Chamberlain College of Nursing MATH 225N Statistics Final EXAM Questions with 100% Correct, Exams of Advanced Education

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Chamberlain College of Nursing MATH 225N Statistics

Final EXAM Questions with 100% Correct Answers |

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MATHi225NiWeeki 8 iFinaliExam Questioni 1 i1/1ipoints Aifitnessicentericlaimsithatitheimeaniamountiofitimeithatiaipersonispendsiatitheigymiperivisitiisi 33 i minutes.iIdentifyitheinullihypothesis,i H 0,ianditheialternativeihypothesis,i Ha ,iinitermsiofitheipara meteri μ. Thatiisicorrect! H 0:i μ ≠33;i Ha :i μ =33i H 0 :i μ =33;i Ha :i μ ≠ H 0:i μ ≥33;i Ha :i μ <33i H 0 :i μ ≤33;i Ha :i μ > AnsweriExplanation Correctianswer: H 0:i μ =33;i Ha :i μ ≠ Letitheiparameteri μi beiuseditoirepresentitheimean.iTheinullihypothesisiisialwaysistatediwithisomeif ormiofiequality:iequali(=),igreaterithanioriequalitoi(≥),iorilessithanioriequalitoi(≤). Therefore,iinithisicase,itheinullihypothesisi H 0 iisi μ =33.iTheialternativeihypothesisiisicontradictoryit oitheinullihypothesis,isoi Hai isi μ ≠33. Questioni 2 i1/ 1 ipoints Theianswerichoicesibelowirepresentidifferentihypothesisitests.iWhichiofitheichoicesiarei right- itailedi tests?iSelectiallicorrectianswers.

Thatiisicorrect!

• H 0: X ≥17.1,i Ha : X <17.
• H 0: X =14.4,i Ha : X ≠14.
• H 0: X ≤3.8,i Ha : X >3.
• H 0: X ≤7.4,i Ha : X >7.
• H 0: X =3.3,i Ha : X ≠3.

AnsweriExplanationiC orrectianswer: H 0: X ≤3.8,i Ha : X >3.8i H 0: X ≤7.4,i Ha : X >7.

Rememberitheiformsiofitheihypothesisitests.

• Right-tailed:i H 0: X ≤ X 0,i Ha : X > X 0.
• Left-tailed:i H 0: X ≥ X 0,i Ha : X < X 0.
• Two- tailed:i H 0: X = X 0,i Ha : X ≠ X 0.iSoiinithisicas e,itheiright-taileditestsiare:
• H 0: X ≤7.4,i Ha : X >7.
• H 0: X ≤3.8,i Ha : X >3. Questioni 3 i1/ 1 ipoints FinditheiTypeiIIierrorigivenithatitheinullihypothesis,i H 0,iis:iaibuildingiinspectoriclaimsithatinoimor eithani15%iofistructuresiinitheicountyiwereibuiltiwithoutipermits. Thatiisicorrect! Theibuildingiinspectorithinksithatinoimoreithani15%iofitheistructuresiinitheicountyiwereibuiltiwith outipermitsiwhen,iinifact,inoimoreithani15%iofitheistructuresireallyiwereibuiltiwithoutipermits. Theibuildingiinspectorithinksithatimoreithani15%iofitheistructuresiinitheicountyiwereibuiltiwithou tipermitsiwhen,iinifact,imoreithani15%iofitheistructuresireallyiwereibuiltiwithoutipermits. Theibuildingiinspectorithinksithatimoreithani15%iofitheistructuresiinitheicountyiwereibuiltiwithouti permitsiwhen,iinifact,iatimosti15%iofitheistructuresiwereibuiltiwithoutipermits. Theibuildingiinspectorithinksithatinoimoreithani15%iofitheistructuresiinitheicountyiwereibuiltiwith outipermitsiwhen,iinifact,imoreithani15%iofitheistructuresiwereibuiltiwithoutipermits. AnsweriExplanationiC orrectianswer: Theibuildingiinspectorithinksithatinoimoreithani15%iofitheistructuresiinitheicountyiwereibuiltiwith outipermitsiwhen,iinifact,imoreithani15%iofitheistructuresiwereibuiltiwithoutipermits. AiTypeiIIierroriisitheidecisioninotitoirejectitheinullihypothesisiwhen,iinifact,iitiisifalse.iInithisicase,it heiTypeiIIierroriisiwhenitheibuildingiinspectorithinksithatinoimoreithani15%iofithe

structuresiwereibuiltiwithoutipermitsiwhen,iinifact,imoreithani15%iofitheistructuresiwereibuiltiwith outipermits.

Questioni 4 i1/ 1 ipoints Supposeiaicheficlaimsithatiherimeatballiweightiisilessithani 4 iounces,ioniaverage.iSeveraliofihericus tomersidoinotibelieveiher,isoitheichefidecidesitoidoiaihypothesisitest,iatiai10%isignificanceilevel,ito ipersuadeithem.iSheicooksi 14 imeatballs.iTheimeaniweightiofitheisampleimeatballsiisi3.7iounces.iTh eichefiknowsifromiexperienceithatitheistandardideviationiforiherimeatballiweightiis 0.5iounces.

• H 0:i μ ≥4;i Ha :i μ <
• α =0.1i(significanceilevel) Whatiisitheitestistatistici( z - score)iofithisione-meanihypothesisitest,iroundeditoitwoidecimaliplaces? Thatiisicorrect! Testistatistici=iminusi 2 ipointi 2 i4$$ Testistatistici=iminusi 2 ipointi 2 i 4 i-icorrect AnsweriExplanation Correctianswers:
• Testistatistici=iminusi 2 ipointi 2 i 4 i$\text{Testistatistici=i}-2.24$

Theihypothesesiwereichosen,ianditheisignificanceileveliwasidecidedion,isoitheinextistepiinihypoth esisitestingiisitoicomputeitheitestistatistic.iInithisiscenario,itheisampleimeaniweight,i x ¯=3.7.iTheisa mpleitheichefiusesiisi 14 imeatballs,isoi n =14.iSheiknowsitheistandardideviationiofitheimeatballs,i σ = 0.5.iLastly,itheichefiisicomparingitheipopulationimeaniweightitoi 4 iounces.iSo,ithisivaluei(foundiini theinulliandialternativeihypotheses)iisi μ 0.iNowiweiwillisubstituteitheivaluesiintoitheiformulaitoico mputeitheitestistatistic: z 0= x ¯− μ 0 σn √=3.7−40.514√≈−0.30.134≈−2. So,itheitestistatisticiforithisihypothesisitestiisi z 0=−2.24.

Questioni 5 i1/ 1 ipoints Whatiisithei p - valueiofiai right-tailedi one- meanihypothesisitest,iwithiaitestistatisticiofi z 0=1.74?i(Doinotiroundiyourianswer;icomputeiyourian sweriusingiaivalueifromitheitableibelow.)i z1.51.61.71.81.90.00 0.9330.9450.9550.9640.971 0.01 0. 340.9460.9560.9650.972 0.02 0.9360.947i0.9570.9660.973 0.03 0.9370.9480.9580.9660.973 0.04 0. 380.9490.9590.9670.974 0.05 0.9390. 0.9600.9680.974 0.06 0.9410.9520.9610.9690.975 0.07 0.9420.9530.9620.9690.976 0.08 0.9430. 0.9620.9700.976 0.09 0.9440.9540.9630.9710. Thatiisicorrect!i 0 ipointi 0 i 4 i1$$ 0 ipointi 0 i 4 i 1 i- icorrecti AnsweriExpl anationi Correctiansw ers:

• 0 ipointi 0 i 4 i 1 i$0.041$

Thei p - valueiisitheiprobabilityiofianiobservedivalueiofi z=1.74i origreateriifitheinullihypothesisiisitrue,ibeca useithisihypothesisitestiisiright- tailed.iThisiprobabilityiisiequalitoitheiareaiunderitheiStandardiNormalicurveitoitheirightiofi z =1.74.

Aistandardinormalicurveiwithitwoipointsilabeledionitheihorizontaliaxis.iTheimeaniisilabelediat 0.00iandianiobservedivalueiofi1.74iisilabeled.iTheiareaiunderitheicurveianditoitheirightiofitheiobser vedivalueiisishaded. UsingitheiStandardiNormaliTable,iweicaniseeithatithei p - valueiisiequalitoi0.959,iwhichiisitheiareaitoitheileftiofi z =1.74.i(StandardiNormaliTablesigiveiareasit oitheileft.)iSo,ithei p - valueiwe'reilookingiforiisi p =1−0.959=0.041. Questioni 6 i1/ 1 ipoints Kenneth,iaicompetitoriinicupistacking,iclaimsithatihisiaverageistackingitimeiisi8.2iseconds.iDurin giaipracticeisession,iKennethihasiaisampleistackingitimeimeaniofi7.8isecondsibasedioni 11 itrials.iAt ithei4%isignificanceilevel,idoesitheidataiprovideisufficientievidenceitoiconcludeithatiKenneth'sime anistackingitimeiisilessithani8.2iseconds?iAcceptiorirejectitheihypothesisigivenitheisampleidataibel ow.

• H 0: μ =8.2iseconds;i Ha : μ <8.2iseconds
• α =0.04i(significanceilevel)
• z 0=−1.
• p =0. Thatiisicorrect!

Doinotirejectitheinullihypothesisibecauseithei p - valuei0.0401iisigreaterithanitheisignificanceilevel α =0.04. Rejectitheinullihypothesisibecauseithei p - valuei0.0401iisigreaterithanitheisignificanceilevel α =0.04. Rejectitheinullihypothesisibecauseitheivalueiofi zi isinegative.iRejecti theinullihypothesisibecausei|−1.75|>0.04. Doinotirejectitheinullihypothesisibecausei|−1.75|>0.04. AnsweriExplanationiC orrectianswer: Doinotirejectitheinullihypothesisibecauseithei p - valuei0.0401iisigreaterithanitheisignificanceilevel α =0.04. Inimakingitheidecisionitoirejectiorinotirejecti H 0,iifi α > p - value,irejecti H 0 ibecauseitheiresultsiofitheisampleidataiareisignificant.iThereiisisufficientievidenceit oiconcludeithati H 0 iisianiincorrectibeliefiandithatitheialternativeihypothesis,i Ha ,imayibeicorrect.iIfi α ≤ p - value,idoinotirejecti H 0.iTheiresultsiofitheisampleidataiareinotisignificant,isoithereiisinotisufficientie videnceitoiconcludeithatitheialternativeihypothesis,i Ha ,imayibeicorrect.iInithisicase,i α =0.04iisilessit hanioriequalitoi p =0.0401,isoitheidecisioniisitoinotirejectitheinullihypothesis.

QUESTIONi 7 i1/1iPOINTS Airecentistudyisuggestedithati81%iofisenioricitizensitakeiatileastioneiprescriptionimedication.iAme liaiisiainurseiatiailargeihospitaliwhoiwouldilikeitoiknowiwhetheritheipercentageiisitheisameiforiseni oricitizenipatientsiwhoigoitoiherihospital.iSheirandomlyiselectsi 59 isenioricitizensipatientsiwhoiwere itreatediatitheihospitaliandifindsithati 49 iofithemitakeiatileastioneiprescriptionimedication.iWhatiarei theinulliandialternativeihypothesesiforithisihypothesisitest? Thatiisicorrect!

{H0:p=0.81Ha:p>0. {H0:p≠0.81Ha:p=0. {H0:p=0.81Ha:p<0. {H0:p=0.81Ha:p≠0. AnsweriExplanationiC orrectianswer: {H0:p=0.81Ha:p≠0. Firstiverifyiwhetherialliofitheiconditionsihaveibeenimet.iLetipibeitheipopulationiproportioniforitheis enioricitizenipatientsitreatediatiAmelia'sihospitaliwhoitakeiatileastioneiprescriptionimedication.

1. Sinceithereiareitwoiindependentioutcomesiforieachitrial,itheiproportionifollowsiaibi nomialimodel.
2. Theiquestionistatesithatitheisampleiwasicollectedirandomly.
3. Theiexpectedinumberiofisuccesses,inp=47.79,ianditheiexpectedinumberiofif ailures,inq=n(1−p)=11.21,iareibothigreaterithanioriequalitoi5. SinceiAmeliaiisitestingiwhetheritheiproportioniisitheisame,itheinullihypothesisiisithatipiisiequalitoi 0 .81ianditheialternativeihypothesisiisithatipiisinotiequalitoi0.81.iTheinulliandialternativeihypothesesi areishownibelow. {H0:p=0.81Ha:p≠0. QUESTIONi 8 i1/1iPOINTS

Airesearchericlaimsithatitheiproportionioficarsiwithimanualitransmissioniisilessithani10%.iToitestithi siclaim,iaisurveyicheckedi 1000 irandomlyiselectedicars.iOfithoseicars,i 95 ihadiaimanualitransmissio n. Theifollowingiisitheisetupiforitheihypothesisitest: {H0:p=0.10Ha:p<0. Finditheitestistatisticiforithisihypothesisitestiforiaiproportion.iRoundiyouriansweritoi 2 idecimaliplac es. Thatiisicorrect! $$Test_Statistic=−0.53i AnsweriExplanationi Correctianswers:

• $\text{Test_Statistic}=- 0.53$Test_Statistic=−0.53iTheiproportioniofisuccessesiisi p^=951000=0.095. Theitestistatisticiisicalculatediasifollows: z=p^−p0p0⋅(1−p0)n−−−−−−√iz=0.095−0. 0.10⋅(1−0.10)1000−−−−−−−−√iz≈−0. QUESTIONi 9 i1/1iPOINTS Aimedicaliresearchericlaimsithatitheiproportioniofipeopleitakingiaicertainimedicationithatidevelop iseriousisideieffectsiisi12%.iToitestithisiclaim,iairandomisampleiofi 900 ipeopleitakingitheimedicatio niisitakeniandiitiisideterminedithati 93 ipeopleihaveiexperiencediseriousisideieffects.i. Theifollowingiisitheisetupiforithisihypothesisitest: H 0: pi =i0.

Ha : pi ≠i0. Finditheip- valueiforithisihypothesisitestiforiaiproportioniandiroundiyouriansweritoi 3 idecimaliplaces. TheifollowingitableicanibeiutilizediwhichiprovidesiareasiunderitheiStandardiNormaliCurve: Thatiisicorrect! $$P- value=0.124i AnsweriE xplanationiCorrectian swers:

• $\text{P-value=}0.124$P-value=0. Hereiareitheistepsineededitoicalculateitheip-valueiforiaihypothesisitestiforiaiproportion:

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.

1.8 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.030 0.

1.7 0.045 0.044 0.043 0.042 0.041 0.040 0.039 0.038 0.038 0.

1.6 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.

1.5 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.

1.4 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.

1. Determineiifitheihypothesisitestiisileftitailed,irightitailed,ioritwoitailed.
2. Computeitheivalueiofitheitestistatistic.
3. Ifitheihypothesisitestiisileftitailed,itheip- valueiwillibeitheiareaiunderitheistandardinormalicurveitoithei lefti ofitheitestistatistici z 0 Ifitheitestiisirightitailed,itheip- valueiwillibeitheiareaiunderitheistandardinormalicurveitoithei righti ofitheitestistatistici z 0 Ifitheitestiisitwoitailed,itheip- valueiwillibei theiareaitoitheilefti ofi−| z 0|i plusitheiareaitoitheirighti ofi| z 0|iunderitheistandar dinormalicurve Forithisiexample,itheitestiisiaitwoitaileditestianditheitestistatistic,iroundingitoitwoidecimaliplaces,iisi z=0.1033−0.120.12(1−0.12)900−−−−−−−−−−−−√≈−1.54. Thusitheip-valueiisitheiareaiunderitheiStandardiNormalicurveitoitheileftiofiaiz-scoreiofi- 1.54,iplusitheiareaiunderitheiStandardiNormalicurveitoitheirightiofiaiz-scoreiofi1.54. FromiailookupitableiofitheiareaiunderitheiStandardiNormalicurve,itheicorrespondingiareaiisitheni2( 0.062)i=i0.124. QUESTIONi 10 i1/1iPOINTS

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.

1.8 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.030 0.

1.7 0.045 0.044 0.043 0.042 0.041 0.040 0.039 0.038 0.038 0.

1.6 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.

1.5 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.

1.4 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.

Anieconomisticlaimsithatitheiproportioniofipeopleiwhoiplanitoipurchaseiaifullyielectricivehicleiasit heirinexticariisigreaterithani65%. Toitestithisiclaim,iairandomisampleiofi 750 ipeopleiareiaskediifitheyiplanitoipurchaseiaifullyielectric ivehicleiasitheirinexticariOfithesei 750 ipeople,i 513 iindicateithatitheyidoiplanitoipurchaseianielectrici vehicle. Theifollowingiisitheisetupiforithisihypothesisitest: H0:p=0.65iHa :p>0. 65 Inithisiexample,itheip-valueiwasidetermineditoibei0.026. Comeitoiaiconclusioniandiinterpretitheiresultsiforithisihypothesisitestiforiaiproportioni(useiaisignifi canceileveliofi5%.) Thatiisicorrect! TheidecisioniisitoirejectitheiNulliHypothesis. Theiconclusioniisithatithereiisienoughievidenceitoisupportitheiclaim. TheidecisioniisitoifailitoirejectitheiNulliHypothesis. Theiconclusioniisithatithereiisinotienoughievidenceitoisupportitheiclaim. AnsweriExplanationiC orrectianswer: TheidecisioniisitoirejectitheiNulliHypothesis. Theiconclusioniisithatithereiisienoughievidenceitoisupportitheiclaim. ToicomeitoiaiconclusioniandiinterpretitheiresultsiforiaihypothesisitestiforiproportioniusingitheiP- iValueiApproach,itheifirstistepiisitoicompareitheip- valueifromitheisampleidataiwithitheileveliofisignificance.

Theidecisionicriteriaiisitheniasifollows: Ifitheip- valueiisilessithanioriequalitoitheigivenisignificanceilevel,ithenitheinullihypothesisishouldibeirejected . So,iifip≤α,irejectiH0;iotherwiseifailitoirejectiH0. Wheniweihaveimadeiaidecisioniaboutitheinullihypothesis,iitiisiimportantitoiwriteiaithoug htfuli conclusioni aboutitheihypothesesiinitermsiofitheigiveniproblem'siscenario. Assumingitheiclaimiisitheinullihypothesis,itheiconclusioniisithenioneiofitheifollowing:

• ifitheidecisioniisitoirejectitheinullihypothesis,ithenitheiconclusioniisithatithereiisienoughiev idenceitoirejectitheiclaim.
• ifitheidecisioniisitoifailitoirejectitheinullihypothesis,ithenitheiconclusioniisithatithereiisino tienoughievidenceitoirejectitheiclaim. Assumingitheiclaimiisitheialternativeihypothesis,itheiconclusioniisithenioneiofitheifollowing:
• ifitheidecisioniisitoirejectitheinullihypothesis,ithenitheiconclusioniisithatithereiisienoughiev idenceitoisupportitheiclaim.
• ifitheidecisioniisitoifailitoirejectitheinullihypothesis,ithenitheiconclusioniisithatithereiisino tienoughievidenceitoisupportitheiclaim. Inithisiexample,itheip-valuei=i0.026.iWeithenicompareitheip- valueitoitheileveliofisignificanceitoicomeitoiaiconclusioniforitheihypothesisitest. Inithisiexample,itheip-valueiisilessithanitheileveliofisignificanceiwhichiisi0.05. Sinceitheip- valueiisigreaterithanitheileveliofisignificance,itheiconclusioniisitoi rejectitheinullihypothesis. QUESTIONi 11 i1/1iPOINTS Becky'sistatisticsiteacheriwasiteachingitheiclassihowitoiperformitheiz- testiforiaiproportion.iBeckyiwasiboredibecauseisheihadialreadyimastereditheitest,isoisheidecideditoi seeiifitheicoinisheihadiiniheripocketiwouldicomeiupiheadsioritailsiiniaitrulyirandomifashioniwhenifl ipped.iSheidiscretelyiflippeditheicoini 30 itimesiandigotiheadsi 18 itimes. Beckyiconductsiaione- proportionihypothesisitestiatithei5%isignificanceilevel,itoitestiwhetheritheitrueiproportioniofiheadsii sidifferentifromi50%.

Whichianswerichoiceishowsitheicorrectinulliandialternativeihypothesesiforithisitest? Thatiisicorrect! H0:p=0.6;iHa:p>0.6,iwhichiisiairight-taileditest. H0:p=0.5;iHa:p<0.5,iwhichiisiaileft-taileditest. H0:p=0.6;iHa:p≠0.6,iwhichiisiaitwo-taileditest. H0:p=0.5;iHa:p≠0.5,iwhichiisiaitwo-taileditest. AnsweriExplanationiC orrectianswer: H0:p=0.5;iHa:p≠0.5,iwhichiisiaitwo-taileditest. Theinullihypothesisishouldibeitrueiproportion:iH0:p=0.5.iBeckyiwantsitoiknowiifitheitrueiproporti oniofiheadsiisidifferentifromi0.5.iThisimeansithatiweijustiwantitoitestiifitheiproportioniisinoti0.5.iSo, itheialternativeihypothesisiisiHa:p≠0.5,iwhichiisiaitwo-taileditest. QUESTIONi 12 i1/1iPOINTS Johniownsiaicomputerirepairiservice.iForieachicomputer,iheichargesi$50iplusi$45iperihouriofiwork .iAilineariequationithatiexpressesitheitotaliamountiofimoneyiJohniearnsipericomputer

isiy=50+45x.iWhatiareitheiindependentiandidependentivariables?iWhatiisitheiy- interceptianditheislope? Thatiisicorrect! Theiindependentivariablei(x)iisitheiamountiofitimeiJohnifixesiaicomputer.iTheidependentivariablei( y)iisitheiamount,iinidollars,iJohniearnsiforiaicomputer. Johnichargesiaione-timeifeeiofi$50i(thisiisiwhenix=0),isoitheiy- interceptiisi50.iJohniearnsi$45iforieachihouriheiworks,isoitheislopeiisi45. Theiindependentivariablei(x)iisitheiamount,iinidollars,iJohniearnsiforiaicomputer.iTheidependentiva riablei(y)iisitheiamountiofitimeiJohnifixesiaicomputer. Johnichargesiaione-timeifeeiofi$45i(thisiisiwhenix=0),isoitheiy- interceptiisi45.iJohniearnsi$50iforieachihouriheiworks,isoitheislopeiisi50. Theiindependentivariablei(x)iisitheiamount,iinidollars,iJohniearnsiforiaicomputer.iTheidependentiva riablei(y)iisitheiamountiofitimeiJohnifixesiaicomputer. Johnichargesiaione-timeifeeiofi$50i(thisiisiwhenix=0),isoitheiy- interceptiisi50.iJohniearnsi$45iforieachihouriheiworks,isoitheislopeiisi45. Theiindependentivariablei(x)iisitheiamountiofitimeiJohnifixesiaicomputer.iTheidependentivariablei( y)iisitheiamount,iinidollars,iJohniearnsiforiaicomputer. Johnichargesiaione-timeifeeiofi$45i(thisiisiwhenix=0),isoitheiy- interceptiisi45.iJohniearnsi$50iforieachihouriheiworks,isoitheislopeiisi50.

AnsweriExplanationiC orrectianswer: Theiindependentivariablei(x)iisitheiamountiofitimeiJohnifixesiaicomputer.iTheidependentivariablei( y)iisitheiamount,iinidollars,iJohniearnsiforiaicomputer. Johnichargesiaione-timeifeeiofi$50i(thisiisiwhenix=0),isoitheiy- interceptiisi50.iJohniearnsi$45iforieachihouriheiworks,isoitheislopeiisi45. Theiindependentivariablei(x)iisitheiamountiofitimeiJohnifixesiaicomputeribecauseiitiisitheivalueitha tichanges.iHeimayiworkidifferentiamountsipericomputer,iandihisiearningsiareidependentionihowi manyihoursiheiworks.iThisiisiwhyitheiamount,iinidollars,iJohniearnsiforiaicomputeriisitheidepende ntivariablei(y). Theiy-interceptiisi 50 i(b=50).iThisiisihisione- timeifee.iTheislopeiisi 45 i(a=45).iThisiisitheiincreaseiforieachihouriheiworks. QUESTIONi 13 i1/1iPOINTS Arianaikeepsitrackiofitheiamountiofitimeisheistudiesianditheiscoreisheigetsioniheriquizzes.iTheidata iareishowniinitheitableibelow.iWhichiofitheiscatteriplotsibelowiaccuratelyirecordsitheidata? Hoursistudying Quiziscore 1 5 2 5 3 7 4 9 5 9

Thatiisicorrect! AiscatterplotihasiaihorizontaliaxisilabelediHoursistudyingifromi 0 itoi 6 iiniincrementsiofi 1 iandiaiverti caliaxisilabelediQuiziscoreifromi 0 itoi 10 iiniincrementsiofi2.iTheifollowingipointsiareiplotted:ileft- parenthesisi 1 icommai 5 iright-parentheses;ileft-parenthesisi 2 icommai 5 iright-parentheses;ileft- parenthesisi 3 icommai 7 iright-parentheses;ileft-parenthesisi 4 icommai 9 iright-parentheses;ileft- iparenthesisi 5 icommai 9 iright-parentheses.iAllivaluesiareiapproximate.

AiscatterplotihasiaihorizontaliaxisilabelediHoursistudyingifromi 0 itoi 10 iiniincrementsiofi 2 iandiaivert icaliaxisilabelediQuiziscoreifromi 0 itoi 6 iiniincrementsiofi1.iTheifollowingipointsiareiplotted:ileft- parenthesisi 5 icommai 1 iright-parentheses;ileft-parenthesisi 5 icommai 2 iright-parentheses;ileft- parenthesisi 7 icommai 3 iright-parentheses;ileft-parenthesisi 9 icommai 4 iright-parentheses;ileft- iparenthesisi 9 icommai 5 iright-parentheses.iAllivaluesiareiapproximate.

AiscatterplotihasiaihorizontaliaxisilabelediHoursistudyingifromi 0 itoi 6 iiniincrementsiofi 1 iandiaiverti caliaxisilabelediQuiziscoreifromi 0 itoi 9 iiniincrementsiofi1.iTheifollowingipointsiareiplotted:ileft- parenthesisi 1 icommai 5 iright-parentheses;ileft-parenthesisi 2 icommai 5 iright-parentheses;ileft- parenthesisi 3 icommai 7 iright-parentheses;ileft-parenthesisi 4 icommai 8 iright-parentheses;ileft- parenthesisi 5 icommai 8 iright-parentheses.

AiscatterplotihasiaihorizontaliaxisilabelediHoursistudyingifromi 0 itoi 6 iiniincrementsiofi 1 iandiaiverti caliaxisilabelediQuiziscoreifromi 0 itoi 12 iiniincrementsiofi2.iTheifollowingipointsiareiplotted:ileft- parenthesisi 1 icommai 5 iright-parentheses;ileft-parenthesisi 2 icommai 5 iright-parentheses;ileft- parenthesisi 3 icommai 8 iright-parentheses;ileft-parenthesisi 4 icommai 8 iright-parentheses;ileft- iparenthesisi 5 icommai 11 iright-parentheses.iAllivaluesiareiapproximate. AnsweriExplanationiC orrectianswer:

AiscatterplotihasiaihorizontaliaxisilabelediHoursistudyingifromi 0 itoi 6 iiniincrementsiofi 1 iandiaiverti caliaxisilabelediQuiziscoreifromi 0 itoi 10 iiniincrementsiofi2.iTheifollowingipointsiareiplotted:ileft- parenthesisi 1 icommai 5 iright-parentheses;ileft-parenthesisi 2 icommai 5 iright-parentheses;ileft- parenthesisi 3 icommai 7 iright-parentheses;ileft-parenthesisi 4 icommai 9 iright-parentheses;ileft- iparenthesisi 5 icommai 9 iright-parentheses.iAllivaluesiareiapproximate. Theivaluesiforihoursistudyingicorresponditoix- values,ianditheivaluesiforiquiziscoreicorresponditoiy- values.iEachirowiofitheitableiofidataicorrespondsitoiaipointi(x,y)iplottediinitheiscatteriplot.iForiexa mple,itheifirstirow,i1,5,icorrespondsitoitheipointi(1,5).iDoingithisiforieveryirowiinitheitable,iweifin ditheiscatteriplotishouldihaveipointsi(1,5),i(2,5),i(3,7),i(4,9),iandi(5,9). QUESTIONi 14 i1/1iPOINTS Dataiisicollectedionitheirelationshipibetweenitimeispentiplayingivideoigamesianditimeispentiwithifa mily.iTheidataiisishowniinitheitableianditheilineiofibestifitiforitheidataiisiy^=−0.27x+57.5. Assumeitheilineiofibestifitiisisignificantiandithereiisiaistrongilinearirelationshipibetweenitheivariabl es. VideoiGamesi(Minutes)i 306090120 iTimeiwithiFamilyi(Minutes)i 50403525 Accordingitoitheilineiofibestifit,itheipredictedinumberiofiminutesispentiwithifamilyiforisomeoneiw hoispenti 95 iminutesiplayingivideoigamesiisi31.85.iIsiitireasonableitoiuseithisilineiofibestifititoimak eitheiaboveiprediction?

Thatiisicorrect! Theiestimate,iaipredicteditimeiofi 31.85iminutes,iisiunreliableibutireasonable. Theiestimate,iaipredicteditimeiofi 31.85iminutes,iisibothiunreliableiandiunreasonable. Theiestimate,iaipredicteditimeiofi 31.85iminutes,iisibothireliableiandireasonable. Theiestimate,iaipredicteditimeiofi 31.85iminutes,iisireliableibutiunreasonable. AnsweriExplanationiC orrectianswer: Theiestimate,iaipredicteditimeiofi 31.85iminutes,iisibothireliableiandireasonable. Theidataiinitheitableionlyiincludesivideoigameitimesibetweeni 30 iandi 120 iminutes,isoitheilineiofibe stifitigivesireasonableipredictionsiforivaluesiofixibetweeni 30 iandi120.iSincei 95 iisibetweenitheseiva lues,itheiestimateiisibothireliableiandireasonable. QUESTIONi 15 i0/1iPOINTS Whichiofitheifollowingiareifeasibleiequationsiofiaileastisquaresiregressionilineiforitheiannualipopu lationichangeiofiaismallicountryifromitheiyeari 2000 itoitheiyeari2015?iSelectiallithatiapply.

That'sinotiright.

yˆ=38,000+2500x

yˆ=38,000−3500x

yˆ=−38,000+2500x

yˆ=38,000−1500x

AnsweriExplanationiC orrectianswer: yˆ=38,000+2500x iyˆ=38,000−1500 x Populationichangeicanibeipositiveiorinegative,iandiiticaniincreaseioridecrease.iBasedionitheigiveni information,ithereiareinoipracticalilimitsitoipopulationichange,ialthoughithereiareilimitsisuchiasithe idecreaseiinipopulationicannotiexceeditheicurrentipopulationi(asiitiwouldileaveia

negativeinumberiofipeopleiinitheicountry),ioritheiincreaseiinipopulationicouldibeilimitedibyiotherir eal-worldifactorsi(suchiasilackiofispaceiorilegaliimmigrationilimits). Yourianswer: yˆ=38,000+2500x QUESTIONi 17 i1/1iPOINTS Aniamateuriastronomeriisiresearchingistatisticalipropertiesiofiknownistarsiusingiaivarietyiofidataba ses.iTheyicollectitheicoloriindex,ioriB−Viindex,iandidistancei(inilightiyears)ifromiEarthifori 30 istars .iTheicoloriindexiofiaistariisitheidifferenceiinitheilightiabsorptionimeasuredifromitheistariusingitwoi differentilightifiltersi(aiBiandiaiVifilter).iThisitheniallowsitheiscientistitoiknowitheistar'sitemperature iandiainegativeivalueimeansiaihotiblueistar.iAilightiyeariisitheidistanceilighticanitraveliini 1 iyear,iwhi chiisiapproximatelyi5.9itrillionimiles.iTheidataiisiprovidedibelow.iUseiExcelitoicalculateitheicorrel ationicoefficientiribetweenitheitwoidataisets,iroundingitoitwoidecimaliplaces. B- ViindexiDista ncei(ly)i 1.1 1380 0.4 556 1.0 771 0.5 304 1.4 532

HelpCopyitoiClipboardDownloadiCSV Thatiisicorrect! $$r=i0.18 AnsweriExplanationiC orrectianswers:

• $\text{r=i}0.18$r=i0.18 TheicorrelationicoefficienticanibeicalculatedieasilyiwithiExceliusingitheibuilt- iniCORRELifunction.

1. OpenitheiaccompanyingidataisetiiniExcel.
2. Inianiopenicell,itypei"=CORREL(A2:A31,B2:B31)",iandithenihiti ENTER. Youicouldilabelitheiresultiofithisicellibyiwritingi"Correlationicoefficient"iori"r"iinianiadjacentiopeni cell. Theicorrelationicoefficient,iroundeditoitwoidecimaliplaces,iisir≈0.18. QUESTIONi 18 i0/1iPOINTS