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Statistical Methods for Estimating Proportions and Confidence Intervals in Real-World Data Analysis

Description: The assignment delves into statistical methods used for data analysis, focusing on proportions and confidence intervals.

Claire Mitchell
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Statistical Methods for Estimating Proportions and ConfidenceIntervals in Real-World Data AnalysisQuiz61.A researcher wants to investigate the proportion of married men who are happywith their marriagetodothis,hetakesasampleof100menandfindsthat72reportedbeinghappywiththeirmarriage.Shouldaconfidenceintervalbeconstructedtodeterminetheproportionofallmenwhoarehappywiththeirmarriage?Why?(giveashortexplanation;1-2sentences)Ans.Yes,aconfidenceintervalshouldbeconstructedbecauseitgivesanintervalaroundthepointestimateof72/100ie0.72inwhichtheresearcherwillfindthepopulationproportionofmarriedmenwhoarehappywiththeirmarriagewithconfidence(90%or95%or99%).2.Supposearandomsampleof64cyclistsontheFredMeijerHeartlandTrailwastaken,ofwhich48werewearinghelmets.Finda95%confidenceintervalfortheproportionofallcyclistsontheFredMeijerHeartlandTrailwhoworehelmets.Calculatethefollowingquantitiestoleadyoutotheconfidenceinterval.a.StandardError:SampleSize(n)=64Pointestimatep̂= 48/64 = 0.75Standard Error = √(p̂*(1-p̂)/n) = √(0.75 * 0.25 /64) = 0.0541b.MarginofError:ConfidenceLevel(C.L.)=0.95α=1-C.L.=1-0.95=0.05zα/2=1.96Marginoferror=z*Standarderror=1.96*0.0541=0.1061c.CriticalValue:ConfidenceLevel(C.L.)=0.95α=1-C.L.=1-0.95=0.05zα/2=1.96=CriticalValued.ConfidenceInterval:LowerLimit=p̂-Margin of error = 0.75–0.1061 = 0.6439Upper Limit=p̂+ Margin of error = 0.75 + 0.1061 = 0.85613.Astudywasmadeinvestigatingstudentenrollmentpersistencewithrespecttohoursworkedperweek.StudentsclassifiedasPreserving(thosewhoreturnedafterthefirstsemesterofcollege)andnon-persevering(thosewhodidnotreturnaftertheirfirstsemesterofcollege)wereaskedabouttheworkschedulesduringthefirstsemesterofcollege.Fromthesestudents,thefollowingdatawascollected.PerseveringNon-persevering(n=144)(n=49)# hrs worked per week in first semesterMean 17.428.64SD 15.210.3

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Statistics

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