OPRE 3360_Ch7.pdf - OPRE 3360 Managerial Methods in...

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OPRE 3360 : Managerial Methods in Decision Making Under Uncertainty OPRE3360‐ ©Naseri 1
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Chapter7:SamplingandSamplingDistributions SelectingaSample PointEstimation IntroductiontoSamplingDistributions SamplingDistributionof ݔ̅ SamplingDistributionof ݌̅ OPRE3360‐ ©Naseri 2
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Introduction Element theentityonwhichdataarecollected Population acollectionofalltheelementsofinterest Sample asubsetofthepopulation SampledPopulation thepopulationfromwhichthesampleisdrawn OPRE3360‐ ©Naseri 3
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SelectingaSample UltimateGoal:Thereasonweselectasampleistocollectdatato answeraresearchquestionaboutapopulation. Thesampleresultsprovideonly estimates ofthevaluesofthe populationcharacteristics. The reason issimplythatthesamplecontainsonly aportion ofthe population. With propersampling methods,thesampleresultscanprovide “good” estimates  ofthepopulationcharacteristics. OPRE3360‐ ©Naseri 4
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SelectingaSample SamplingfromaFinitePopulation SamplingfromanInfinitePopulation OPRE3360‐ ©Naseri 5
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SamplingfromaFinitePopulation FinitePopulation Oftendefinedbylistssuchas: Organizationmembershiproster Creditcardaccountnumbers Inventoryproductnumbers Asimplerandomsampleofsize fromafinitepopulationofsize is asampleselectedsuchthateachpossiblesampleofsize ݊ hasthe sameprobabilityofbeingselected.( In fact we want to choose  unbiased! ) OPRE3360‐ ©Naseri 6
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SamplingfromaFinitePopulation Replacingeachsampledelementbeforeselectingsubsequent elementsiscalled samplingwithreplacement . Samplingwithoutreplacement istheprocedureusedmostoften. Inlargesamplingprojects,computer‐generatedrandomnumbersare oftenusedtoautomatethesampleselectionprocess. OPRE3360‐ ©Naseri 7
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Example:St.Andrew’sCollege (SamplingfromaFinitePopulation) St.Andrew’sCollegereceived900applicationsforadmissionin the upcomingyearfromprospectivestudents.Theapplicantswere numbered,from1to900,astheirapplicationsarrived.TheDirectorof Admissionswouldliketoselectasimplerandomsampleof30 applicants. OPRE3360‐ ©Naseri 8
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Example:St.Andrew’sCollege (SamplingfromaFinitePopulation) Step1:Assignarandomnumbertoeachofthe900applicants. TherandomnumbersgeneratedbyExcel’s RAND functionfollowa uniformprobabilitydistributionbetween0and1. Step2:Selectthe30applicantscorrespondingtothe30smallest randomnumbers. OPRE3360‐ ©Naseri 9
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SamplingfromaFinitePopulationUsingExcel ExcelFormulaWorksheet Note: Rows 10-901 are not shown. A B 1 Applicant Number 2 1 =RAND() 3 2 =RAND() 4 3 =RAND() 5 4 =RAND() 6 5 =RAND() 7 6 =RAND() 8 7 =RAND() 9 8 =RAND() Random Number OPRE3360‐ ©Naseri 10
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