利用excel进行统计分析-chapter 8-confidence interval estimation

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1、StatisticsforManagersUsingMicrosoft®Excel5thEditionChapter8ConfidenceIntervalEstimationChap8-1LearningObjectivesInthischapter,youwilllearn:ToconstructandinterpretconfidenceintervalestimatesforthemeanandtheproportionHowtodeterminethesamplesizenecessarytodevelopaco

2、nfidenceintervalforthemeanorproportionHowtouseconfidenceintervalestimatesinauditing2ChapterOutlineConfidenceIntervalsforthePopulationMean,μwhenPopulationStandardDeviationσisKnownwhenPopulationStandardDeviationσisUnknownConfidenceIntervalsforthePopulationProportion,

3、πDeterminingtheRequiredSampleSize3PointEstimatesApointestimateisasinglenumber.Forthepopulationmean(andpopulationstandarddeviation),apointestimateisthesamplemean(andsamplestandarddeviation).AconfidenceintervalprovidesadditionalinformationaboutvariabilityPointEstimat

4、eLowerConfidenceLimitUpperConfidenceLimitWidthofconfidenceinterval4ConfidenceIntervalEstimatesAconfidenceintervalgivesarangeestimateofvalues:TakesintoconsiderationvariationinsamplestatisticsfromsampletosampleBasedonalltheobservationsfrom1sampleGivesinformationabout

5、closenesstounknownpopulationparametersStatedintermsoflevelofconfidenceEx.95%confidence,99%confidenceCanneverbe100%confident5ConfidenceIntervalEstimatesThegeneralformulaforallconfidenceintervalsis:PointEstimate±(CriticalValue)(StandardError)6ConfidenceLevelConfidenc

6、eLevelConfidenceinwhichtheintervalwillcontaintheunknownpopulationparameterApercentage(lessthan100%)7ConfidenceLevelSupposeconfidencelevel=95%Alsowritten(1-)=.95Arelativefrequencyinterpretation:Inthelongrun,95%ofalltheconfidenceintervalsthatcanbeconstructedwillcont

7、aintheunknowntrueparameterAspecificintervaleitherwillcontainorwillnotcontainthetrueparameter8ConfidenceIntervalforμ(σKnown)AssumptionsPopulationstandarddeviationσisknownPopulationisnormallydistributedIfpopulationisnotnormal,uselargesampleConfidenceintervalestimate:

8、(whereZisthestandardizednormaldistributioncriticalvalueforaprobabilityofα/2ineachtail)910FindingtheCriticalValue,ZCommonlyusedconfidencelevelsare