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CHAPTER8
EstimatingwithConfidence8.1ConfidenceIntervals:TheBasics
DETERMINEthepointestimateandmarginoferrorfromaconfidenceinterval.INTERPRETaconfidenceintervalincontext.INTERPRETaconfidencelevelincontext.DESCRIBEhowthesamplesizeandconfidencelevelaffectthelengthofaconfidenceinterval.EXPLAINhowpracticalissueslikenonresponse,undercoverage,andresponsebiascanaffecttheinterpretationofaconfidenceinterval.ConfidenceIntervals:TheBasics
Activity:TheMysteryMeanSupposeyourteacherhasselecteda“MysteryMean”valueμandstoreditas“M”intheircalculator.Yourtaskistoworktogetherwith3or4studentstoestimatethisvalue.Thefollowingcommandwasexecutedontheircalculator:mean(randNorm(M,20,16))Theresultwas240.79.ThistellsusthecalculatorchoseanSRSof16observationsfromaNormalpopulationwithmeanMandstandarddeviation20.Theresultingsamplemeanofthose16valueswas240.79.Yourgroupmustdetermineanintervalofreasonablevaluesforthepopulationmeanμ.Usetheresultaboveandwhatyoulearnedaboutsamplingdistributionsinthepreviouschapter.Shareyourteam’sresultswiththeclass.
ConfidenceIntervals:TheBasicsWelearnedinChapter7thatanidealpointestimatorwillhavenobiasandlowvariability.Sincevariabilityisalmostalwayspresentwhencalculatingstatisticsfromdifferentsamples,wemustextendourthinkingaboutestimatingparameterstoincludeanacknowledgementthatrepeatedsamplingcouldyielddifferentresults.Apointestimatorisastatisticthatprovidesanestimateofapopulationparameter.Thevalueofthatstatisticfromasampleiscalledapointestimate.
TheIdeaofaConfidenceIntervalRecallthe“MysteryMean”Activity.Isthevalueofthepopulationmeanμexactly240.79?Probablynot.However,sincethesamplemeanis240.79,wecouldguessthatμis“somewhere”around240.79.Howcloseto240.79isμlikelytobe?Toanswer
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