Lecture Business statistics in practice (7/e): Chapter 9 - Bowerman, O'Connell, Murphree

Chapter 9 - Hypothesis testing. After mastering the material in this chapter, you will be able to: Set Up appropriate null and alternative hypotheses, describe Type I and Type II errors and their probabilities, use critical values and p-values to perform a z test about a population mean when s is known,...
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Lecture Business statistics in practice (7/e): Chapter 9 - Bowerman, OConnell, Murphree Chapter9 HypothesisTestingMcGrawHill/Irwin Copyright©2014byTheMcGrawHillCompanies,Inc.Allrightsreserved.HypothesisTesting9.1 NullandAlternativeHypothesesand ErrorsinTesting9.2 zTestsaboutaPopulationMean σKnown9.3 tTestsaboutaPopulationMean σUnknown9.4 zTestsaboutaPopulationProportion9.5 TypeIIErrorProbabilitiesandSample SizeDetermination(Optional) 92LO9-1: Specifyappropriate null andalternative hypotheses. 9.1NullandAlternativeHypotheses andErrorsinHypothesisTesting  Nullhypothesis,H0,isastatementofthebasic propositionbeingtested ◦ Representsthestatusquoandisnotrejectedunlessthereis convincingsampleevidencethatitisfalse  Alternativehypothesis,Ha,isanalternative acceptedonlyifthereisconvincingsample evidenceitistrue  OneSided,“GreaterThan”H0:μ μ0vs.Ha:μ>μ0  OneSided,“LessThan”H0:μ μ0vs.Ha:μLO9-1 TypesofDecisions  AsaresultoftestingH0vs.Ha,willdecideeitherof thefollowingdecisionsforthenullhypothesisH0: ◦DonotrejectH0orrejectH0  To“test”H0vs.Ha,usethe“teststatistic” x 0 x 0 z x n  zmeasuresthedistancebetweenμ0andonthe samplingdistributionofthesamplemean  Ifthepopulationisnormalornislarge*,thetest statisticzfollowsanormaldistribution 94LO9-2: Describe Type Iand Type II errors andtheir probabilities. ErrorProbabilities TypeIError:RejectingH0whenitistrue ◦ istheprobabilityofmakingaTypeIerror ◦1– istheprobabilityofnotmakingaTypeI error TypeIIError:FailingtorejectH0whenitis false ◦βistheprobabilityofmakingaTypeIIerror ◦1–βistheprobabilityofnotmakingaTypeII error Table9.1 95LO9-2 TypicalValues Usuallyset toalowvalue ◦SothereisasmallchanceofrejectingatrueH0 Typically, =0.05 ◦StrongevidenceisrequiredtorejectH0 ◦Usuallychooseαbetween0.01and0.05  =0.01requiresverystrongevidencetorejectH0 Tradeoffbetween andβ ◦Forfixedsamplesize,thelower ,thehigherβ  Andthehigher ,thelowerβ 96LO9-3: Use criticalvalues and p-values toperform a z test about apopulation mean whenσ is known. 9.2zTestsaboutaPopulationMean: σKnown Testhypothesesaboutapopulationmean usingthenormaldistribution Calledztests Requirethatthetruevalueofthepopulation standarddeviationσisknown ◦Inmostrealworldsituations,σisnotknown  Butoftenisestimatedfromsofasinglesample  Whenσisunknown,testhypothesesabouta populationmeanusingthetdistribution ◦Here,assumethatweknowσ 97LO9-3 StepsinTestinga“GreaterThan” Alternative 1. Statethenullandalternativehypotheses 2. Specifythesignificancelevelα 3. Selecttheteststatistic 4. Determinethecriticalvaluerulefordeciding whetherornottorejectH0 5. Collectthesampledataandcalculatethevalueof theteststatistic 6. DecidewhethertorejectH0byusingthetest statisticandtherejectionrule 7. Interpretthestatisticalresultsinmanagerialterms andassesstheirpracticalimportance 98LO9-4: Use criticalvalues and p-values toperform a t test about apopulation mean whenσ is unknown. 9.3tTestsaboutaPopulationMean: σUnknown Assumethepopulationbeingsampledis normallydistributed Thepopulationstandarddeviationσis unknown,asistheusualsituation ◦Ifthepopulationstandarddeviationσis unknown,thenitwillhavetoestimatedfroma samplestandarddeviations Underthesetwoconditions,havetousethet distributiontotesthypotheses 99LO9-5: Use critical 9.4zTestsaboutaPopulationvalues and p-values toperform a large samplez test about a Prop ...