satyajit Behera
 

Ähnlich wie Hypothesis (20)

Hypothesis Testing Lesson 1
Hypothesis Testing Lesson 1Hypothesis Testing Lesson 1
Hypothesis Testing Lesson 1
 
hypothesis test
 hypothesis test hypothesis test
hypothesis test
 
Ch 7. HYPOTHESIS TESTING.doc
Ch 7. HYPOTHESIS TESTING.docCh 7. HYPOTHESIS TESTING.doc
Ch 7. HYPOTHESIS TESTING.doc
 
Chapter 8-hypothesis-testing-1211425712197151-9
Chapter 8-hypothesis-testing-1211425712197151-9Chapter 8-hypothesis-testing-1211425712197151-9
Chapter 8-hypothesis-testing-1211425712197151-9
 
Chapter 8 – Hypothesis Testing
Chapter 8 – Hypothesis TestingChapter 8 – Hypothesis Testing
Chapter 8 – Hypothesis Testing
 
Chapter 8 – Hypothesis Testing
Chapter 8 – Hypothesis TestingChapter 8 – Hypothesis Testing
Chapter 8 – Hypothesis Testing
 
Chapter10
Chapter10Chapter10
Chapter10
 
Hypothesis testing
Hypothesis testingHypothesis testing
Hypothesis testing
 
Hypothesis
HypothesisHypothesis
Hypothesis
 
Top schools in delhi ncr
Top schools in delhi ncrTop schools in delhi ncr
Top schools in delhi ncr
 
Testing of hypothesis
Testing of hypothesisTesting of hypothesis
Testing of hypothesis
 
11 hypothesis testing
11 hypothesis testing11 hypothesis testing
11 hypothesis testing
 
Testing of hypothesis and tests of significance
Testing of hypothesis and tests of significanceTesting of hypothesis and tests of significance
Testing of hypothesis and tests of significance
 
Chapter10
Chapter10Chapter10
Chapter10
 
Ch5 Hypothesis Testing
Ch5 Hypothesis TestingCh5 Hypothesis Testing
Ch5 Hypothesis Testing
 
STA101 presentations.pdf
STA101 presentations.pdfSTA101 presentations.pdf
STA101 presentations.pdf
 
HYPOTHESIS TESTING.ppt
HYPOTHESIS TESTING.pptHYPOTHESIS TESTING.ppt
HYPOTHESIS TESTING.ppt
 
Hypothesis, Types of errors - Parametric and Non-Parametric tests - Critical ...
Hypothesis, Types of errors - Parametric and Non-Parametric tests - Critical ...Hypothesis, Types of errors - Parametric and Non-Parametric tests - Critical ...
Hypothesis, Types of errors - Parametric and Non-Parametric tests - Critical ...
 
Research methodology module 3
Research methodology module 3Research methodology module 3
Research methodology module 3
 
TEST OF HYPOTHESIS
TEST OF HYPOTHESISTEST OF HYPOTHESIS
TEST OF HYPOTHESIS
 

Kürzlich hochgeladen

IaC & GitOps in a Nutshell - a FridayInANuthshell Episode.pdf
IaC & GitOps in a Nutshell - a FridayInANuthshell Episode.pdfIaC & GitOps in a Nutshell - a FridayInANuthshell Episode.pdf
IaC & GitOps in a Nutshell - a FridayInANuthshell Episode.pdfDaniel Santiago Silva Capera
 
COMPUTER 10 Lesson 8 - Building a Website
COMPUTER 10 Lesson 8 - Building a WebsiteCOMPUTER 10 Lesson 8 - Building a Website
COMPUTER 10 Lesson 8 - Building a Websitedgelyza
 
Igniting Next Level Productivity with AI-Infused Data Integration Workflows
Igniting Next Level Productivity with AI-Infused Data Integration WorkflowsIgniting Next Level Productivity with AI-Infused Data Integration Workflows
Igniting Next Level Productivity with AI-Infused Data Integration WorkflowsSafe Software
 
UiPath Studio Web workshop series - Day 8
UiPath Studio Web workshop series - Day 8UiPath Studio Web workshop series - Day 8
UiPath Studio Web workshop series - Day 8DianaGray10
 
Anypoint Code Builder , Google Pub sub connector and MuleSoft RPA
Anypoint Code Builder , Google Pub sub connector and MuleSoft RPAAnypoint Code Builder , Google Pub sub connector and MuleSoft RPA
Anypoint Code Builder , Google Pub sub connector and MuleSoft RPAshyamraj55
 
How Accurate are Carbon Emissions Projections?
How Accurate are Carbon Emissions Projections?How Accurate are Carbon Emissions Projections?
How Accurate are Carbon Emissions Projections?IES VE
 
AI Fame Rush Review – Virtual Influencer Creation In Just Minutes
AI Fame Rush Review – Virtual Influencer Creation In Just MinutesAI Fame Rush Review – Virtual Influencer Creation In Just Minutes
AI Fame Rush Review – Virtual Influencer Creation In Just MinutesMd Hossain Ali
 
Bird eye's view on Camunda open source ecosystem
Bird eye's view on Camunda open source ecosystemBird eye's view on Camunda open source ecosystem
Bird eye's view on Camunda open source ecosystemAsko Soukka
 
Using IESVE for Loads, Sizing and Heat Pump Modeling to Achieve Decarbonization
Using IESVE for Loads, Sizing and Heat Pump Modeling to Achieve DecarbonizationUsing IESVE for Loads, Sizing and Heat Pump Modeling to Achieve Decarbonization
Using IESVE for Loads, Sizing and Heat Pump Modeling to Achieve DecarbonizationIES VE
 
Meet the new FSP 3000 M-Flex800™
Meet the new FSP 3000 M-Flex800™Meet the new FSP 3000 M-Flex800™
Meet the new FSP 3000 M-Flex800™Adtran
 
Linked Data in Production: Moving Beyond Ontologies
Linked Data in Production: Moving Beyond OntologiesLinked Data in Production: Moving Beyond Ontologies
Linked Data in Production: Moving Beyond OntologiesDavid Newbury
 
Designing A Time bound resource download URL
Designing A Time bound resource download URLDesigning A Time bound resource download URL
Designing A Time bound resource download URLRuncy Oommen
 
Machine Learning Model Validation (Aijun Zhang 2024).pdf
Machine Learning Model Validation (Aijun Zhang 2024).pdfMachine Learning Model Validation (Aijun Zhang 2024).pdf
Machine Learning Model Validation (Aijun Zhang 2024).pdfAijun Zhang
 
Videogame localization & technology_ how to enhance the power of translation.pdf
Videogame localization & technology_ how to enhance the power of translation.pdfVideogame localization & technology_ how to enhance the power of translation.pdf
Videogame localization & technology_ how to enhance the power of translation.pdfinfogdgmi
 
OpenShift Commons Paris - Choose Your Own Observability Adventure
OpenShift Commons Paris - Choose Your Own Observability AdventureOpenShift Commons Paris - Choose Your Own Observability Adventure
OpenShift Commons Paris - Choose Your Own Observability AdventureEric D. Schabell
 
VoIP Service and Marketing using Odoo and Asterisk PBX
VoIP Service and Marketing using Odoo and Asterisk PBXVoIP Service and Marketing using Odoo and Asterisk PBX
VoIP Service and Marketing using Odoo and Asterisk PBXTarek Kalaji
 
COMPUTER 10: Lesson 7 - File Storage and Online Collaboration
COMPUTER 10: Lesson 7 - File Storage and Online CollaborationCOMPUTER 10: Lesson 7 - File Storage and Online Collaboration
COMPUTER 10: Lesson 7 - File Storage and Online Collaborationbruanjhuli
 
ADOPTING WEB 3 FOR YOUR BUSINESS: A STEP-BY-STEP GUIDE
ADOPTING WEB 3 FOR YOUR BUSINESS: A STEP-BY-STEP GUIDEADOPTING WEB 3 FOR YOUR BUSINESS: A STEP-BY-STEP GUIDE
ADOPTING WEB 3 FOR YOUR BUSINESS: A STEP-BY-STEP GUIDELiveplex
 

Kürzlich hochgeladen (20)

IaC & GitOps in a Nutshell - a FridayInANuthshell Episode.pdf
IaC & GitOps in a Nutshell - a FridayInANuthshell Episode.pdfIaC & GitOps in a Nutshell - a FridayInANuthshell Episode.pdf
IaC & GitOps in a Nutshell - a FridayInANuthshell Episode.pdf
 
COMPUTER 10 Lesson 8 - Building a Website
COMPUTER 10 Lesson 8 - Building a WebsiteCOMPUTER 10 Lesson 8 - Building a Website
COMPUTER 10 Lesson 8 - Building a Website
 
Igniting Next Level Productivity with AI-Infused Data Integration Workflows
Igniting Next Level Productivity with AI-Infused Data Integration WorkflowsIgniting Next Level Productivity with AI-Infused Data Integration Workflows
Igniting Next Level Productivity with AI-Infused Data Integration Workflows
 
UiPath Studio Web workshop series - Day 8
UiPath Studio Web workshop series - Day 8UiPath Studio Web workshop series - Day 8
UiPath Studio Web workshop series - Day 8
 
Anypoint Code Builder , Google Pub sub connector and MuleSoft RPA
Anypoint Code Builder , Google Pub sub connector and MuleSoft RPAAnypoint Code Builder , Google Pub sub connector and MuleSoft RPA
Anypoint Code Builder , Google Pub sub connector and MuleSoft RPA
 
How Accurate are Carbon Emissions Projections?
How Accurate are Carbon Emissions Projections?How Accurate are Carbon Emissions Projections?
How Accurate are Carbon Emissions Projections?
 
AI Fame Rush Review – Virtual Influencer Creation In Just Minutes
AI Fame Rush Review – Virtual Influencer Creation In Just MinutesAI Fame Rush Review – Virtual Influencer Creation In Just Minutes
AI Fame Rush Review – Virtual Influencer Creation In Just Minutes
 
Bird eye's view on Camunda open source ecosystem
Bird eye's view on Camunda open source ecosystemBird eye's view on Camunda open source ecosystem
Bird eye's view on Camunda open source ecosystem
 
Using IESVE for Loads, Sizing and Heat Pump Modeling to Achieve Decarbonization
Using IESVE for Loads, Sizing and Heat Pump Modeling to Achieve DecarbonizationUsing IESVE for Loads, Sizing and Heat Pump Modeling to Achieve Decarbonization
Using IESVE for Loads, Sizing and Heat Pump Modeling to Achieve Decarbonization
 
Meet the new FSP 3000 M-Flex800™
Meet the new FSP 3000 M-Flex800™Meet the new FSP 3000 M-Flex800™
Meet the new FSP 3000 M-Flex800™
 
Linked Data in Production: Moving Beyond Ontologies
Linked Data in Production: Moving Beyond OntologiesLinked Data in Production: Moving Beyond Ontologies
Linked Data in Production: Moving Beyond Ontologies
 
20150722 - AGV
20150722 - AGV20150722 - AGV
20150722 - AGV
 
Designing A Time bound resource download URL
Designing A Time bound resource download URLDesigning A Time bound resource download URL
Designing A Time bound resource download URL
 
Machine Learning Model Validation (Aijun Zhang 2024).pdf
Machine Learning Model Validation (Aijun Zhang 2024).pdfMachine Learning Model Validation (Aijun Zhang 2024).pdf
Machine Learning Model Validation (Aijun Zhang 2024).pdf
 
Videogame localization & technology_ how to enhance the power of translation.pdf
Videogame localization & technology_ how to enhance the power of translation.pdfVideogame localization & technology_ how to enhance the power of translation.pdf
Videogame localization & technology_ how to enhance the power of translation.pdf
 
OpenShift Commons Paris - Choose Your Own Observability Adventure
OpenShift Commons Paris - Choose Your Own Observability AdventureOpenShift Commons Paris - Choose Your Own Observability Adventure
OpenShift Commons Paris - Choose Your Own Observability Adventure
 
VoIP Service and Marketing using Odoo and Asterisk PBX
VoIP Service and Marketing using Odoo and Asterisk PBXVoIP Service and Marketing using Odoo and Asterisk PBX
VoIP Service and Marketing using Odoo and Asterisk PBX
 
201610817 - edge part1
201610817 - edge part1201610817 - edge part1
201610817 - edge part1
 
COMPUTER 10: Lesson 7 - File Storage and Online Collaboration
COMPUTER 10: Lesson 7 - File Storage and Online CollaborationCOMPUTER 10: Lesson 7 - File Storage and Online Collaboration
COMPUTER 10: Lesson 7 - File Storage and Online Collaboration
 
ADOPTING WEB 3 FOR YOUR BUSINESS: A STEP-BY-STEP GUIDE
ADOPTING WEB 3 FOR YOUR BUSINESS: A STEP-BY-STEP GUIDEADOPTING WEB 3 FOR YOUR BUSINESS: A STEP-BY-STEP GUIDE
ADOPTING WEB 3 FOR YOUR BUSINESS: A STEP-BY-STEP GUIDE
 

Hypothesis

  • 2.  We develop a procedure to test the validity of a statement about a population parameter. Examples:  The mean starting salary for graduates of four year business schools is Rs. 32,000 per month.  Eighty percent of those who play the state lottery regularly never win more than $ 100 in any one play.
  • 3. What is Hypothesis?  Is a statement about a population developed for the purpose of testing.  In most cases the population is too large that it is not feasible to study all items in the population.  We can, therefore, test a statement to determine whether the sample does or does not support the statement concerning the population.
  • 4. HYPOTHESIS TESTING  A procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement.
  • 5. Five-Step Procedure for Testing a Hypothesis  State the Null Hypothesis (Ho) and the Alternate Hypothesis (Hı)  Select a level of significance.  Identify the test statistic.  Formulate a decision rule.  Make a decision
  • 6. Step 1: State the Null Hypothesis (Ho) and the Alternate Hypothesis (Hı)  The first step is to state the hypothesis being tested. It is called the null hypothesis, designated (Ho).  The capital H stands for hypothesis, and the subscript zero implies “no difference”.  There is usually a “not” or a “no” term in the null hypothesis, meaning that there is “no change”.
  • 7.  For example, the null hypothesis is that the number of miles driven on the steel- belted tire is not different from 60,000.  Therefore, Ho: μ = 60,000.  We either reject or fail to reject the null hypothesis.  The null hypothesis is a statement that is not rejected unless our sample data provide convincing evidence that it is false.
  • 8. ALTERNATE HYPOTHESIS  The alternate hypothesis describes what you will conclude if you reject the null hypothesis. It is written as Hı.  It is also called the research hypothesis.  The alternate hypothesis is accepted if the sample data provide us with enough statistical evidence that the null hypothesis is false.
  • 9. Example:  A recent article indicated that the mean age of U.S. commercial aircraft is 15 years.  The null hypothesis represents the current or reported condition.  Ho: μ = 15.  The alternate hypothesis is that the statement is not true: H1: μ ≠15.
  • 10. Select a level of significance  The level of significance is designated α , the Greek letter alpha. It is also sometimes called level of risk.  There is no one level of significance that it is applied to all tests.  The common choices for α are .05, .01 and .10. LEVEL OF SIGNIFICANCE The probability of making a Type 1 error when the null hypothesis is true as an equality.
  • 11.  Traditionally, .05 level is selected for consumer research projects, .01 for quality assurance, and .10 for political polling.
  • 12. Type I and Type II Errors Population Condition Ho True Hı True Accept Ho Correct Type II Conclusion Error Conclusion Reject Ho Type I Correct Error Conclusion
  • 13. Type I Error from Indian Epic It may be recalled that in “Abhigyan Shakuntalam” , king Dushyanta had married shakuntala when he met her in her village, while wandering in a jungle. He gave her his royal ring as a gift which could also serve as her identity when she would come to meet him, in future. However, while going to meet him, she lost the ring in the river. When she reached Dushayant’s place and met him, he failed to recognize her especially since she did not have the ring. Thus Dushayant committed Type I error as he rejected Shankutla as his wife when, in fact, she was his true wife.
  • 14. Type II Error from Indian Epic In Mahabharta epic, Dronacharya – the ‘guru’ of both Pandavas and Kauravas – was fighting from the Kaurav’s side. However, he had taken a vow that he would stop fighting if and when his son Aswathama was killed in the war. It so happened that during the war, one elephant named Aswathama was killed. Lord - Krishna the mentor of Pandavas – thought of a strategy to make Dronacharya lay down his arms. Yudhishter on advice of lord Krishna, went to Dronacharya and pronounced
  • 15. Aswathama was dead-but was it a human or an elephant? Dronacharya, on listening the first part of Yudhishtir’s sentence, presumed that his son was dead, and he left for his heavenly abode without waiting to listen to the second part of Yudhishter’s sentence. Thus, Droncharya could be said to have committed Type II error i.e. accepting a statement when it was not true.
  • 16. Select a Test Statistic  A value, determined from sample information, used to determine whether to reject the null hypothesis.  The test criteria that are frequently used in hypothesis testing are Z, t, F, Χ test.
  • 17. Formulate the Decision Rule  A decision rule is a statement of the specific conditions under which the null hypothesis is rejected and the conditions under which it is not rejected .
  • 18. Step 5: Make a Decision  Make a decision regarding the null hypothesis on the sample information .  Interpret the results of the test.
  • 19. Population Mean: known One - tailed Test Lower Tail Test Upper Tail Test Ho: μ ≥ μo Ho: μ ≤ μo H1: μ < μo H1: μ > μo σ
  • 20. Example:  The Federal trade Commission (FTC) periodically conducts statistical studies designed to tests the claims that manufacturers make about their products.  For example, the label on a large can of Hilltop Coffee States that the can contains 3 pounds of coffee.  The FTC knows that Hilltop production process cannot place exactly 3 pounds of coffee, even if the mean filling weight is for the population of all cans filled is 3 pounds per can.
  • 21.  However, as long as the population mean filing weight is at least 3 pounds per can, the rights of consumers can be protected.  Thus, the FTC interprets the label information on a large can of coffee as a claim by Hilltop that the population mean is at least 3 pounds per can.  We will show how the FTC can check the hilltops claim by conducting the lower tail hypothesis test?
  • 22. Develop Null and Alternative Hypothesis If the population mean filling weight is at least 3 pounds per can, Hilltop’s claim is correct. Ho: μ ≥ 3 Hı: μ < 3 The hypothesized value of population mean is μo = 3
  • 23.  Suppose a sample of 36 cans of coffee is selected.  Sample mean is computed as an estimate of population mean μ.  If < 3 pounds, the sample results will cast a doubt on null hypothesis.  We want to know how much less than 3 pounds must be before we would be willing to declare the difference significant and risk making a Type I error by falsely accusing Hilltop of a label violation. x x x
  • 24. The director of FTC’s program made the following statement: If the company is meeting its weights specifications at µ = 3, I would like 99% chance of not taking any action against the company. Although I do not want to accuse the company wrongly of under filling its product, I am willing to risk a 1% chance of making such an error.” Therefore from the director’s statement we would set a = .01 Thus we must design the hypothesis test so that probability of making a type I error when µ = 3 is .01
  • 25. Test Statistic  For the Hilltop Coffee study, previous FTC test show that the population standard deviation can be assumed known with the value of σ = .18  In addition these tests also show the population of filling weights can be assumed to have a normal distribution.
  • 26. Sampling distribution of x 36n 03.018. ===σσx
  • 27. TEST STATISTIC FOR HYPOTHESIS TESTS ABOUT A POPULATION MEAN: σ KNOWN n/ 0 σ µ−=xz
  • 28. Suppose the sample of 36 Hilltop coffee cans provides a sample mean of = 2.92 small enough to cause us to reject Ho ? = 2.92; σ = .18 and n = 36 x x 36.18/n/ 67.2392.20 σ µ −=−=−= xz
  • 29. Critical Value Approach  The critical value is the value of the test statistic that corresponds to the area of α = .01 in the lower tail of the standard normal distribution.  Using standard normal distribution table, we find that z = -2.33 provides an area of .01 in the lower tail.
  • 30. For Hilltop Coffee Study Critical Value Rejection Rule for a level of significance of . 01 is Reject Ho if Z ≤ -2.33
  • 33.  = 2.92  z = -2.67  Since z = -2.67 < -2.33, we can reject Ho and conclude that Hilltop coffee is under filling cans. x
  • 34. Two – Tailed Test Ho: μ = μo H1: μ ≠ μo
  • 35. Example:  The U.S. Golf Association (USGA) establishes rules that manufacturers of golf equipment must meet if their products are to be acceptable for use in USGA events.  MaxFlight uses a high technology manufacturing process to produce golf balls with average distances from 295 yards.  When the average distance passes 295 yards, MaxFlight’s golf balls may be rejected by the USGA for exceeding the overall distance standard concerning carry and roll.
  • 36.  MaxFlights’s quality control program involves taking periodic samples of 50 golf balls to monitor the manufacturing process.  For each sample, a hypothesis test is conducted to determine whether the process has fallen out of adjustment.
  • 37.  We assume that the process is functioning correctly; i.e. the golf balls produced have a mean distance of 295 yards. H0: μ = 295 H1: μ ≠ 295  If the sample mean is less than is significantly less than 295 yards or significantly greater than 295 yards, we will reject H0.
  • 38.  The quality control team selected = .05 as the level of significance for the test. Data from previous tests conducted when the process was known to be in adjustment show that the population standard deviation can be assumed known with a value of = 12. Thus, with a sample size of n = 50, the standard error of is x x 50n 7.112 ===σσx
  • 39.  Because the sample size is large, the central limit theorem allows us to conclude that the sampling distribution of can be approximated by a normal distribution. Suppose that a sample of 50 golf balls is selected and that the sample mean is = 297.6 yards. This sample mean provides support for the conclusion that the population mean is larger than 295 yards.
  • 40. Computing z - statistic 5012// 53.12956.2970 n xz σ µ =−=−=
  • 41. Critical Value Approach  With a level of significance of = .05  The area in each tail beyond the critical values is  Using the table of of areas of standard normal distribution. 025.2/05.2/ ==α
  • 44. 96.1and96.1 025.025. =−=− zz Reject H0 if z ≤ 1.96 or if z ≥ 1.96 Because the value of the test for the MaxFlight study is z = 1.53, The statistical evidence will not permit us to reject the null hypothesis at the .05 level of significance.
  • 45. Example: • The Jamestown Steel Company manufactures and assembles desks and other office equipment at several plants in Western New York State. The weekly production of Model A325 desk at the Fredonia Plant follows a normal distribution, with a mean of 200 and a standard deviation of 16. recently because of market expansion, new production methods have been introduced and new employees hired.
  • 46.  The vice president of manufacturing would like to investigate whether there has been a change in the weekly production of the model A325 desk. To put it another way, is the mean number of desk produced at the Florida plant different from 200 at the .01 significance level?
  • 47. Solution  State the null hypothesis and alternate hypothesis:  This is a two-tailed test because the alternative hypothesis does not state a direction. 200: 200: 1 0 ≠ = µ µ H H
  • 48.  As noted, the .01 level of significance is used.  It is the probability of committing a Type I error, and it is the probability of rejecting a true null hypothesis.
  • 49. Select the test statistic n/σ µ−=xz
  • 50. Formulate the decision Rule  The decision rule is formulated by finding the critical values of z.  Since it is a two tailed test, half of . 01, or .005, is placed in each tail.  The area where H0 is not rejected, located between the two tails, is therefore .99.
  • 51. Make a decision and interpret the result 50/16n/ 55.12005.203 σ µ =−=−= xz Because H0 does not fall in the rejection region, H0 is not rejected We conclude that population mean is not different from 200.