Section 101 Point and Interval Estimation101节点估计和区间估计.pptVIP

PointandIntervalEstimation

withConfidenceAnotherSpectacularPowerPointPresentation

PointEstimatesDefinition: Asinglenumberthatisbasedonsampledata,andrepresentsareasonablevalueofthecharacteristicofinterest.ThingsLike: x s M-Thesimplestapproachtoestimatingapopulationvalue.

LetsLookatanExampleArecentsurveyaskedhighschoolseniorshowmanyhourstheyspentonlineeachday.Findthepointestimateofμwiththedatabelow.47.2555.256.25 6.254.53.54.25Whatcouldweusetoestimateμ?MorxFindboth:x=46.25=4.62510M=4.75Whichoneisbetter?Recallwhenitisbesttouseeachone…

ConfidenceIntervals

(estimatingμ)ThingstoRememberAbouttheDistributionofx: 1)Hasanormaldistribution(byCLT) 2)Isanunbiasedestimatorofμ(x=μ) 3)Ifpermissionisgranted: s=σ/√nIssueswithPointEstimates:ifwere–dothesample,willwegetsamestat?

ConfidenceIntervalsDef:theintervalofreasonablevaluesofthecharacteristicofinterestPatternfortheformula:(what’sonAPtest)statistic±criticalvalue(standarddeviationofstat)ForEstimatingμ:x±z*(σ/√n) MarginofError

ConfidenceLevelsDef:thesuccessrateofthemethodusedtoconstructtheinterval.Ex:A95%confidenceinterval=ifwetooklotsofsamplesandfoundthemeanoverandoveragain,inthelongrun95%oftheresultingintervalswouldcapturethetruevalueoftheparameter.Ifwegothroughthesameprocesswiththesamesamplesize,σ,andz*,butdifferentx,95%ofthoseintervalswillcontainμ.(CIapplet)

CalculatingConfidenceIntervalsWhatisz*? Alocationonthenormalcurvethatresultsintheneededconfidencelevel. Ex: UseTableC!z*=1.96-z*z*95%

CalculatingConfidenceIntervalsLet’stryanotherz*:Whatisz*?z*=2.326-z*z*98%

CriticalValuesz*isalsocalledacriticalvalue.Anyideaswhy?Theareaoutsideoftheintervalarecalledcriticalareas

PANIC(notatthedisco…)