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Lecture 18

STATS 2B03 Lecture 18: STATS 2B03 LECTURE 18 NOTES


Department
Statistics
Course Code
STATS 2B03
Professor
Aaron Childs
Lecture
18

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Wewanttouseasampletotestoneofthefollowingthingsaboutpopulationmean
1.:
2.:
3.:
whereisagivennumber
e.g.ForTest#1,Imightwanttotest:72
e.g.Forapainreliever:4
iscalledthealternative (orresearch)hypothesis
Thenullhypothesis istheoppositeof
e.g.:72
: 4
ConclusionofaHypothesisTest
Reject andconcludethatisprobablytrue
Donotreject andconcludethatthereisnotsufficientevidencetoreject,thatthereisnotstrong
evidenceinfavourof(wedonot concludethatisprobablytrue)
Analogy:
:notguilty(notstrongenoughevidenceforguilt)
:guilty
PossibleErrors:
Thetruth
istrue istrue
Conclusionbasedonsample RejectTypeIerror CorrectDecision
DonotrejectCorrectDecision TypeIIError
e.g.SupposethatIsample15studentsandfindthat
̅
78.6andreject: 72,butthetest
averageendsupbeing68.thenaTypeIerrorhasoccurred.
Thesignificancelevel ofahypothesistestistheprobabilityaTypeIerroroccurs.
TheprobabilityofaTypeIIerrorisdenotedby,andthepower ofatestisdefinedtobe1.(Agood
testhasahighpower).
Ingeneral(orequivalentlythepowerofatest)isunknown.Butforagivensignificancelevel,increasing
thesamplesizealwaysdecreases,andincreasesthepowerofatest.
ProcedurefortestingaboutaPopulationmeanfor(frontofindexcard)
Step1Calculate

̅

/
(replacewithifisunknown)
Step2
CaseI::
Rejectif

CaseII::
Rejectif

7.17.2HypothesisTestingforamean
October0912 11:07AM
Stats 2B03 Pa
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e 1
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