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Lecture

Lecture 3

8 Pages
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Department
Quantitative Methods
Course Code
QMS 202
Professor
Clare Chua

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1/25/2011
1
Chapter10
FundamentalsofHypothesisTesting :
OneSampleTests
HypothesisTesting
•Basedonsampleinformation
•Typicallybeginswithatheoryor
claimaboutµ
HypothesisTesting
Steps/Rational
1. What parameter are you testing? µorS
H T
O P
FundamentalsofHypothesisTesting:One
SampleTests
P
Mean, µP
PE
HypothesisTesting
Steps/Rational
1. What parameter are you testing? µorS
2. Check the assumption/condition of normality
Hypothesis Test
One Population
Population
Mean,
µ
Population
Proportions, p
Ati
Is the pop
normal?
1known
Z-test
Is the pop
normal?
1unknown
T-test
Are np5 and
n(1-p)5
Z-test
A
ssump
ti
ons
www.notesolution.com
1/25/2011
2
Isthisnormallydistributed? HypothesisTesting
Steps/Rational
1. What parameter are you testing? µorS
2. Check the assumption/condition of normality
3. State the hypothesis: Ho and Ha
Summary:HypothesisTestingforonesample
If Ho is Then Ha is And the test
is called
Ho: µ = µ0Ha: µ µ0Two-tailed
Note:wealwayshypothesizedthepopulationMean,
Thevalueofµotakesonanyvalueandisgivenintheproblem
Ho: µ µ0Ha: µ > µ0Right-tailed
Ho: µ µ0Ha: µ < µ0Left-tailed
Note:thenullhypothesis,Ho,assumesthepopulationisequal
tosomespecificdistribution,thusHoalwayscontainstheequals
statement.
HypothesisTesting
Steps/Rational
1. What parameter are you testing? µorS
2. Check the assumption/condition of normality
3. State the hypothesis: Ho and Ha
4. Which test? z-test or t-test
Hypothesis Test
One Population
Population
Mean,
µ
Population
Proportions, p
Ati
Is the pop
normal?
1known
Z-test
Is the pop
normal?
1unknown
T-test
Are np5 and
n(1-p)5
Z-test
A
ssump
ti
ons
ParametricTest
ParametricTe st
Specifiescertainconditionsaboutthedistributionof
responsesinthepopulationfromwhichtheresearchsample
wasdrawn.
Theyarenormallyassumedtohold
statisticianmakestheassumption thatbothof thesepopulations are
statistician
makes
the
assumption
that
both
of
these
populations
are
normalandhavethesameerrorvariance
Themeaningfulnessoftheresultsofaparametrictest
dependsonthevalidityoftheseassumptions.
asetofassumptionsaboutnormality(shapeofthedistribution)
homogeneityofvariance(similargroups)
independenterrors
www.notesolution.com
1/25/2011
3
HypothesisTesting
Steps/Rational
1. What parameter are you testing? µorS
2. Check the assumption/condition of normality
3. State the hypothesis: Ho and Ha
4. Which test? z-test or t-test
5. Is there evidence to reject Ho?
6. Write a non-statistical conclusion.
ZTestofHypothesisfortheMean(known)
TherearetwoapproachestoHypothesisTesting
1. UsingTestStatistic/criticalvalueapproach
2. UsingtheprvalueAPPROACH1
UsingTestStatistic/criticalvalue
approach
UsingTestStatistics/criticalvalueapproachtoHypothesis
Testing
“TheCriticalApproachtoHypothesisTesting”
Ifa0.05levelofsignificanceisusedina(twortailed)hypothesistest,whatwill
youdecideifthecomputedvalueoftheteststatisticsisr2.21
Area=r/2=0.025
Zcrit=r1.96 Zcrit=1.96
Area=r/2=0.025
Z
Criticalvalue Criticalvalue
Regionof“FailtoRejectHo
or“DoNotRejectHo
Regionof“RejectHo” Regionof“RejectHo”
0
UsingTestStatistics/criticalvalueapproachtoHypothesis
Testing
“TheCriticalApproachtoHypothesisTesting”page254
Ifa0.05levelofsignificanceisusedina(twortailed)hypothesistest,whatwill
youdecideifthecomputedvalueoftheteststatisticsisr2.21
Isknownasteststatistic
Area=r/2=0.025
Zcrit=r1.96 Zcrit=1.96
Area=r/2=0.025
Z
Criticalvalue Criticalvalue
Regionof“FailtoRejectHo
or“DoNotRejectHo
Regionof“RejectHo” Regionof“RejectHo”
0
Zcalc=r2.21 Zcalc=2.21
www.notesolution.com

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Description
1252011 Chapter10 HypothesisTesting FundamentalsofHypothesisTesting: Basedonsampleinformation OneSampleTests Typicallybeginswithatheoryor claimabout HypothesisTesting FundamentalsofHypothesisTesting:One SampleTests StepsRational 1. What parameter are you testing? or5 H T O P P P Mean, P - HypothesisTesting Hypothesis Test StepsRational One Population 1. What parameter are you testing? or5 PoMean,ion Population 2. Check the assumptioncondition of normality Proportions, p Assumpttins Is the pop Is the pop Are np5 and normal? normal? n(1-p)5 known unknown Z-test Z-test T-test 1 www.notesolution.com
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