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www.LionTutors.com STAT200(Wisener)–Exam3–PracticeExamSolutions 1. A–Thestrongestlinearrelationshipis–0.9.Correlationmusthaveavalue between–1and+1soanswerchoiceEisnotanoption.Todeterminethe strongestlinearrelationship,youwantthevalueclosesttotheabsolutevalue of1. 2. C–Testoftwoindependentmeansbecausewearedealingwithtwodifferent gendersandtheamountofmoneyspentontextbookseachyearisa quantitativevariable. 3. B–Staticscomefromsamples,andparameterscomefrompopulations. 4. C–Ho:p=0.71 Ha:p>0.71.Sincewearedealingwithproportions,we usethepopulationparameter,p.Weknowitisagreaterthanalternative hypothesistestbecausethedoctorwantstoseeifthenewmethodismore effectivethanthecurrentmethod. 5. A–Testofonemeanbecausewearelookingfortheaveragevalueofasingle quantitativevariable. 6. F–Chi-squaretestbecausetheresearcheristestingtoseeifthereisa relationshipbetweentwoqualitativevariables. 7. B–Yourscoreonexam1isusedtopredictyourscoreonexam2.The predictorvariablewillbethevariablelistedinthepredictorcolumnofthe Minitaboutputundertherowwiththeinformationabouttheconstant. 8. B–Positivesquarerootof0.439.YouaregivenR-Sq(r2)intheregression output.Youareaskedtofindcorrelation(r).Thismeansyouneedtotakethe squarerootofr2.Youknowtheansweristhepositivesquarerootbecause thecoefficientforthepredictorvariable(Exam1)isapositivenumber.This meansthattheregressionlinehasapositiveslope.Whenaregressionline hasapositiveslope,correlation(r)willbepositive. 9. A–Exam2=45.1+0.469(Exam1).Theconstantvalue(y-intercept)inthe equationisthecoefficientforthe“constant”rowintheregressionoutput. Theslopeoftheregressionequationisthecoefficientforthepredictor variable(Exam1). 10. C–43.9%becauseitisthevalueofR-Sq. 11. B–Ho:B1=0 Ha:B1≠0 12. E–Sincetheteststatisticis12.46andthep-valueis0.000yourejectHoand concludethatExam1isasignificantlinearpredictorofExam2. 13. C–0.100to0.200.Sincethesamplesizeis5,youknowthatdegreesof freedomis4.Youcanfindthat1.988isbetween1.533and2.132inthedf=4 row.Youcanseefromthetoprowofthetablethatateststatisticof1.988 willhaveap-valuebetween0.100and0.050foraone-sidedtest.However, theproblemtellsyouthatthetestisanotequaltestwhichmeansitisa two-sidedtest.Sinceitisatwosidedtest,youneedtodoublethep-values. 14. E–Regressionbecausethedoctorwantstofindtherelationshipbetween twoquantitativevariables. 15. B–Testofpairedmeansbecauseyouarecomparingestimatesoftwolawn servicefirmstocutthesamelawns. 16. D–18.17to37becausethisisQ3tothemaximum,whichisonly25%ofthe valuesinafivenumbersummary. 17. B–Thenewweightlossmethodhasasuccessratethatisgreaterthan60%. Youknowthatitisagreaterthantestbecausethedoctorwanttoseeifthe methodismoreeffective.Youcantellthatthenewweightlossmethoddoes haveagreatersuccessratethanthecurrentmethodbecausethep-valueis lessthan0.05. 18. F–One-wayAnalysisofVariance(ANOVA)becausetheproblemis comparingsalary,aquantitativevariable,acrossfourdifferentgroups. 19. B–0.050to0.100.Sincethesamplesizeis5,youknowthatdegreesof freedomis4.Youcanfindthat1.988isbetween1.533and2.132inthedf=4 row.Youcanseefromthetoprowofthetablethatateststatisticof1.988 willhaveap-valuebetween0.100and0.050foraone-sidedtest. 20. C–Thegroupofpeoplefromwhichthesamplewastaken. 21. A–Themeanwouldbegreaterthanthemedian. 22. B–Parameterbecausewearetalkingabouttheentirepopulationofout-ofstatePennStatestudents. 23. C–Itshouldberepresentativeofthepopulation. 24. C–Thelargerstandarddeviationwasnotmorethantwicethesmaller standarddeviation.Youneedtocomparethetwostandarddeviationsinthe outputwhendeterminingifyoucanusepooledvariances. 25. A–Ho:μ1–μ2=0 Ha:μ1–μ2≠0 26. C–4.604.Youknowthatdegreesoffreedomisfourbecausethesamplesize isfive.Soyouneedtolookupthemultipliervalueinthe99%columninthe rowforfourdegreesoffreedom. 27. D–Testoftwoproportionsbecausewearecomparingtwocategorical variables. 28. A–Statisticbecauseonlyasubsetofthepopulation(allPennStatestudents) wasusedinthestudy. 29. C–4 dfFactor(betweengroups)=k–1 3=k–1 k=4 30. E–19 dfTotal=N–1 18=N–1 N=19 31. C–RejectHoandconcludethatnotallofthemeansareequalbecausepvalueis0.001. 32. A–Thereisadifferencebetweenthemeansofgroup1andgroup3because theconfidenceintervaldoesnotcontain0. 33. D–Thereisarelationshipinthepopulationbetweengenderandheart attacksbecausethealternativehypothesisalwaysstatesthereisa relationshipwhilethenullhypothesisstatesthereisnotarelationship. 34. D–85/420 Risk=(Numberincategory)/(Totalnumberingroup)=85/420 35. B–(150/380)/(85/420) Relativerisk=(Riskincategory1)/(Riskincategory2) Theproblemtellsyoutocomparemalerisktofemalerisksomaleriskwill becategory1andfemaleriskwillbecategory2. Malerisk=150/380 Femalerisk=85/420 Relativerisk=(150/380)/(85/420) 36. A–Statisticallysignificantinthepopulationbecausethep-valueislessthan 0.05. 37. C–150/380becausetheprobabilityofhavingaheartattackisthesame thingastheriskofhavingaheartattack. Malerisk=150/380 38. B–Estimatethepopulationparameter 39. C–Negative0.9becauseyouarelookingforthecorrelationwithanabsolute valueclosestto1. 40. A–Positive0.1becauseyouarelookingforthecorrelationwithanabsolute valueclosestto0. 41. B–82and4becausethemeanwillincreasebythefourpointsaddedto everyone’sscore;however,thestandarddeviationwillnotbeaffected. 42. B–Negative1 𝑧= 𝑂𝑏𝑠𝑒𝑟𝑣𝑒𝑑𝑣𝑎𝑙𝑢𝑒 − 𝑀𝑒𝑎𝑛 74 − 78 = = −1 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 4 43. D–90 z= 3= Observedvalue − Mean Standarddeviation 𝑥 − 78 4 x=90 44. C–70to86because95%ofvalueswillfallwithin2standarddeviationsof themean. 45. C–Inastatisticalstudy,asampleshouldberepresentativeofthepopulation. 46. C–Orange,orange,orangebecauseorangeisthemostlikelyeventtooccur eachtimethediceisrolled. 47. C–Theyareusedtoestimatetheaccuracyofthesamplestatistic. 48. D–18.17to37 49. B–Statisticallysignificantinthepopulationbecausethep-valueislessthan 0.05. 50. B–Testofpairmeans 51. C–Testoftwoindependentmeans 52. D–Testoftwoproportions 53. A–Testofonemean 54. G–Chi-squaretestbecausetheresearcheriscomparingtwocategorical variables. 55. G–One-wayAnalysisofVariance(ANOVA)becausewearecomparingthe meansalaryacrossmorethantwogroups. 56. B–92%ofallPennStatethinkthatmarijuanashouldbedecriminalizedis thepopulationproportion. 57. A–56/1626 58. B–(70/650)/(56/1626)Theproblemtellsuswewant“thosewhotookthe placebocomparedtothosewhotookthemalariapills.”Soweneedtotake theriskoftheplacebogroupdividedbytheriskofthemalariapillsgroup. 59. A–Peopletakingtheplaceboare3.13timesmorelikelytogetmalariathan thosewhoreceivedthemalariapills. 60. D–Thereisnorelationshipinthepopulationbetweenthetreatmentand whetherornotsomeonegetsmalaria.Thenullhypothesisalwaysstates thereisnorelationshipinthepopulation. 61. B–Thereisarelationshipinthepopulationbetweenthetreatmentand whetherornotsomeonegetsmalaria.Thealternativehypothesisalways statesthereisarelationshipinthepopulation. 62. B–Inthepopulation,thereisastatisticallysignificantrelationshipbetween thetreatmentandgettingmalariabecausethep-valueislessthan0.05. 63. B–Ho:p=0.5 Ha:p>0.5 64. C–Ho:μ=10,000 Ha:μ≠10,000 65. A–Testofonemean.ThesamplestatisticwouldbetheaverageACTverbal scoreforincomingfreshmen.Youwouldgetthescorefromeachfreshmen sampledandtakeanaverage.Theresultwouldbeonemean.Thepartabout comparingthescoretoascoreof26isincludedtomaketheproblem “tricky.” 66. B–Testofpairmeans.Youarecomparingthedifferenceinperson freshmen’smathandverbalscore. 67. C–Testoftwoindependentmeans.Highschoolstudentsandcollege studentsareindependentgroups. 68. D–Testoftwoproportions.Youarecomparingpercentagesformalesand females. 69. A–Comparingtheaverageamountoftarforfivebrandsofcigarettes.You arecomparingonemeanacrossfivecategoricalvariables. 70. E–ComparingtestscoresofstudentsinaMondaylabtostudentsina Wednesdaylab.StudentsinMondayandWednesdaylabsareindependent groups. 71. D–Comparingstudentgenderandwhethertheyattendedacollegein-state orout-of-state.Youarecomparingtwocategoricalvariables. 72. A–92%ofPennStatestudentssampledthinkmarijuanashouldbe decriminalized.Statisticsaretheresultofasample. 73. B–0.050to0.100.Thesamplesizeis5sodf=4.Lookingacrossthedf=4 row,2.01fallsbetween0.050and0.100.Thistableisgiving“right-tail probabilities”whichmeanstheareatotherightofthepositiveteststatistic. Theareatotherightoftheteststatisticcorrespondstoagreaterthantest. However,inthisproblemyouweretoldtheteststatisticwasnegative2.01 andthealternativehypothesiswasalessthantest.Becauseofthesymmetry ofthet-distribution,weknowtheareatotheleftofnegative2.01isthesame areatotherightofpositive2.01. 74. C–0.100to0.200.Thisproblemtellsusthealternativehypothesisisanot equaltest.Thus,weneedtodoubletheanswerfromthepreviousproblem. 75. A–Standarddeviationmeasuresthevariationinanindividualsample; Standarderroristheestimatedstandarddeviationinasampling distribution.Thismeansthatitmeasuresthevariabilityamongthe distributionofpossiblevaluesofastatistic. 76. C–Thenullhypothesis:μ1–μ2=0isrejectedbecausewewouldbe concludingthatμ1–μ2=0isdifferencefrom0. 77. B–Theyhavethesamevaluesforthestandarderrorintheteststatistic. Lookingattheequationsbelow,itisclearthattherewillbedifferentvalues forstandarderror. IndependentSamples(Two-sampletprocedure) 𝒕 = 𝑺𝒂𝒎𝒑𝒍𝒆𝒔𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄– 𝑵𝒖𝒍𝒍𝒗𝒂𝒍𝒖𝒆 (𝒙𝟏 − 𝒙𝟐 ) − 𝟎 = 𝑺𝒕𝒂𝒏𝒅𝒂𝒓𝒅𝒆𝒓𝒓𝒐𝒓 𝟐 𝟐 𝒔𝟏 𝒔 + 𝟐 𝒏𝟏 𝒏𝟐 DependentSamples(Pairedtprocedure) 𝑺𝒂𝒎𝒑𝒍𝒆𝒔𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄– 𝑵𝒖𝒍𝒍𝒗𝒂𝒍𝒖𝒆 𝒅 − 𝟎 𝒕 = = 𝒔 𝒅 𝑺𝒕𝒂𝒏𝒅𝒂𝒓𝒅𝒆𝒓𝒓𝒐𝒓 𝒏 AtfirstitwouldalsoseemthatanswerAwouldbefalsebecausetheylookto havedifferencevaluesinthenumeratoraswell.However,youneedto rememberthat 𝒅 = 𝒙𝟏 − 𝒙𝟐 78. D–Twooddswillbedifferent.Ifthechi-squaredstatisticisequalto0,the actualcountwillequaltheexpectedcountforeachcell.Thismeansitisnot possibleforthetwooddstobedifferent. 79. C–Themultiplelinearregressionequationusestheconstantplusthe coefficienttimeseachexplanatoryvariable. 80. A–Thepredictedfinalscorewillincreasebytheslopeforeach1point increaseinthemidtermscore. 81. B–Adummyvariablewilleitherbeequalto1or0.Sincetheslopeis-1.158, thepredictedfinalscorewilldecreaseby1.158whenthevariableispresent. 82. B–Quizaverageisasignificantlinearpredictoroffinalexamscorebecause ithasap-valuelessthan0.05.Thisonlyholdstruewhenallexplanatory variablesarepresentinthemodel. 83. D–DummyGenderhasap-valuegreaterthan0.05,soitisnotasignificant linearpredictorwhencombinedwiththeotherexplanatoryvariablesinthis model. 84. C–IntheANOVAtable,weseethatthep-valueislessthan0.05.Thattellsus thatatleastoneoftheslopesinthemodeldiffersfrom0,orisasignificant linearpredictoroffinalexamscore.Itdoesnottellusthatalloftheslopes differfrom0. 85. C–R-squared=38.5% 86. B–Odds=(Numberincategory/Numbernotincategory) Oddsforwomen=(Female“yes”/Female“no”)=196/387 87. D–Oddsratio=(Oddsforcategory1/Oddsforcategory2) Oddsforwomen=(Female“yes”/Female“no”)=196/387 Oddsformen=(Male“yes”/Male“no”)=196/387 Oddsratioforwomencomparedtomen=(Oddsforwomen/Oddsformen) =(196/387)/(196/387)