MATH 225N Week 8 Final Exam (Collection)VERSION 1&2 100% GRADED [A], Exams of Mathematics

Download MATH 225N Week 8 Final Exam (Collection)VERSION 1&2 100% GRADED [A] and more Exams Mathematics in PDF only on Docsity! 1/1POEZNTS Afitnesscenterclaimsthathemeanamounto rermethatapersonspendsathegym pervisitis33 minutes .Ildentifythenullhypothesis,Ho,a ndthealternative C Ho= W#33>Ha=y 233 Koo W=33 > Hat B35 Ho: W233 > Hay <33 Ho = US33 > Ha = p>33 AnswerExplIanation Corectianswer: Ho : u=33 ; Ha: W#33 Letheparameteryu beusedtorepresenthemean .Thenullhypothesisisa Iways statedwithsomeform ofequality: equal C=),greaterthanorequaltoce= >,orlessthan orequaltocs).Therefore, inthiscase,thenulihyp othesisHo isyw=33.The alternativehypothesisiscontradictorytothenu Bhypothesis,soHa isy¥33. QUEST EKON2 1/1POENTS Theanswerchoicesbelowre nthypothesistests ._.Which areright-tailedtests? Selectallcorrectanswers. r pre ° Ho:X217.1, Ha:X<17.1 thanl15% ofthestructureswerebuiltwithoutpermi tswhen, infact,more than15% efthestructu reswerebuiltwithoutpermi s. Youranswer: Thebuildinginspectorthinksthatmorethan 15% ofthestructures inthecountywere builtwithoutpermitswhen, infact,atmostl SOS SHS Oo ureswerebuiltwithout QUEST HON4 1/1POENTS Sup oseachefclaimsthathermeatbaliweightisle ssthan4 ounces ,onaverage. Severalofhercustomersdonotbelieveher,s othechefdecidestodoahypothesistest, atal0% significancelevel , topersuadethem.Sheco ks14 meatballs .Themean weightofthesamplemeatbalsis3.7 ounces .Thechefknows from experiencethathe standarddeviationforhermeatbaliweightis 0.5 ounces. . Ho: H=4; Ha: <4 . a=0.1 Csignificancelevel > Whatistheteststatisticcz- score JOFthisone- meanhypothesistest, roundedtotwo $$Test statistic = —2.24 decimalplaces? AnswerExplIanation Corecttanswers: . $\text{Test statistic = }-2.24$Test statistic = —2.24 Thehypotheseswerechosen,andthesignificancele velwasdecidedon,sothenext stepinhypothesistestingistocomputethetestst atistic.Inthisscenario,thesample meanweight,x =3.7.Thesamplethechefusesisl4 meatbalis,son=14.She Knowsthestandarddeviationofthemeatbals,o=0.5 -Lastly,thechefiscomparing thepopulationmeanweighto4 ounces .So,thisvalueC foundinthenullandalterna tive hypotheses )isWo-Nowwewi §substitutethe valuesintothe formulatocomputethe teststatistic: Zo=X° —Woonv=3.7—40.514V=—0.30.134=-2.24 So,theteststatisticforthishypothesistestiszo =-2.24. QUEST IONS 1/1POENTS Whatisthep-valueofaright-tailedone- meanhyps othesistest, withateststatistic ofzo=1 <Bonctrcupdyouranswer; compureyouranswe ebelow.)> b zi, 51. él. Tie gi. ‘90; 000. 9330, 0.9450 3550 .¢ 9640.9710.010.9340. 9460.9560.9650.9720.020.9360.9470.9570.9660.9730.030.9 370.9480.9580.9660.9730.040.9380.9490.9590.9670.9740.0 50.9390.9510.9600.9680.9740.060.9410.9520.9610.9690.97 50.070.9420.9530.9620.9690.9760.080.9430.9540.9620.970 0.9760.090.9440.9540.9630.9710.977 $$0.041 AnswerExplIanation Corecttanswers: $0.041$0.041 hep- valueistheprobabilityofanobservedvalu eofz=1.74 orgreateri fthenul hypothesisistrue,becausethishypothesi stestisright- tailed-Thisprobabilityisequalto theareaundertheStandardNormal curvetot herightofz=1.74. Donotrejecthenubhypothesisbecausethep- value0.0401 isgreaterthanthe significance evel a=0.04 - Rej ecthenulhypothesisbecausethep-valu isgreaterthanthesignificance level a=0.04 - q ajecthenulbhypothesisbecau §etheval ueofz isnegative. Rejecthenulbhypothesisbecau S©|-1.75|>0.04 ~ 0.0401 Donotrej ecthenulhypothesisbecause|—1.75|>0.04 - AnswerExplIanation Corectianswer: Donotrejecthenulhypothesisbecausethep- vaehak)AGthesgacd at entbaefsetornotreject Ho, i fFa>p-value, rej ectHo becausethe resultsofthesampledataaresignificant.Th ereissuffc i entevidencetoconclude thatHo isanincorrectbel iefandthathealternati vehypothesis,Ha,maybecorrect. 1 fasp- value, donotrejectHo.Theresultsofthesam pledataarenotsignificant,so thereisnotsuffcientevidencetoconcludeth athealternativehypothesis,Ha,maybe correct..Inthiscase, a=0.04 islessthanorequal top=0.0401, sothedecisio nis tonotrejecthenulhypothesis. QUEST AON7 1/1POENTS Arecentstudysugestedthat81% ofseniorcitizenstakeatleastoneprescrip tion medication-.Ameliaisanurseatalargehospi talwhowouldliketoknowwhetherthe percentageisthesameforseniorcitizenpat fentswhogotoherhospital .Sherandomly selects59 seniorcitizenspatientswhoweretreatedat hehospitalandfindsthat49 of them takeatleastoneprescriptionmedication.Whatar ethenullandalternative hatiscorect! hypotheses forthishypothesistest? Q {Ho:p=0.81Ha:p>0.81 c {Ho:p#0.81Ha:p=0.81 A {Ho:p=0.81Ha:p<0.81 é {Ho:p=0.81Ha:p#0.81 AnswerExplIanation Corectanswer : {Ho:p=0.81Ha:p#0.81 Firstverifywhetheralloftheconditionshavebe nmet .Letp bethepopulation proportionforthesentiorcitizenpatientstreated atAmelia"™shospitalwhotakeatleast oneprescriptionmedication. lL Sincetherearetwoindependentoutcome sforeachtrial,theproportionfollowsa binomialmodel . 2 Thequestionstatesthathesamplewasco Hectedrandomly. 3.Theexpectednumberofsucesses , np=47.79 »andtheexpectednumberof failures, ng=n(1—p)=11.21, arebothgreaterthano requaltod. SinceAmeliaistestingwhethertheproport ionisthesame, thenulhypothesisis thatp isequalto0.81 andthealternativehypothesisisthatp isnotequalto0.81. Thenullandalternativehypothesesareshow nbelow. {Ho:p=0.81Ha:p#0.81 QUEST AONS8 1/1POENTS Aresearcherclaimsthatheproportionofcar swithmanualtransmissionisless thanld0%.Totesthisclaim, asurveycheckedl 000 randomlyselectedcars .Of thosecars ,95 hadamanualtransmission. Thefotlowingtablecanbeuti lizedwhichpro vVidesareasundertheStandardNormal Curve: Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -1.8 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.030 0.029 -1.7 0.045 0.044 0.043 0.042 0.041 0.040 0.039 0.038 0.038 0.037 -1.6 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.046 -15 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.056 -14 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.068 hatiscorect! $$P-value=0.124 AnswerExplIanation Corecttanswers: . $\text{P-value=}0.124$P-value=0.124 Herearethestepsnededtocalculatethep- valueforahypothesistestforaproportion: 1.Determinei Fenehypothesistestisleftailed, rightailed,ortwotailed. 2-Computethevalueoftheteststatistic. 3.1 fthehypothesistestisleftailed,thep- valuewi Ebetheareaunderthestandard normalcurvetotheleftoftheteststatisticzo I fFthetestisrightailed, thep- valuewi fbetheareaunderthestandardnormal curvetotherightoftheteststatisticzo I Fehetestistwotailed, thep- valuewi Ebetheareatotheleftof—|zo|[plusthe areatotherightof|zZzo| underthestandardnormalcurve Forthisexample, thetest'isatwotai ledte standtheteststatistiic, roundingtotwo decimalplaces, isz=0.1033—0.120.12(1—0.12)900 Zz -1.8 -L.7 -1.6 -1.5 -14 Thusthep- valueistheareaundertheStandardNormalcurvet otheleftofaz-scoreof 1.54,plustheareaundertheStandardNormalcurve totherightofaz-scoreofl . 54. 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.030 0.029 0.045 0.044 0.043 0.042 0.041 0.040 0.039 0.038 0.038 0.037 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.046 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.056 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.068 Fromalo kuptableoftheareaundertheStandardNormalcurv e,thecoresponding areaisthen2CoO.062 )=0.124. QUESTION10 1/1POENTS Aneconomistclaimsthatheproportionofpeop!ewho plantopurchaseafullyelectric vehicleasthei rnextcarisgreaterthant5%. Totesthisclaim,arandom sampleof750 peopleareaskedi fFtheyplantopurchasea Fublyelectricvehicleastheirnextcar Ofthese750 people,513 indicatethatheydo plantopurchaseanelectricvehicle. Thefotowingisthesetupforthishypothesistest: Ho:p=0.65 Ha:p>0.65 Inthisexample, thep- valuewasdeterminedtobe0.026 . Cometoaconclusionandinterpretheresults forth ishypothesistestforaproportion Cuseasignificancelevelof5s%. > € AnswerExplIanation Corectianswer: ThedecisionistorejectheNulHypothesis. Theconclusionisthathereisenougheviden Tocometoaconclusionandinterpretheres ultsforahypothesistestforproportion usingtheP-ValueAp roach, thefirststepistocomparethep- valuefrom thesample datawiththelevelofsignificance. Thedecisioncriteriaisthenasfollows: I fFehep- valueisltessthanorequaltothegivensignificance level ,thenthenul hypothesisshouldberejected. So, ifpsa, rej ectHo; otherwisefai ltorej ectHo. Whenwehavemadeadecisionabouthenulbhypothesis »itisimportantowritea thought Ffulconcliusionabouthehypothesesinterm softhegivenproblem"sscenario. Assumingtheclaim isthenuhypothesis,theconclusionisthenoneofF the following: * Pfthedecisionistorejecthenulbhypoth esis, thentheconclusionisthathereis enoughevidencetorejecthecliaim. * Pfthedecisionistofai ltorejecthenul hypothesis, thentheconclusionistha t thereisnotenoughevidencetorejecth ght-tailedtest. Ho:p=0.5 > Haip<O.5,whichisale fFt-tailedtest. Ho:p=0.6 ; Haip#0.6, whichisatw o-tailedtest. © Ho:p=0.5 ; Ha:p#0.5, whi chisatwo-tailedtest. AnswerExplIanation Corectianswer: Ho:p=0.5; Ha:p#0.5, whichisatwo-tailedtest. Thenulhypothesisshouldbetrueproportion : Ho:p=0.5-Beckywantstoknowi fF thetrueproportionofheadsisdi ferent from 0.5.Thismeansthatwej ustwantotest i F theproportionisnot0.5.So, thealternative hypothesisisHa:p40.5, whichisatwo- tailedtest. QUEST EON12 1/1POENTS Johnownsacomputerepairservice.Foreachcomput er,he charges$50 plus$45 7 perhourofwork.Alinearequationthatexpr essesthetotal amountofmoneyJ ohnearnspercomputerisy =50+45x.Whatarethe independentanddependentvariables? € TheindependentvariableCx)yistheamountoftime) ohnfixesacomputer.The dependentvariablecy)istheamount, indollars,jJo hnearnsforacomputer. Cthisiswhenx=0),sothey- interceptis50.John earns$45 Foreachhourheworks,sotheslopeis45. e TheindependentvariablecCx)istheamount,indolla rs,jJohnearnsforacomputer.The dependentvariablecy)istheamountoFfti mej ohnfixe sacomputer. Johnchargesaone-timefe of$50 r Sohn chargesaone tinete orf$45 Cthisiswhenx=0),sothey- i ntercepti s45-John earns$50 Foreachhourheworks,sotheslopeiss50. C TheindependentvariablecCx)istheamount,indolla rs,jJohnearnsforacomputer.The - | dependentvariablecy)istheamountoFfti mej ohnfixe sacomputer. 2 3 u w ° ° N 5 oO % 2 3 4 5 6 Hours studying AscaterplothasahorizontalaxislabeledHo ursstudyingfrom OtoGinincrementsofi1 andaverticalaxislabeledQuizscorefrom OtolO0inincrementsof2 .Thefolowing pointsareploted:left- parenthesisilcomma5bri ght, parentheses; left-parenthesis2 commasd5right-parentheses; left- parenthesis3conmma7right- parentheses; left- parenthesis4tconmma?right- parentheses ; left- parenthesisS5comma®Sright- parentheses .Alvaluesareap roximate. HH} c Quiz score b No Wu yn np e e e * % y 4 6 3 To Hours studying thasahorizontalaxislabeledHo ursstudyingfrom otol0inincrementsof 2ZandaverticalaxislabeledQuizscorefrom OtoGinincrementsofl.-.Thefolowing pointsarep|!oted: left- parenthesisScommalright-_ parentheses; left-parenthesis5 comma2right-parentheses; left- Ascaterploth parenthesis7comma3right- ° * Quiz score a OO ee >) en oe e eS T 2 3 q 5 6 Hours studying parentheses; left- parenthesis9commad4right- parentheses; left- Oo parenthesis9comma5right- parentheses -Alvaluesareap roximate. nthevariables. Video Games (Minutes) 306090120 Time with Family (Minute s) 50403525 Acordingtothelineofbestfit, thepredicte dnumberofminutesspentwithfami lyfor someonewhospent95 minutesplayingvideogamesis31.85_Isitre asonableto usethislineofbestfitomaketheabovepred q Theestimate, apredi ctedti meof31.85 thi nutes, isunreliablebutreasonable. fheestimate, apredi ctedtimeof31.85 mi nutes, isbothunreliableandunreasonable. Theesti mate, apredictedti meof31.85 minutes, isbothreliableandreasonable. Theestimate, apredi ctedti meof31.85 minutes,isreliablebutunreasonable. AnswerExplIanation Corectianswer: Theestimate, apredictedtimeof31.85 minutes, isbothreliableandreasonable. Thedatainthetableonlyincludesvideogametimes betwe n30 and120 minutes, sothelineofbestfitgivesreasonablepredictionsf orvalues ofx betwe n30 and120.Since95 isbetwe nthesevalues,theestimateisboth reliableandreasonable. QUESTION15 0/1POENTS Whichofthe followingarefeasibleequation sofaleastsquaresregressionlineforthe an ual populationchangeofasmasicountry from theyear2000 totheyear2015? Selectalthatap ly. hatiscor ect! $$r= 0.18 AnswerExplIanation Corecttanswers: y $\text{r= }0.18$r= 0.18 Thecorelationcoeffcientcanbecal culate deasilywithExcelusingthebuilt-in CORREL function. 1 OpentheacompanyingdatasetiinExcel . 2 Enanopencell, type" =CORREL €A2:A31,B2:B31) "™, andthenhitENTER. Youcouldliabeltheresultofehisceilbywri ting"Correlationcoeffcient"or"'r"'inan adjacentopencel. Thecorelationcoeffcient, roundedtotwodecimalpl aces,isr=0.18. QUESTION18 0/1POENTS Theweightofacarcaninfiluencethemileageth athecarcanobtain.Arandomsample of20 cars’ weightsandmileageiscolected.Theta blefortheweightandmileageoF thecarsisgivenbelow.UseExceltofindthebe stftlinearegressionequation, where weightistheexplanatoryvariable~.Roundth eslopeandinterceptothre decimal places. 45.0 16.7 25.0 42.2 5.0 13.2 17.5 65.4 Hel pCopytocl ipboa rdDown loadCsSv hat" snot right. y=$$1.181 x+$$71.374 AnswerExplIanation yoiss x-€ ss Corecttanswers: $-1.181$-1.181 $71.374$71.374 Tofindthebestfit Forthegivendata, useExcel . 1 OpenExcel .Enterthevaluesofweighti ncolumnAandmi leageincolumnB. Highlightasmtheceliscontainingthedat a. 2 From thelnsertab,selectScater .UseScaterwit honlyMarkers, thefirstypeof scaterchart.Asimpleplotisshown. 3 Toad thelinearfitothegraph,clickanywherelinsi dethegrapharea.Select thelLayouttabFfromthecChartto Is .-ClickontheTrendlineiconandselectheL inear Trendlineoption.Thelineofbestfitisad edtothegraph. 4 Fortheequationofthelineofbestfit, clic konTrendlineandselectMoreTrendline ropriateprocess ;however,noatemptismad eto controlanyaspectofthesampleeventhough thevariablesofinterestarerecorded for eachgroup. QUEST ION20 1/1POENTS Totestheeffecti venessofadrugproposedtoreliev esymptomsofheadache, Physiciansincludedparticipantsforastudy.The ygavethedrugtoonegroupandadrug withnotherapeuticeffectoanothergroup.Whichgr hatiscorect! q thephysicians Ehegroupthatrecei vedthedru @ Forheadache Ehegroupthatrecei vedthedru gQwithnotherapeuticeffect allofthepeopleinthestudy AnswerExplIanation Corectianswer: thegroupthatreceivedthedrugwithnotherapeuti cefiect Whentheexperimentalunitsarepeople,ap lyingtreatmentsthatshouldbeinertcan actualiyhaveeffects.Inthisstudy, thedrugwithno therapeuticeffectsistheplacebo,so thegroupthatreceivesthatdrugreceivestheplac ebo. QUEST ION21 1/1POENTS Adoctornotesherpatient" stemperatureindegre sFahrenheiteveryhourtomakesure thepati entdoesnotgetafever .Whatisthelevelof AnswerExplIanation Corectianswer: interval Thisisintervaldatabecausedegre sFahrenheitisanumericalscalewhered i ffer ences aremeaningful -However, becauseFahrenhe itdoesnothaveatruezerovalue, itisnot ratiodata. QUEST EON2 0/1POENTS Asamemberofamarketingteam, yvouhavebe ntaskedwithdeterminingthenumber ofDVDsthatpeop!lenaverentedoverthepastsi xmon ths .Yousampletwentyadults anddecidethathebestdisplayofdataisafrequenc ytableforgroupeddata.Cconstruct thistableusingfourclasses. 15,31,28,19,14,18,28,19,10,19,10,24,14,18,24,27,10,18,16,2 3 lar) ated a t= pm $$10 $$15 $$16 $$21 Tofindthe Frequency foreachclass, counthen umberofdatavaluesthatfaliwithinthe rangeofeachclass.Forexample,thedatava fues15,14,10,10,14,and10Ofalwithin therangeofthefirstclass, 10- 15.So,thefrequencyofthisclassis6. Lower Class Limit Upper Class Limit Frequent 10 15 16 21 22 27 28 33 QUEST ION23 1/1POENTS Thehistogram belowdisplaystheweightsofrainbowtroutC inpounds dca ughtbyal visitorsatalakeonaSaturdayafterno n-Acordingtothishistogram, whichrangeof weightsCinpounds Ycontainsthel owest Frequency ? 4.5-6.5 | 6.5:8.5 | 8.5-10/5 |10.5-12.5|12.5-14.5/14.5-16.5 Ahistogram hasaverticalaxislabeledFrequencyandha sahorizontalaxisthat measuressixcategoriesofrainbowtroutwei QhtCinpounds) -Readingfrom left-to-right, theweightandfrequencyofeachcategoryar e:4.5to06.5hasfrequencyof4,6.5to0s.5 hatiscorect! $$greater than 12.5 but less than 14.5 hasfrequencysd5, 8.5to010.5hasfrequency/7, 10.5to012 ._.5hasfrequency3,12.5to0o14_5 hasfrequency1,14.5to0ol6.5hasfrequency2 AnswerExplIanation Corecttanswers: $\text{ greater than }12.5\ \text{but less than }14.5$greater than 12.5 but less than 14.5 Therangel2 57145 | 7 7 hastheTowestbarinthehistogram, whichm eansthathis rangeofvaluesalsohasthelowest frequen cy.Therefore,1 vVisitorcaughtarainbow trouthatweighedgreaterthanl2.5 butlessthanl14.5 pounds. QUEST EON24 1/1POENTS Describetheshapeofthegivenhistogram. 10 8 Frequency 6 4 2 0 0246 8 10121416 Ahistogramhasahorizontalaxisfrom OtolGinincrementsof2andaverticalaxis labeledFrequency from OtolOinincrementsof2 ._Thehistogram containsverticalbars ofwidthistartingathehorizontalaxisvalu e0.Theheightsofthebarsareas follows, wherethelefthorizontalaxislabelisliste dfirstandthefrequencyislistedsecond:0,0 1,0:2,6:3,6:4,7:5,6:6,6:7,6:8,7:9,6:;10 € uniform Gnimodalands ymmetric Wnimodalandl eft-skewed Gnimodalandr ight-skewed $$23 AnswerExplIanation Corecttanswers: MW $23$23 TofindthenumberofstudentsinMs .James"scl ass, findtheheightsofthebars forthat classandad them. tnthiscase, wefinditisl1+12=23. QUEST ION26 0/1POENTS Thelinegraphshownbelowrepresentsthenu mberofivVvsinahousebysquare Fo tagecCinhundredsofet > -Acordingtotheinf ormationabove, whichofthe following isanap ropriateanalysisofsquarefo tageandTvs? S Number of TVs w 0 1 2 3 4 5 6 7 8 9 lo 1 2 3 Ww 1 616 OU Square Footage Al inegraphhasanx-axislabeledSquareFo tage Cinhundredsofet dinincrementsof one, anday- axislabeledNumberofliv" sinincrementsofo ne.Begin ingathepoint startparentheses6G, 2endparentheses,alin eincreasestothepointstartparentheses 8.5, 3endparentheses.Thelineremainscons tantothepointstartparenthesesi10,3 endparentheses .Thelinethenincreases,pa ssingthroughthepointstartparentheses 12,5end parenthesesandcontinuesincreasinguntil itreachesthepointstart 8.5 10 thedata,thereisasteadydecreaseinthes quarefotageandnumberofltvVvs. From thedata,thereisasteadyincreaseinthes quarefo tageandnumberoflvs. $$mode=3 cards AnswerExplIanation Corecttanswers: . $\text{mode=}3\text{ cards}$mode=3 cards I Fwecounthenumberoftimeseachvalueap earsinthelist', wegethefollowing Frequencytable: Value Frequency 3 3 5 2 10 1 11 1 12 2 Notethat3 ocurs3 times,whichisthegreatest frequency, so3 isthemodeofthe numberofcardsdrawnfrom adeckuntilaquenapears. QUEST IONSO 1/1POEKNTS Giventhe fFolowinghistogram,decidei fthedatais skewedorsymmetrical . 200 150 Frequency be So o 50 i 2 4 6 8 10 12 14 16 18 Values AbargraphhasahorizontalaxistitledValu eslabeledfrom 2to1l8inincrementsof2 andaverticalaxistitlhedFrequencylabele dfrom 0020 inincrementsofso.i14bars areploted, abovethenumbers2to1i6.From leftoright, theheightsofthebarsareas Follows :1-.5.10.40,75,125,190,180,130,125 ,60,25,20,10-AE~valuesare Thedataareskewedtotheleft. e Thedataareskew é edtotheright. Thedataaresymm AnswerExplIanation plotabovetheclasslabelDhasthefolowingfive- numbersummary :2,63,7 ,92,and a gpa m1 D AnswerExplIanation Corectianswer: Cc Rememberthathestandarddeviationisamea sureofhowspreadouthedatais.I fthe valuesareconcentratedaroundthemean,th enadatasethasalowerstandard deviation. Aboxandwhiskerplotwithshortwhiskersandashort boxhasvaluesthatareless spreadout, andhencehasasmallerstandarddeviati on. QUEST IONS32 1/1POENTS Taegraphbelowshowsthe raphs potsqgveratinor maldistributions, labe ~B,and onthesameaxis .Determinewhi ar a chnormaldistr ibutionhasthesmaleststandard deviation. A Afigureconsistsofthre curvesalongahorizontalaxis, LlabeledUp erA,UperBand UperC.CurveUp erAisshortandthemostspreadout, curvevup hatiscorect! erBistallandthe leastspreadout, andcurveCisfarthertoth elefthanaA. abs 10 Cc AnswerExplIanation Corectianswer: B RememberthathestandarddeviationtelShowsprea douthenormaldistributionis.So ahighstandarddeviationmeansthegraphwi lbesho rtandspreadout -.Alowstandard deviationmeansthegraphwi §lbetallandskiny. Thedistrributionthatisthetallestandleastsprea doutisB,sothathasthesmallest standarddeviation. QUEST ION3 1/1LPOINTS Braydentossesacoin500 times .Ofthose500 times ,heobservesheadsatotal of times .Calculationsshowthatheprobabilit yofethisocurringbychanceisless than0.01, assumingthecoinisfair.Determin q Weexpecthat416 ofeverys5s00 Eoi ntosseswi lresultinheads. fen e001 hevel ofsignificance,thecoinislike lynotafai rcoin. Thereiscertaintythathecoinisnota Faircoin. Theresultsarenotstatisticallysignificantatheo.0 5levelofsignificance. AnswerExplIanation Corectianswer: Athe0.01 levelofsignificance,thecoinislikelynotafairco in. Theresultsoftheexperimentaresignificantathed. 01 levelofsignificance.This meanstheprobabilitythatheoutcomewastheresul tofchanceis0.01 orless. Becauseofthis,wecanbefairlyconfident, butnotc ertain,thathecoinisnotafair coin. QUEST EZON34 1/1POENTS Isthestatementbelowtrueorfalse? Independentisthepropertyoftwoeventsinwhicht otpossibl yocurtogether. QUEST EONS6 1/1POENTS Filinthefolowingcontingencytableandfindthenu mberofstudentswhobothgotothe beachANDgotothemountains. StudentsgotothebeachdonotgotothebeachTotalgotothemount ains48donotgotothemountains21Total3695 $$10 AnswerExplIanation Corecttanswers: hd $10$10 Byusingtheknowntotalsalongtherowsandcolumns youcanfilintherestofthe contingencytable.Forexample,lo kingatherowoftotalsinthetable, weknowthat theunknownnumberp!us48& 1s95,sothemissingnumbermustbe47 .Continuingin thisway,wecanfilintheentiretable: StudentsgotothebeachdonotgotothebeachTotalgotothemount ains103848donotgotothemountains262147Total365995 Fromthis,wecanse thathenumberofstudentswhobothgotothebeachan dgoto themountainsisl0. QUEST EONS3S7 1/1POENTS Astatisticsprofessorecentl ygradedfin alexamsforsttudentsinherintroductory statisticscourse.Inareviewotfhergrad ing,shefoundthemeanscoreout of100 pointswasax =77,withamarginoferrorofl 0. Constructaconfidenceinterval forthemea nscoreCoutofl00 points Yonthefinal exam. $$(67, 87) AnswerExplIanation Corecttanswers: . $\left(67,\ 87\right)$(67, 87) Aconfidenceintervalisanintervalofvalues,cent eredonapointestimate, oftheform (pointestimate—marginof error,pointestimate+marginof error) Usingthegi venpointestimateforthemean, xX =77 andmarginoferrorl0, the confidenceintervalis: (77—10,77+10)(67,87) QUEST ION38 1/1POENTS Arandom sampleofadultswereaskedwhethertheypre fFereadingane-bo kovera printedbo k.Thesurveyresultedinasampleproportio nofp=0.14, withasampling standarddeviationofop =0.02, whopreferredreadingane-bok. UsetheempiricalruletoconstructaI5% confidenceinterval forthetrueproportiono fF adultswhoprefere-bo ks. $$(0.10, 0.18) AnswerExplIanation Corecttanswers: . $\left(0.10,\ 0.18\right)$(0.10, 0.18) BytheEmpiricalRule,a95% confidenceinterval correspondstoaz-scoreofz=2. Substitutingthegivenvaluesp=0.14 andop '=0.02, aconfidenceintervalis (P~2:g010.+2.091(0.14-2-0,02,0.1442-0 02) P78 146 64.0.144.0.04)(0,10,0.18) O/1POINTS Whichofthe Folowingfrequencytablesshowas keweddataset PSelectalianswersthat aply. lar) ated a t= pm r Value Frequency 5 1 6 2 7 10 8 11 9 17 10 17 11215 12. 12 13 7 14 7 15 0 16 1 i Value Frequency 5 1 6 3 7 8 8 10 9 13 10 26 11 «(14 12. 12 13 8 14 3 15 1 16 1 iw Value Frequency 12 1 13 1 14 3 15 6 16 23 17. 29 18 #19 19 #15 20 3 r Value Frequency 5 16 23 19 22 9 4 2 NOUBWNEFO AnswerExplIanation Corectanswer : Value Frequency 12 1 13 1 14 3 15 6 16 23 17 29 18 19 19 15 20 3 Value Frequency 0 5 1 16 2 23 3 19 4 22 5 9 6 4 7 2 Rememberthatdataareleftskewedi fthereisamain concentrationoflargevalueswith severalmuchsmallervalues.Similarly, rightskew eddatahaveamainconcentrationoF smalivalueswithseveralmuchlargervalues.Weca nse thathefollowingislefre skewedbecauseoftheconcentrationoflargevalue swithmanysmallervalues: Value Frequency 12 1 13 1 14 3 15 6 Theresultsarestatisticalysigni ficantatheo.05 levelofsigni ficanceinshowingthat theproportionofpeopl nruralareaswhowanthed efendingchampi onstowinthe i gQameisdifferenthantheproportionofpeopleinurba nNareas. nh t n c Thedataisnotstatisticalysigni ficantatheo.05 levelofsigni ficanceinshowingthat theproportionofpeopleinruralareaswhowanthed efendingchampionsto nt i rtionofpeopleinurba nareas. AnswerExplIanation Corectianswer: Theresultsarestatisticallysignificantat he0.05 levelofsigni ficanceinshowingthat TREBFSBSEETI PEG TAT CeLS OH SUEYISD D8 OPM Psistes sthan0.05, soweconcludethat thedataarestatisticallysignificantinshowingth atheproportionofpeopleinruralareas whowanthedefendingchampionstowinthegameisdi fferenthantheproportionof peopleinurbanareas. QUEST ION42 1/1POENTS Inapsychologicalstudyaimedatestingadrugthat reducesanxiety, theresearcher groupedtheparticipantsinto2 groupsandgavetheanxiety- reductionpi #toonegroup andaninertpi #toanothergroup.Whichgrouprecei hatiscorect! C thegroupthatrecei vedt Rieanxiety- feductionpil thepsychologicalstudy allthepeopleinthestudy © thegroupthatreceivedtheinertpil AnswerExplIanation Byusingtheknowntotalsalongtherowsand columnsyoucanfilintherestofthe contingencytable.Forexample,lo kingathesecondrowinthetable, weknow that33 ad edtotheunknownnumberinthemid leis67, sothatunknownnumber 1s34.Continuinginthisway,wecanfilintheentiret able: StudentsplaysportsdonotplaysportsT otal playaninstrument273 Odonotplayaninstrument353469 otal6267129 Fromthis,wecanse thathenumberofstudentswhobothdonotplaysport Sanddo notplayaninstrumentis34. FEEDBACK Content attribution- Opens a dialog QUEST ION4S 1/1POENTS Filinthefolowingcontingencytableandfindthenu mberofstudentswhobothdonot PplaysportsANDdonotplayaninstrument. Studentsplaysportsdonotpla sports otalplayaninstrument33d onotplayaninstrument69T otal6267 $$34 AnswerExplIanation Corecttanswers: ba $34$34 Byusingtheknowntotalsalongtherowsandcolumns youcanfilintherestofthe contingencytable.Forexample,lo kingathesecondrowinthetable, weknow that33 ad edtotheunknownnumberinthemid leis67, sothatunknownnumber i $34 -Continuinginthisway,wecanfilintheenti ret able: StudentsplaysportsdonotplaysportsT otalplayaninstru ment273 360donotplayaninstrument3534697 otal6267129 Fromthis,wecanse thathenumberofstudentswhobothdonotplaysport Sanddo notplayaninstrumentis34. QUEST EON4G6 1/1 POENTS Theanswerchoicesbelo nthypothesistests.Wh areleft-tailedtestser Selectallcorectanswers. r a5 Ho:X=17.3 , Ha:X#17.3 w Ho:X219.7, Ha:X<19.7 i Ho:X211.2, Ha:X<11.2 Ho:X=13.2, Ha:X#13.2 r Ho:X=17.8, Ha:X#17.8 AnswerExplIanation Corectianswer: Ho:X219.7, Ha:X<19.7 Hak mehhte HeXstbemsoFfth ehypothesistests. * Right-tai led -:Ho:XsXo, Ha:X>Xo. * Left-tai led: Ho:X=Xo, Ha:X<Xo. * Two-tai led -: Ho:X=Xo, Ha:X#Xo - Sointhiscase,theleft-tailedtestsare: ¢ Ho:X211.2, Ha:X<11.2 * Ho:X219.7, Ha:X<19.7 QUEST ION47 1/1POENTS Assumethenu phy pothes is,Ho,is:Jacobearnsenoug hmoneytoaffordaluxury . . . apartment .FindtheTypelterrorinthisscenario. ThestandarddeviationsofA andB areequal . AnswerExplIanation Corectanswer : ThemeansofA andB areequal . Remehbetencensheaderddermiatd pstributionisth ex-valueofitscentralpointcthe topofthe"hil''>).Therefore,adistributionwitha largermeanwi §becenteredfartherto therighthanadistributionwithasmalliermean. BecauseA andB arecenteredathesamepoint, theirmeansareequa I. RememberthathestandarddeviationtelShowsprea douthenormaldistributionis.So ahighstandarddeviationmeansthegraphwi lbesho rtandspreadout -.Alowstandard deviationmeansthegraphwi §lbetallandskiny. BecauseA isshorterandmorespreadouthanB, wefindt hatA hasthelarger standarddeviation. QUEST ION49 1/1POENTS Hugoaverages/2 . . wordsperminuteonatypingtestwithast andarddeviation of12 wordsperminute. Sup oseHugo" swordsperminuteonatypingte stare normallydistributed.LetX= thenumberofwordsperminuteonatyping test. Then, X~N(72,12) - Sup oseHugotypes54 wordsperminuteinatypingtestonWwednesda y -Thez-score whenx=54 is -Thisz- scoretelsyouthatx=54 is standard deviationstothe Cright/leftt Jofthemean, - Sup oseHugotypess54 - wordsperminuteinatypingtestonwednesday -Thezscore whenx=54 §Ss—-1.2.- Thi sz- scoreteEsyouthatx=54 is1.2 standarddeviationsto theleftofthemean, 72. ec Sup oseHugotypes54 - wordsperminuteinatypingtestonWwednesday - Thezscore whenx=54 9s1.2.- Thi sz- scoretessyouthatx=54 isl.2 ec tandarddeviationsto “Nerightofthemean,72. Sup oseHugotypes54 - wordsperminuteinatypingtestonwednesday -Thezscore whenx=54 9s1.5.-Thisz- scoreteisyouthatx=54 is1.5 standarddeviationsto therightofthemean,?72. e Sup oseHugotypes54 - wordsperminuteinatypingtestonwednesday - Thez-score whenx=54 §S—1.5.ThHisz- scoretelEsyouthatx=54 is1.5 standarddeviationsto theleftofthemean, 72. AnswerExplIanation Corectianswer: Sup oseHugotypes54 . wordsperminuteinatypingtestonWwednesda y -Thez-score whenx=54 is—1.5.Thisz- scorete ls youthatx=54 is1.5 Thez-scorecanbeFoundusingtheformula z=x—yo=54—7212=—-1812=-1.5 Anegativevalueofz . meansthathathevalueisbelowCortotheleftof oth emean, whichwasgivenintheproblem asy=72 wordsperminuteinatypingtest.Thez- scoreteEsyouhowmanystandarddeviationstheval uex isaboveCtotherightof or belowCtotheleftof pthemean,UW.So,typing54 wordsperminuteis1l.5 standard deviationsaway from themean. QUEST ION50 or Mo for 30 stars. The absolute magnitude of a star is the intensity of light that would be observed from the star at a distance of 10 parsecs from the star. This is measured in terms of a particular band of the light spectrum, indicated by the subscript letter, which in this case is V for the visual light spectrum. The scale is logarithmic and an Mv that is 1 less than another comes from a star that is 10 times more luminous than the other. The stellar mass of a star is how many times the sun's mass it has. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets, rounding to two decimal places. Correct! You nailed it. r=—0.93 Answer Explanation The correlation coefficient, rounded to two decimal places, is r=—0.93. A market researcher looked at the quarterly sales revenue for a large e-commerce store and for a large brick-and-mortar retailer over the same period. The researcher recorded the revenue in millions of dollars for 30 quarters. The data are provided below. Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places. Yes that's right. Keep it up! Answer Explanation The correlation coefficient, rounded to two decimal places, is r=—0O.81. The table below contains the geographic latitudes, X, and average January temperatures, y, of 2Ocities. Use Excel to find the best fit linear regression equation. Round the slope and intercept to two decimal places. x y 46 23 32 60 39 40 33 59 38 57 40 33 42 33 30 64 34 56 HelpCopy to ClipboardDownload CSV Yes that's right. Keep it up! y = —2.68, x147.24 Thus, the equation of line of best fit with slope and intercept rounded to two decimal places is y°=—2.68x+147.24. An organization collects information on the life expectancy (in years) of a person in certain countries and the fertility rate per woman in those countries. The data for 21 randomly selected countries for the year 2011 is given below. Use Excel to find the best fit linear regression equation, where fertility rate is the explanatory variable. Round the slope and intercept to two decimal places. y = -4.21, x 83.68 AnSwer Explanationy*=—4.21, x+83.68. y = 2.89, x 4.69 Thus, the equation of line of best fit with slope and intercept rounded to two decimal places is y“=2.86x+4.69. In the following table, the age (in years) of the respondents is given as the X value, and the earnings (in thousands of dollars) of the respondents are given as the y value. Use Excel to find the best fit linear regression equation in thousands of dollars. Round the slope and intercept to three decimal places. Yes that's right. Keep it up! y = 0.433, x=24.493 Answer Explanation Thus, the equation of line of best fit with slope and intercept rounded to three decimal places is y°-=0.433x+24.493. PREDICITONS USING LINEAR REGRESSION Question The table shows data collected on the relationship between the time spent studying per day and the time spent reading per day. The line of best fit for the data is y°=0.16x+36.2. Assume the line of best fit is significant and there is a strong linear relationship between the variables. Studying (Minutes) 507090110 Reading (Minutes) 44485054 (a) According to the line of best fit, what would be the predicted number of minutes spent reading for someone who spent 67 minutes studying? Round your answer to two decimal places. Yes that's right. Keep it up! The predicted number of minutes spent reading is $$46.92. Answer Explanation The predicted number of minutes spent reading is $$. Correct answers: o 46.92 Substitute 67 for X into the line of best fit to estimate the number of minutes spent reading for someone who spent 67 minutes studying: y-=0.16(67)+36.2=46.92. Question The table shows data collected on the relationship between the time spent studying per day and the time spent reading per day. The line of best fit for the data is y°=0.16x+36.2. Studying (Minutes) 507090110 Reading (Minutes) 44485054 (a) According to the line of best fit, the predicted number of minutes spent reading for someone who spent 67 minutes studying is 46.92. (b)\s it reasonable to use this line of best fit to make the above prediction? hat's incorrect - mistakes are part of learning. Keep trying! cy The estimate, a predicted time of 46.92 minutes, is both reliable and reasonable. CC The estimate, a predicted time of 46.92 minutes, is both unreliable and c unreasonable. The estimate, a predicted time of 46.92 minutes, is reliable c but unreasonable. The estimate, a predicted time of 46.92 minutes, is unreliable but reasonable. Answer Explanation