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GPHY247/POLS385

IntroductiontoStatisticsBLW18

PracticeFinalExam

__________________________________________________________________IMPORTANT:READTHEFOLLOWINGBEFOREYOUBEGIN.• Thisexamis3hrsinduration.Theexamis17pageslong.• WriteyourstudentnumberANDnameonthecoversheetforthisexam,butnot

ontheremainingpages.TheQRcodeconnectseachpageforyou.• Youareonlypermittedtohavepensand/orpencilswhilewritingtheexam.

Pencilcasesarenotpermitted.• Answerallquestionsusinganinkpen,andanswerallquestionsdirectlyonthis

sheet.• Formultiple-choicequestions,writethemostappropriateanswerinthespace

provided.Onlytheanswerinthisspacewillbegraded.• Forshortanswerquestions,answerinthespaceprovided.• Universityapprovedcalculatorsareallowed.• Readeachquestioncarefullybeforeyouanswer.• Takecaretoallocatetimeamongallthequestions.

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MULTIPLECHOICE–WriteasingleanswerinthespaceprovidedusingUPPERCASEletters.Illegibleanswerswillbemarkedincorrect.YouDONOTneedtojustifyyouranswer.1) Youwanttoplantabutterflygardenonthebalconyofyourapartment,butare

notsurewhatspeciesofmilkweedisbestsuitedforpots.Yougrow10plantsofthe‘CommonMilkweed’and10plantsofarelatedspeciescalledthe‘ButterflyWeed’andmeasuretheirheightafter2months.Whichofthefollowingstatementsisaboutthedescriptivestatisticsforyourdata?[1mark]I. Aboxplotshowingthattheinterquartilerangeforthecommonmilkweed

isgreaterthanforthebutterflyweed.II. Thedifferenceinmedianheightbetweenthetwospeciesis3.2cm.III. Theheightdifferencebetweenthetwospeciesisunexpectedfrom

samplingerror.

A. Ionly.B. IIonly.C. IandII.D. IandIII.E. IIandIII.

ANSWER:_____C_____

STUDYAUsethefollowingstudytoanswerquestions2&3.Airbnbisanaccommodation-sharingplatformthatreliesheavilyonguestratings.Thefigurebelowshowsthenumberofaccommodationsineachrankcategorywhere5.0isexcellentand1.0ispoor.

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2) IfyoutookrepeatedsamplesofpotentialaccommodationsforSTUDYA,whichof

thefollowingstatementsaboutthedistributionofthemeanratingswouldbeINCORRECT?[1mark]

A. SincethedataarenotNormallydistributed,thedistributionofmeanratingscannotbeNormallydistributed.

B. Themeanofthedistributionisthesameasthemeanofthepopulationdistribution.

C. Thevarianceofthedistributiondependsonsamplesize.D. Samplingerrorcausesthevariationinthedistribution.E. Thestandarddeviationofthedistributioncanbeestimatedfromasingle

sample.

ANSWER:____A_____

3) Youcollectasampleof32accommodationsforSTUDYAandfindthefollowinginformationabouttheratings:Mean=4.2,Median=4.5,SD=0.2,IQR=1.5.Basedonthisinformation,whatistheestimatedstandarddeviationofthedistributionofmeanratings?[1mark]

A. 0≤ANSWER<0.05B. 0.05≤ANSWER<0.1C. 0.1≤ANSWER<0.2D. 0.2≤ANSWER<0.5E. 0.5≤ANSWER<1.0

ANSWER:_____A_____

4) Inwhichofthefollowingwaysarecase-controlandcohortstudiessimilar?[1mark]

A. BothareretrospectivestudiesB. BothareusedinexperimentalstudiesC. Bothstartwithgroupsofsubjectsthatdifferinsomefactorsuspectedof

influencingtheoutcomeD. BothareusedinobservationalstudiesE. Bothareformsofinferentialstatistics

ANSWER:_____D_____

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STUDYBUsethefollowingstudytoanswerquestions5&6.Youarestudyingwhetherphysicalfitnessandthepropensityforexercisetoimprovefitnessdifferbetweenmenandwomen.Yousample200menand200womenbetween30–40yearsoldchosenrandomlyfromtheKingstoncommunityanddeterminehowmanyminutesofexerciseeachpersonengagesinperday.5) Whatanalysiswouldyouusetotestthenullhypothesisthatminutesofexercise

donotdifferbetweenmenandwomeninSTUDYB?[1mark]A. Chi-squaretestB. Paired-samplet-testC. 2-samplet-testD. Single-factoranalysisofvariance(ANOVA)E. Regression

ANSWER:_____C_____

6) WhatisthestatisticalpopulationforSTUDYB?[1mark]A. AllresidentsofKingstonB. AllresidentsofKingstonbetweentheagesof30-40C. AllresidentsofKingstonbetweentheagesof30-40whoexcerciseD. AlltheresidentsofCanadaE. Noneoftheabove

ANSWER:_____B_____

7) Saraisananthropologistwhohasbeenstudyingstresshormones(ug/ml)in

peopleoverthewintermonths.Shecollectsbloodsamplesfrom10randompeopleinacity,10randompeoplefromthesuburbs,and10randompeoplefromruralareas.Whatstatisticaltestshouldbeusedtoevaluatewhethertherearedifferencesinstresshormonesamongpeoplelivingindifferentlocations?[1mark]

A. Chi-squaretestB. Paired-samplet-testC. 2-samplet-testD. Single-factoranalysisofvariance(ANOVA)E. Regression

ANSWER:_____D_____

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8) Below is a regression of mushroom density in relation to the fertility (nutrient content) of the soil among 41 woodlots in eastern Ontario. The dashed line is the fit regression line. Do you think that these data meet the assumptions of linear regression?[1mark]

A. Yes.TheresidualvariationlooksreasonableB. No.TheresidualvariationisclearlynotnormallydistributedC. No.TheinterceptisnotzeroD. No.TheslopeisnotzeroE. No.Theresidualvariationisclearlynothomoscedastic.

ANSWER:_____A_____

9) Youhavebeeninvestigatingthehumanhealtheffectsofafactorythathasbeenreleasingcontaminatedwaterintoariverfromwhichalllocalcommunitiesdrawtheirdrinkingwater.Thetoxininquestionisknowntocauselivercancerinlabrats.Todeterminewhetherpollutionintheriverisaffectinghumanhealth,yourandomlysample200peoplelivinginthecommunityupstreamfromthefactor(thatdon’tdrinkthepollutedwater)and200individualsthatlivedownstream(hencetheydodrinkthecontaminatedwater).Foreachpersonsampled,youperformaliverenzymetesttolookforthetelltalesignsoflivercancer.Whattypeofstatisticaltestwouldbebestsuitedtoanalyzethesedata?[1mark]

A. Chi-squaretestB. Paired-samplet-testC. 2-samplet-testD. Single-factoranalysisofvariance(ANOVA)E. Regression

ANSWER:_____C_____

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10) Consideradatasetthatcontainsgradesforstudentswhohavebeeninvolvedina

studylookingattheeffectofpeer-to-peerteaching.Onegroupofstudentswasaskedtospend1hreachweekstudyingforthecourse,andasecondgroupwasaskedtospend1hreachweekteachingtheirpeersthematerialthattheyunderstoodwellfromthecourse.Thedifferenceiscalculatedasmeangradeforpeer-to-peerminusmeangradeforstudying.Whichofthefollowingtestdistributionsismostappropriatetoevaluatethehypothesisthatpeer-to-peerteachingisabetterwaytostudyforexaminations?[1mark]

ANSWER:_____A_____11) Selectwhichofthefollowingnullandalternativehypothesesaremost

appropriateforatwo-samplet-testthatanswersthefollowingquestion:“Arethemeansofmysamplesdifferent?”.[1mark]

A. H0:μ≤0 HA:μ>0B. H0:μA=μB HA:μA≠μBC. H0:μA≥μB HA:μA<μBD. H0:μ>0 HA:μ≤0E. H0:μA≠μB HA:μA=μB

ANSWER:____B_______

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12) Youconductedastudyofthepracticalskillsamongsurgeonsincardiacversusneurologicaldisciplines.Youselected20hospitalsatrandomandselectedonecardiacandoneneurologicaldoctorwithineachhospital.Eachdoctorcompletedastandardtesttoevaluateher/hissurgicalskills.Meanperformanceonthetestwascomparedbetweendisciplinesusinga2-samplet-test.Basedonwhatyou’velearnedaboutstatisticalsleuthing,isthereaproblemwiththisanalysis?Ifso,whatisthatproblem?[1mark]

A. Thereisnoproblem.A2-samplet-testisdesignedforsituationswhereyouhaveonecategoricalpredictorwith2levelsandonenumericalresponsevariable.

B. Thereisaproblem.Theunitsofobservationwithineachgrouparenotstatisticalindependentofoneanother.

C. Thereisaproblem.Thesedatacanonlybeanalyzedwitha1-factorANOVA.

D. Thereisaproblem.ThesedatacanonlybeanalyzedwithaChi-squaretest.

E. Thereisaproblem.Thereisnoreplicationinthestudy.ANSWER:_____B_____

13) Which of the following statements about statistical errors is TRUE?[1mark]

A. TypeIerror,theprobabilityofrejectinganullhypothesiswhenitisfalse,issetbytheresearcher.

B. TypeIIerror,theprobabilityofrejectinganullhypothesiswhenitisfalse,isnotsetbytheresearcherbutdependslargelyonsamplesize.

C. TypeIerror,theprobabilityofrejectinganullhypothesiswhenitistrue,issetbytheresearcher.

D. TypeIIerror,theprobabilityofrejectinganullhypothesiswhenitistrue,isnotsetbytheresearcherbutdependslargelyonsamplesize.

ANSWER:____C_______

14) Whichofthefollowingstatementsbestdescribesthedifferencebetweenobservationalandexperimentalstudies?[1mark]

A. Experimentalstudiessufferfromproblemswithconfoundingvariables,whereasobservationalstudiescanbedesignedtominimizethese

B. Observationalstudiescreateproblemswithinterpretingthecorrectstatisticalpopulation,whileexperimentalstudiesdonot

C. Observationalstudiesareprospectivewhereasexperimentalstudiesareretrospective

D. Observationalstudiesarecorrelative,whereasexperimentalstudiesarecausal

ANSWER:_____D_____

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15) Muchstatisticaltheoryisbasedonthedistinctionbetweenthesample,thesamplingdistributionandthepopulation.Whichofthefollowingisunaffectedbythesamplesize(n)?[1mark]

A. ThemeanofthesampleB. ThestandarddeviationofthesamplingdistributionC. ThepopulationmeanD. Thestandarddeviationofthesample

ANSWER:____C_______

16) Whichofthefollowingstatementsaboutap-valueiscorrect?[1mark]A. ItistheprobabilityofobservingaTypeIerrorunderthenullhypothesis.B. Itisunderthecontroloftheresearcher.C. Itcanbeusedtodecidewhethertorejectanullhypothesisornotwithout

referencetoathreshold.D. Itistheprobabilityofobservingyourtestscoreorsomethingmore

extremeunderthenullhypothesis.E. Itisusedfort-testsandregression,butnotforChi-squaretestsor

ANOVA.

ANSWER:_____D_____

17) ThedatabelowgivethewaittimesinminutesatStarBucksfor6peopleorderingcoffee.Calculatethelower95%confidenceintervalforthisdataset.[1mark]

{5.7,4.2,5.0,3.7,3.4,2.8}A. 1≤ANSWER<1.5B. 1.5≤ANSWER<2.0C. 2.0≤ANSWER<2.5D. 2.5≤ANSWER<3.0E. 3.0≤ANSWER<3.5

ANSWER:_____E_____

18) Whichofthefollowingstatementsarecorrectabout95%confidenceintervals?[1mark]

A. Theintervalincludesthetruepopulationvalue5%ofthetime.B. Thewidthoftheintervalisdifferentfordifferentsamplesbecauseof

samplingerror.C. Theintervalincludesthesamplemean95%ofthetime.D. ConfidenceintervalsareanalternativewaytodrawconclusionsinChi-

squaretests.E. Theintervalisfixedat+/-2.

ANSWER:_____B_____

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19) Whichofthefollowingquestionsshouldbeanalyzedusinga1-tailedt-test?[1mark]

A. IsthefluorineconcentrationinKingston’swaterabovetherecommendedguideof0.7mg/L?

B. DoesthemeanpatientwaittimedifferbetweenanAfter-Hourshealthcliniccomparedtoaregulardoctor’soffice?

C. HasthefirstcalendardatethatstoresputouttheirChristmasornamentsforsalechangedoverthepast20years?

D. IstheamountofseaiceinourArcticwatersdifferentnowfromwhatitwas10yearsago?

ANSWER:_____A_____20) ThefollowingRoutputisforalinearregressionofpercentagevoterturnoutat

20electoraldistrictsasafunctionofmeanage.Whichofthefollowingvaluesisusedtoconductthestatisticaltestthatevaluatesthehypothesisthatmeanageofthepeopleinanelectoraldistrictcanbeusedtopredictvoterturnout?[1mark]

A. Theestimatevalueof0.41983B. Thet-valuevalueof1.171C. ThemultipleR-squaredvalueof0.0483D. Thet-valuevalueof0.530E. Theestimatevalueof0.0251

ANSWER:_____B_____21) In2003agroupof300NorthAmericanswithType1diabetesbetweentheages

of21and30wereselectedbyamedicalresearchgroup.In2014adifferentgroupofresearchersusedbothmedicalhistoriesandquestionnairestoevaluatewhetherdifferencesineatinghabitsoverthepastyearcorrelatedwithchangesintheirhealth.Thisstudydesignisbestcharacterizedas:[1mark]

A. ClusterB. BlockedC. ExperimentalD. CohortE. Case-control

ANSWER:_____D_____

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SHORTANSWER-Writeallyouranswersinthespaceprovided.1. Thefollowingquestionslookatdifferentaspectsofhypothesistesting.

i. TheF-testisusedforsomeofthestatisticalteststhatcoveredinthecourse.ExplaininwordswhatanobservedF-ratiorepresentsusingasingle-factorANOVAasanexample.[1mark]TheF-ratioistheratioofthevariationexplainedbythegroupsovertheunexplainedvariation.

ii. Defineap-valueusingterminologythatisgeneraltoalltests.[1mark]Ap-valueistheprobabilityofobservingyourdata(ortestscore)orsomethingmoreextremeunderthenulldistribution.

iii. Anulldistributiondescribesthepossiblerangeofoutcomesfromrepeatedsampling.Explaininwordswherethisvariationcomesfrom.[1mark]Thevariationinanulldistributioniscausedbysamplingerror.Itisthevariationintestscoresthatwouldoccurifweresampledapopulationwherethenullhypothesisistrue.

2. ThefourthcriterionforanIdealSamplingProcessisthat“Eachpossiblesamplehasequalchanceofbeingselected”.Useanexampletoexplainwhatthiscriterionmeans,andhowitisdistinctfromthefirstcriterionthatstates“Unitshaveknown&non-zeroprobabilityofbeingincludedinyoursample”.[2marks]

Thefourthcriterionmeansthateverycombinationofsamplingunitsthatcouldmakeupasamplecanbeachievedbythesamplingprocess.Forexample,ifyouwantedtosampleof10addressesfromKingston,thenyoursamplingunitisanaddressandanycombinationofhousescanbeselected.However,ifyoudecidetofirstflipacoinandgotojusttheeastorwestside,thenyouwillneverhaveasamplecomposedofhousesfrombotheastandwestsides.Thefourthcriterionisdistinctfromthefirstbecausethefourthcriterionisaboutthecompositionofthesamplewhereasthefirstcriterionisaboutthesamplingunit.

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3. Drawaboxplotdirectlyonthefollowingfigure.Theboxplotshouldbedrawntoscaleusingthedatapointsprovided.Makesuretoincludethemedian,interquartilerange,anywhiskersandanyextremevalues.[2marks]

4. Foreachofthefollowingstudies,identifyandrationalizethemostappropriate

statisticaltest(e.g.,t-test,regressionetc.).Includethenullandalternativehypotheses(bemindfulofdirectioninthetest),aswellastheappropriateteststatistic(e.g.,F-scoreforanF-test).STUDY1Ageneticistwasinterestedinthedegreetowhichbehaviorisdeterminedbygender.Sheconductedasurveyof40randomstudents.Thescientistcategorizedeachstudentasbeingmaleorfemale,andtheirstudybehaviorasdiligent,procrastinationorreactive.Shewantstoknowwhetherstudystyledependsongender

i. Identifyandrationalizethemostappropriatestatisticaltest[1mark]

ThisisaChi-squareanalysisbecausebothfactorsarecategorical.

ii. Statethenullandalternativehypothesis[1mark]Ho:thereisnodifferencebetweenexpectedandobservedfrequencies.HA:thereisadifferencebetweenexpectedandobservedfrequnecies.(studentscouldalsousetheindependent/nonindependentterminology)

iii. Identifytheappropriateteststatistic[1mark]ThisisaChi-squaretestandtheteststatisticistheChi-squarescore.

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STUDY2Youaretheleadscientistatastartupcompanyproposingtosequesteratmosphericcarbondioxideusingageneticallymodifiedstrainofpinetrees.Toevaluatetheeffectivenessofnutrientaddition,yourunaseriesofexperimentsandmonitorgrowthratesofreplicatetreesunderfivelevelsnutrientofaddition(0,1.0,2.0,3.0,4.0and5.0ugN/gmSoil).Youareinterestedinevaluatingwhethernutrientadditioncanbeusedtopredicttreegrowth.

i. Identifyandrationalizethemostappropriatestatisticaltest[1mark]

Thisisalinearregressionbecausetheindependentfactorisnumerical,andthequestionislookingtopredicttreegrowth.

ii. Statethenullandalternativehypothesis[1mark]ThenullhypothesisisH0:b=0,HA:b≠0,wherebistheslope.

iii. Identifytheappropriateteststatistic[1mark]Thetestisat-test,andtheteststatisticisat-score.

STUDY3ResearchersinterestedintheeffectoftakingEchinaceaonthelikelihoodofcontractingthecommoncolddesignedastudythatfollowed30subjectsduringafourmonthtimeperiod.Asampleofbloodwastakenfromeachsubject,whichwasusedtoquantifythebaselineviralload.EachsubjectthentookEchinaceaforfourmonths,afterwhichtimeasecondbloodsamplewastakentoquantifytheafter-treatmentviralload.TheyareinterestedinevaluatingwhetherEchinaceahadaninfluenceonviralload.

i. Identifyandrationalizethemostappropriatestatisticaltest[1mark]

Thisisapaired-samplet-testbecauseweareinterestedinwhethertheviralloadchangesoverthe4monthsandthemeasurementsaretakenfromthesamesamplingunit.

ii. Statethenullandalternativehypothesis[1mark]ThenullhypothesisisH0:d=0,HA:d≠0,wheredisthedifferencebetweeninitialandfinalviralload.

iii. Identifytheappropriateteststatistic[1mark]Thetestisat-test,andtheteststatisticisat-score.

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5. AstheChiefSupplyOfficerforStarbucks,Jeanisinchargeofpurchasingrawcoffeebeansfromanumberoflargeandsmallproducers.Tomonitorbeanquality,Jeandesignsanongoingmonitoringprogramthatisrunatthepeakofthegrowingseason.Themonitoringprogramistorandomlyselectabagofrawbeansfrom20randomlyselectedproducerswithineachofthe5mainproducingcountries(Brazil,Vietnam,Colombia,Indonesia&Ethiopia).Eachselectedbagisroastedandgroundintocoffee.Thecoffeeisthenbrewedfromeachbagandapanelofexpertsrankstheflavoronascaleof1to5where1isPoorTasteand5isExcellent.Identifythefollowingelementsinthisstudy.Beasspecificaspossible.

i. Sample[20bagsofcoffeewithineachcountry(orallsampledcoffeebags)] [0.5marks]

ii. Samplingunit[coffeeproducer] [0.5marks]iii. Population[allcoffeeproducers] [0.5marks]iv. Observationunit[coffeebagorcoffeefromcoffeebag]

[0.5marks]v. Datatype(e.g.,categorical)[categorical] [0.5marks]vi. Studydesign[stratified] [0.5marks]

6. DefineSamplingUnitandanObservationUnit.Identifythekeycriterionthatis

differentbetweenthem.[Thesamplingunitistheelementthatisselectedatrandom.Theobservationunitistheelementthatthequestionisbeingaskedabout.Thesamplingunitisalwaysselectedatrandom,whereastheobservationunitdoesnotneedtobeselectedatrandom.][2marks]

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7. ThefigurebelowshowstheprobabilitydistributionforthenumberofFacebook

FriendsforCanadianFacebookusers.ThetypicaluserwhoisactiveinFacebookhasatleast20friends,butuserswhohaveblogshaveatleast40fiends.Youareanactiveuser,butreallydon’thavethetimetomaintainblogs.

i. Onthefigureabove,shadeintheprobabilitythatyouwillhaveatleast

thesamenumberoffollowersassomeonewhoisactiveandmaintainsblogs.[shadedareawillbefrom40totheright][1mark]

ii. Onthefigureabove,shadeintheprobabilitythatyouwillhavefewerfollowersthanatypicalFacebookuserwhoisactive.Makesuretodistinguishthisareafromtheonedrawninparti. [shadedareawillbefrom20totheleft][1mark]

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8. As a political strategist, you are interested in the best way to get the message out to a large number of people about the policy platform for your political party. You decide to try four methods: i) public town hall, ii) TV ads, iii) news paper ads and iv) door-to-door canvasing. Since it’s not an election year, your party agrees to let you try out these different methods for a series of small announcements. You decide to evaluate the effectiveness of each method by monitoring the number of re-tweets each announcement receives. A. Indicate the most appropriate statistical test (be as specific as possible) [1 mark]

[single-factor ANOVA]

B. Explain why you selected this test [1 mark] [There are four categories being compared, which can only be done using ANOVA. There is just one factor.]

C. Indicate the null and alternative hypothesis (be mindful of direction in the test) [1 mark] [The null hypothesis is H0: u1=u2=u3=u4, HA: u1= u2= u3= u4, where ui is the mean for the ith type of method of messaging. *grade part c based on the answer in part a, even if that was incorrect]

D. Name the appropriate test statistic (e.g., Chi-square score) (You do not need to find its value.) [1 mark] [F-score. *grade part d based on the answer in part a, even if that was incorrect]

E. The following R output shows the results of the statistical test. Based on this output, what is the observed test score for this test? [1 mark]

[Fobs=8.401]

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F. Explain in words what the VALUE of the observed test score means for this test

in terms of a ratio of variances. [1 mark] [The group variation is 8.4 times that of the residual variation]

G. What is the critical test score for this test assuming an alpha value of 0.05? [1

mark] [Fcrit= 2.92 or 2.84]

H. Based on the observed and critical test scores, what is your statistical? [1 mark] [Since Fobs>Fcrit, we reject the null hypothesis

9. The figure below shows a boxplot of what your data might look like for the above question. Assume for this question that the overall ANOVA test was significant. Use the output below from a TukeyHSD test to identify what levels are different. Indicate this directly on the boxplot using the lettering scheme shown in lecture and used in tutorial. [2 mark]

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