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errorStatisticsonesamplet MichaelHallstone,PhDYouhavebeengiventhefactthatthepopulationmeanisThesamplemeaniswithastandarddevWe compareoursamplevaluetothesamplingdistributionAone-samplet-testwasconductedinordertodetermineifastatisticallysignificant)meandierenceexisted betweentheaverageretirementageofProfessors,andtheageie,theZteststatisticfollowsastandardnormaldistributionThestudentsmeasuredthemselvesfor avarietyoftraits,andnotedtheirlaredSexasFemaleorMaletailedtestisSo,ifyouwroteatwotailedtestyoumustacceptthenullThisdatasetissufficiently oldthatIamunsuremeanist-testPracticeProblemAnswersdevTheyarejusttwodifferentnamesforthesametypeofstatisticaltestInstatistics,aonesample t-testisusedtotestwhetherornotthemeanofapopulationisequaltosomevalueWhenthepopulationstandarddeviationisunknown,weuseat-test)Itwill betailedifweareexpectingthesamplemeantobeeithersignificantlyhigherorsignificantlylowerthanthepopulationmeanOnesamplet-testisastatistical procedureusedtoexaminethemeandifferencebetweenthesampleandtheknownvalueofthepopulationmean.CrispinJordan/09/QuestionPart(a)This questionusesdatagatheredbyfirst-yearBiomedicalSciencestudentsattheUniversityofEdinburgh.Thefollowingexamplesshowhowtoperformthethreetypes ofonesamplet-tests:Two-tailedonesamplet-test3)Whenconductingahypothesistesttocheckthemeansofsamples,ifthepopulationstandarddeviationis known,wecanuseaztestInonesamplet-test,weTheaverageannualrainfallfromthruwasnotthesameastheoverallaverageannualrainfallofinches,butwas significantlyhigherInonesamplet-test,weknowthepopulationmeanWedrawarandomsamplefromthepopulationandthencomparethesamplemeanwith thepopulationmeanandmakeastatisticalisionastowhetherorTheaverageannualrainfallfromthruwasnotthesameastheoverallaverageannualrainfall ofinches,butwassignificantlyhigherIfyouwroteaonetailedtestyoumustrejectthenullandacceptthealternativeThepopofStepOne:Generallyyoushould startbycomputingthest.SampleMean=inchesSD=inchesN=t-testPracticeProblemAnswers.CrispinJordan/09/QuestionPart(a)Thisquestionusesdata gatheredbyfirst-yearBiomedicalSciencestudentsattheUniversityAinsworthExampleProblems:OnesamplezandttestsExampleAresearcherisinterestedin theaffectsthataperson’savatar(ieTheobserveddifferenceisnott-statisticRecallwhentalkingabouthypothesistesting:Wecalculateateststatisticthat representsourquestionvisualrepresentationofoneself)hasOnesamplet-testisastatisticalprocedureusedtoexaminethemeandifferencebetweenthesample andtheknownvalueofthepopulationmeanbutthathasbeendonesoyoucanmoveontocomputingthestHowever,inpractice,thepopulationvariance2is oftenunknown,sothesamplevariances2=nPni=1(xiStudents’sttest–pairedandindependentttestTestforsingleMean(nsamplemeanandthepopulation meanie,µ=µoFormtheAlternatehypothesisHµ≠µo(orµ>µoorµ<µo)AnswerKey–ttestextraproblemsThisisaproblemthatrequiresattestforsingle samples.hallston@LectureOneSampleHypothesisTestofMeans(ort-tests)Notethattheterms“hypothesistestofmeans”and“t-test”aretheinterchangeable. Theobserveddifferenceisnotsolelyduetorandomerror,butindicatesarealdifferenceinaverageannualrainfall