MATH 225N Week 4 Statistics Quiz - Question and Answers, Exams of Mathematics

Download MATH 225N Week 4 Statistics Quiz - Question and Answers and more Exams Mathematics in PDF only on Docsity! Thatiscorect! Thatiscorect! MATH 225N Week 4 Statistics Quiz – Question and Answers 1/1POINTS Afitnesscenterclaimsthathemeanamounto ftimethatapersonspendsathegym pervisitis33 minutes.Identifythenulhypothesis,H0,a ndthealternative hypothesis,Ha,intermsoftheparameterμ. H0:μ≠33;Ha:μ =33 H0:μ=33;Ha:μ ≠33 H0:μ≥33;Ha:μ <33 H0:μ≤33;Ha:μ>33 AnswerExplanation Corectanswer: H0:μ=33;Ha:μ≠33 Letheparameterμ beusedtorepresenthemean.Thenulhypothesisisa lways statedwithsomeform ofequality:equal(=),greaterthanorequalto(≥ ),orlessthan orequalto(≤).Therefore,inthiscase,thenulhyp othesisH0 isμ=33.The alternativehypothesisiscontradictorytothenu lhypothesis,soHa isμ≠33. QUESTI ON2 1/1POI NTS Theanswerchoicesbelowrepresentdiffere nthypothesistests.Whichofthechoices areright-tailedtests? Selectalcorrectanswers. MATH 225N Week 4 Statistics Quiz – Question and Answers • H0:X≥17.1,Ha:X<17.1 MATH 225N Week 4 Statistics Quiz – Question and Answers Ierroristhedecisionnotorejecthenulhypothesi swhen,infact,itisfalse.In thiscase,theType Ierroriswhenthebuildinginspectorthinksthatno more • $\text{Test statistic = }-2.24$Test statistic = −2.24 Thebuildinginspectorthinksthatmorethan 15% ofthestructuresinthecountywere builtwithoutpermitswhen,infact,atmost1 5% ofthestructureswerebuiltwithout Thatiscorect! $$Test statistic = −2.24 MATH 225N Week 4 Statistics Quiz – Question and Answers than15% ofthestructureswerebuiltwithoutpermi tswhen,infact,more than15% ofthestructureswerebuiltwithoutpermi ts. Youranswer: Content attribution- Opens a dialog QUESTI ON4 1/1POI NTS Sup oseachefclaimsthathermeatbalweightisle ssthan4 ounces,onaverage. Severalofhercustomersdonotbelieveher,s othechefdecidestodoahypothesistest, ata10% significancelevel,topersuadethem.Sheco ks14 meatbals.Themean weightofthesamplemeatbalsis3.7 ounces.Thechefknowsfrom experiencethathe standarddeviationforhermeatbalweightis 0.5 ounces. • H0:μ≥4;Ha:μ<4 • α=0.1 (significancelevel) Whatistheteststatistic(z- score)ofthisone- meanhypothesistest,roundedtotwo decimalplaces? AnswerExplanation Corectanswers: Thehypotheseswerechosen,andthesignificancele velwasdecidedon,sothenext MATH 225N Week 4 Statistics Quiz – Question and Answers stepinhypothesistestingistocomputethetestst atistic.Inthisscenario,thesample meanweight,x¯=3.7.Thesamplethechefusesis14 meatbals,son=14.She knowsthestandarddeviationofthemeatbals,σ=0.5 .Lastly,thechefiscomparing thepopulationmeanweighto4 ounces.So,thisvalue(foundinthenulandalterna tive Thatiscorect! MATH 225N Week 4 Statistics Quiz – Question and Answers • α=0.04 (significancelevel) • z0=−1.75 • p=0.0401 Donotrejecthenulhypothesisbecausethep- value0.0401 isgreaterthanthe MATH 225N Week 4 Statistics Quiz – Question and Answers Donotrejecthenulhypothesisbecausethep- value0.0401 isgreaterthanthe significancelevelα=0.04. Rejecthenulhypothesisbecausethep-value0.0401 isgreaterthanthesignificance levelα=0.04. Rejecthenulhypothesisbecau sethevalueofz isnegative. Rejecthenulhypothesisbecau se|−1.75|>0.04. Donotrejecthenulhypothesisbecause|−1.75|>0.04. AnswerExplanation Corectanswer: Inmakingthedecision orejectornotreject H0,ifα>p-value,rejectH0 becausethe resultsofthesampledataaresignificant.Th ereissufficientevidencetoconclude thatH0 isanincorrectbeliefandthathealternati vehypothesis,Ha,maybecorrect. Ifα≤p- value,donotrejectH0.Theresultsofthesam pledataarenotsignificant,so thereisnotsufficientevidencetoconcludeth athealternativehypothesis,Ha,maybe correct.Inthiscase,α=0.04 islessthanorequaltop=0.0401,sothedecisio nis tonotrejecthenulhypothesis. QUESTI ON7 1/1POI NTS Arecentstudysugestedthat81% ofseniorcitizenstakeatleastoneprescrip tion medication.Ameliaisanurseatalargehospi talwhowouldliketoknowwhetherthe percentageisthesameforseniorcitizenpat ientswhogotoherhospital.Sherandomly selects59 seniorcitizenspatientswhoweretreatedat Thatiscorect! MATH 225N Week 4 Statistics Quiz – Question and Answers hehospitalandfindsthat49 of them takeatleastoneprescriptionmedication.Whatar ethenulandalternative hypothesesforthishypothesistest? • $\text{Test_Statistic}=-0.53$Test_Statistic=−0.53 Thatiscorect! $$Test_Statistic=−0.53 MATH 225N Week 4 Statistics Quiz – Question and Answers Findtheteststatisticforthishypothesi stestforaproportion.Roundyouranswer to2 decimalplaces. AnswerExplanation Corectanswers: Theproportionofsucessesisp ^=951000=0.095. Theteststatisticiscalculat edasfolows: z=p^−p0p0⋅(1−p0)n−−−−−−√ z=0.095−0.100.10⋅(1−0.10)1000−−−−−−−−√ z≈−0.53 QUESTI ON9 1/1POI NTS Amedicalresearcherclaimsthatheproportionofp eopletakingacertainmedication thatdevelopserioussideeffectsis12%.Totesthis claim,arandom sampleof90 peopletakingthemedicationistakenanditisdete rminedthat93peoplehave experiencedserioussideeffects. Thefolowingisthesetupforthishypothesistest: H0:p=0.12 Ha:p≠ 0.12 Findthep- valueforthishypothesistestforapropor MATH 225N Week 4 Statistics Quiz – Question and Answers tionandroundyouranswerto3 decimalplaces. • $\text{P-value=}0.124$P-value=0.124 Thatiscorect! $$P-value=0.124 MATH 225N Week 4 Statistics Quiz – Question and Answers Thefolowingtablecanbeutilizedwhichpro videsareasundertheStandardNormal 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 -1.5 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.056 -1.4 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.068 AnswerExplanation Corectanswers: Herearethestepsne dedtocalculatethep- valueforahypothesistestforaproportion: 1.Determineifthehypothesistestisleftailed, rightailed,ortwotailed. 2.Computethevalueoftheteststatistic. 3.Ifthehypothesistestisleftailed,thep- valuewilbetheareaunderthestandard normalcurvetothel e f t oftheteststatisticz0 Ifthetestisrightailed,thep- valuewilbetheareaunderthestandardnormal curvetother i g h t oftheteststatisticz0 Ifthetestistwotailed,thep- valuewilbetheareatotheleftof−|z0|p l u s the areatotherightof|z0| underthestandardnormalcurve Forthisexample,thetestisatwotailedte standtheteststatistic,roundingtotwo decimalplaces,isz=0.1033−0.120.12(1−0.12)900 −−−−−−−−− −−−√≈−1.54. Thatiscorect! MATH 225N Week 4 Statistics Quiz – Question and Answers ThedecisionistorejectheNulHypothesis . Theconclusionisthathereisenoughevide ncetosup ortheclaim. ThedecisionistofailtorejectheNulHypothesis. Theconclusionisthathereisnotenoughevidencet osup ortheclaim. AnswerExplanation Corectanswer: Tocometoaconclusionandinterpretheres ultsforahypothesistestforproportion usingtheP-ValueAp roach,thefirststepistocomparethep- valuefrom thesample datawiththelevelofsignificance. Thedecisioncriteriaisthenasfolows: Ifthep- valueislessthanorequaltothegivensignificance level,thenthenul hypothesisshouldberejected. So,ifp≤α,rejectH0;otherwisefailtorejectH0. Whenwehavemadeadecisionabouthenulhypothesis ,itisimportantowritea thoughtfulconclusionabouthehypothesesinterm softhegivenproblem'sscenario. Assumingtheclaim isthenulhypothesis,theconclusionisthenoneof thefolowing: • ifthedecisionistorejecthenulhypoth esis,thentheconclusionisthathereis enoughevidencetorejectheclaim. • ifthedecisionistofailtorejecthenul hypothesis,thentheconclusionistha t thereisnotenoughevidencetorejecth ThedecisionistorejectheNulHypothesis. Theconclusionisthathereisenougheviden MATH 225N Week 4 Statistics Quiz – Question and Answers eclaim. Assumingtheclaim isthealternativehypothesis,theconclu sionisthenoneofthe folowing: Thatiscorect! MATH 225N Week 4 Statistics Quiz – Question and Answers • ifthedecisionistorejecthenulhypoth esis,thentheconclusionisthathereis enoughevidencetosup ortheclaim. • ifthedecisionistofailtorejecthenul hypothesis,thentheconclusionistha t thereisnotenoughevidencetosup ortheclaim. Inthisexample,thep- value=0.026.Wethencomparethep- valuetothelevelof significancetocometoaconclusionforthehypothe sistest. Inthisexample,thep- valueislessthanthelevelofsignificancewhichis 0.05. Sincethep- valueisgreaterthanthelevelofsignificance,the conclusionistor e j e c t h e n u l h y p o t h e s i s . QUESTI ON1 1/1POI NTS Becky'sstatisticsteacherwasteachingt heclasshowtoperform thez-testfora proportion.Beckywasboredbecauseshehad alreadymasteredthetest,soshe decidedtose ifthecoinshehadinherpocketwouldcomeup headsortailsinatruly random fashionwhenflip ed.Shediscretelyflip edthecoin30 timesandgot heads18 times. Beckyconductsaone- proportionhypothesistestathe5% significancelevel,totest whetherthetrueproportionofheadsisdifferentfro m 50%. Whichanswerchoiceshowsthecorrectnulandalter MATH 225N Week 4 Statistics Quiz – Question and Answers Johnchargesaone-timefe of$45 (thisiswhenx=0),sothey- interceptis45.John earns$50 foreachhourheworks,sotheslopeis50. Theindependentvariable(x)istheamount,indola rs,Johnearnsforacomputer.The dependentvariable(y)istheamountoftimeJohnfixe sacomputer. Theindependentvariable(x)istheamounto ftimeJohnfixesacomputer.The dependentvariable(y)istheamount,indol ars,Johnearnsforacomputer. Johnchargesaone-timefe of$50 (thisiswhenx=0),sothey-interceptis50. MATH 225N Week 4 Statistics Quiz – Question and Answers Johnchargesaone-timefe of$50 (thisiswhenx=0),sothey- interceptis50.John earns$45 foreachhourheworks,sotheslopeis45. Theindependentvariable(x)istheamountoftimeJ ohnfixesacomputer.The dependentvariable(y)istheamount,indolars,Jo hnearnsforacomputer. Johnchargesaone-timefe of$45 (thisiswhenx=0),sothey- interceptis45.John earns$50 foreachhourheworks,sotheslopeis50. AnswerExplanation Corectanswer: Theindependentvariable(x)istheamountoftimeJ ohnfixesacomputerbecauseitis thevaluethatchanges.Hemayworkdifferentamount spercomputer,andhisearnings aredependentonhowmanyhoursheworks.Thisiswhy theamount,indolars,John earnsforacomputeristhedependentvariable(y). They-interceptis50 (b=50).Thisishisone- timefe.Theslopeis45 (a=45). Thisistheincreaseforeachhourheworks. QUESTI ON13 1/1POIN TS Arianake pstrackoftheamountoftimeshestudiesandthesco reshegetsonher quizzes.Thedataareshowninthetablebelow.Whic hofthescaterplotsbelow acuratelyrecordsthedata? Hoursst udying Quizs core MATH 225N Week 4 Statistics Quiz – Question and Answers 1 5 2 5 3 7 4 9 MATH 225N Week 4 Statistics Quiz – Question and Answers parenthesis9comma5right- parentheses.Alvaluesareap roximate. MATH 225N Week 4 Statistics Quiz – Question and Answers AscaterplothasahorizontalaxislabeledHo ursstudyingfrom 0to6inincrementsof1 andaverticalaxislabeledQuizscorefrom 0to9inincrementsof1.Thefolowing pointsareploted:left- parenthesis1comma5right- parentheses;left-parenthesis2 comma5right-parentheses;left- parenthesis3comma7right- parentheses;left- parenthesis4comma8right- parentheses;left- parenthesis5comma8right- parentheses. AscaterplothasahorizontalaxislabeledHo ursstudyingfrom 0to6inincrementsof1 andaverticalaxislabeledQuizscorefrom 0to12inincrementsof2.Thefolowing pointsareploted:left- parenthesis1comma5right- parentheses;left-parenthesis2 comma5right-parentheses;left- parenthesis3comma8right- parentheses;left- parenthesis4comma8right- parentheses;left-parenthesis5comma1 right- parentheses.Alvaluesareap roximate. AnswerExplanation Corectanswer: AscaterplothasahorizontalaxislabeledHoursstudyingfrom 0to6inincrementsof1 andaverticalaxislabeledQuizscorefrom 0to10inincrementsof2.Thefolowing pointsareploted:left-parenthesis1comma5right-parentheses;left-parenthesis2 comma5right-parentheses;left-parenthesis3comma7right-parentheses;left- parenthesis4comma9right-parentheses;left-parenthesis5comma9right- parentheses.Alvaluesareap roximate. MATH 225N Week 4 Statistics Quiz – Question and Answers Thevaluesforhoursstudyingcorrespondt ox-values,andthevaluesforquizscore correspondtoy- values.Eachrowofthetableofdatacores pondstoa point(x,y) plotedinthescaterplot.Forexample,thefirstrow, 1,5,correspondsto thepoint(1,5).Doingthisforeveryrowinthetable, wefindthescaterplotshould havepoints(1,5),(2,5), (3,7),(4,9),and(5,9). QUESTI ON14 1/1POIN TS Dataiscolectedontherelationshipbetwe ntimespentplayingvideogamesandtime That'snotright. MATH 225N Week 4 Statistics Quiz – Question and Answers TS Whichofthefolowingarefeasibleequation sofaleastsquaresregressionlineforthe an ualpopulationchangeofasmalcountryfrom theyear2000 totheyear2015? Selectalthatap ly. yˆ=38,000+2500x yˆ=38,000−1500x MATH 225N Week 4 Statistics Quiz – Question and Answers • yˆ=38,000+2500x • • yˆ=38,000−3500x • • yˆ=−38,000+2500x • • yˆ=38,000−1500x • AnswerExplanation Corectanswer: Populationchangecanbepositiveornegati ve,anditcanincreaseordecrease.Based onthegiveninformation,therearenopracti calimitstopopulationchange,although therearelimitssuchasthedecreaseinpopu lationcan otexce dthecurentpopulation (asitwouldleaveanegativenumberofpeopl einthecountry),ortheincreasein populationcouldbelimitedbyothereal- worldfactors(suchaslackofspaceorlegal immigrationlimits). MATH 225N Week 4 Statistics Quiz – Question and Answers Youranswer: yˆ=38,000+2500x QUESTI ON17 1/1POIN TS Anamateurastronomerisresearchingstati sticalpropertiesofknownstarsusinga varietyofdatabases.Theycolecthecolori ndex,orB−V index,anddistance(inlight years)from Earthfor30 stars.Thecolorindexofastaristhedifferen ceinthelight absorptionmeasuredfrom thestarusingtwodifferentlightfilters(aBa ndaVfilter). Thisthenalowsthescientistoknowthestar 'stemperatureandanegativevalue meansahotbluestar.Alightyearisthedist ancelightcantravelin1 year,whichis ap roximately5.9 trilionmiles.Thedataisprovidedbelow.U seExceltocalculatethe correlationcoefficientr betwe nthetwodatasets,roundingtotwodecimalp laces. B-Vindex Distance(ly) 1.1 1380 0.4 5 6 1.0 7 1 0.5 304 1.4 532 1.0 751 0.5 267 0.8 2 9 MATH 225N Week 4 Statistics Quiz – Question and Answers 19.5 40.0 23.6 1 2 • • 1$-1.181$−1.181 2$71.374$71.374 MATH 225N Week 4 Statistics Quiz – Question and Answers 45.0 16.7 25.0 42.2 5 .0 13.2 17.5 65.4 HelpCopytoClipboa rdDownloadCSV That'snot right. y=$$1.181 x+$$71.374 AnswerExplanation y= $$ x+ $$ Corectanswers: Tofindthebestfitforthegivendata,useExcel. 1. OpenExcel.Enterthevaluesofweighti ncolumnAandmileageincolumnB. Highlightalthecelscontainingthedat a. 2. From theInsertab,selectScater.UseScaterwit honlyMarkers,thefirstypeof scaterchart.Asimpleplotisshown. 3. Toad thelinearfitothegraph,clickanywhereinsi dethegrapharea.Select theLayouttabfrom theChartTo ls.ClickontheTrendlineiconandselectheL inear Trendlineoption.Thelineofbestfitisad edtothegraph. 4. Fortheequationofthelineofbestfit,clic konTrendlineandselectMoreTrendline MATH 225N Week 4 Statistics Quiz – Question and Answers Options .. Thatiscorect! MATH 225N Week 4 Statistics Quiz – Question and Answers QUESTI ON20 1/1POIN TS Totestheeffectivenessofadrugproposedtoreliev esymptomsofheadache, physiciansincludedparticipantsforastudy.The ygavethedrugtoonegroupandadrug withnotherapeuticeffectoanothergroup.Whichgr oupreceivestheplacebo? thephysicians thegroupthatreceivedthedru gforheadache thegroupthatreceivedthedru gwithnotherapeuticeffect alofthepeopleinthestudy AnswerExplanation Corectanswer: thegroupthatreceivedthedrugwithnotherapeuti ceffect Whentheexperimentalunitsarepeople,ap lyingtreatmentsthatshouldbeinertcan actualyhaveeffects.Inthisstudy,thedrugwithno therapeuticeffectsistheplacebo,so thegroupthatreceivesthatdrugreceivestheplac ebo. QUESTI ON21 1/1POIN TS Thatiscorect! MATH 225N Week 4 Statistics Quiz – Question and Answers Adoctornotesherpatient'stemperatureindegre sFahrenheiteveryhourtomakesure thepatientdoesnotgetafever.Whatisthelevelof measurementofthedata? nominal That'snotright. MATH 225N Week 4 Statistics Quiz – Question and Answers ordinal int erv al rat io AnswerExplanation Corectanswer: interval Thisisintervaldatabecausedegre sFahrenheitisanumericalscalewherediffer ences aremeaningful.However,becauseFahrenhe itdoesnothaveatruezerovalue,itisnot ratiodata. QUESTI ON2 0/1POI NTS Asamemberofamarketingteam,youhavebe ntaskedwithdeterminingthenumber ofDVDsthatpeoplehaverentedoverthepastsixmon ths.Yousampletwentyadults anddecidethathebestdisplayofdataisafrequenc ytableforgroupeddata.Construct thistableusingfourclasses. 15,31,28,19,14,18,28,19,10,19,10,24,14,18,24,27,10,18,16,2 3 Lower Class Limit Upper Class Limit $$10 $$15 $$16 $$21 MATH 225N Week 4 Statistics Quiz – Question and Answers Tofindthefrequencyforeachclass,counthen umberofdatavaluesthatfalwithinthe rangeofeachclass.Forexample,thedatava lues15,14,10,10,14,and10falwithin therangeofthefirstclass,10- 15.So,thefrequencyofthisclassis6. QUESTION2 3 1/1POINTS Thehistogram belowdisplaystheweightsofrainbowtrout(inpounds)ca ughtbyal visitorsatalakeonaSaturdayafterno n.Acordingtothishistogram,whichrangeof weights(inpounds)containsthelowestfrequency? Lower Class Limit Upper Class Limit Frequency 10 15 6 16 21 7 22 27 4 28 33 3 • $\text{greater than }12.5\ \text{but less than }14.5$greater than 12.5 but less than 14.5 Thatiscorect! $$greater than 12.5 but less than 14.5 MATH 225N Week 4 Statistics Quiz – Question and Answers Ahistogram hasaverticalaxislabeledFrequencyandha sahorizontalaxisthat measuressixcategoriesofrainbowtroutwei ght(inpounds).Readingfrom left-to-right, theweightandfrequencyofeachcategoryar e:4.5to6.5hasfrequencyof4,6.5to8.5 hasfrequency5,8.5to10.5hasfrequency7, 10.5to12.5hasfrequency3,12.5to14.5 hasfrequency1,14.5to16.5hasfrequency2 . AnswerExplanation Corectanswers: Thatiscorect! MATH 225N Week 4 Statistics Quiz – Question and Answers Therange12.5−14.5 hasthelowestbarinthehistogram,whichm eansthathis rangeofvaluesalsohasthelowestfrequen cy.Therefore,1 visitorcaughtarainbow trouthatweighedgreaterthan12.5 butlessthan14.5 pounds. QUESTI ON24 1/1POIN TS Describetheshapeofthegivenhistogram. Ahistogram hasahorizontalaxisfrom 0to16inincrementsof2andaverticalaxis labeledFrequencyfrom 0to10inincrementsof2.Thehistogram containsverticalbars ofwidth1startingathehorizontalaxisvalu e0.Theheightsofthebarsareasfolows, wherethelefthorizontalaxislabelisliste dfirstandthefrequencyislistedsecond:0,0 ; 1,0;2,6;3,6;4,7;5,6;6,6;7,6;8,7;9,6;10 ,6;1 ,6;12,6;13,7;14,0;15,0. uniform unimodalands ymmetric unimodalandl eft-skewed MATH 225N Week 4 Statistics Quiz – Question and Answers answer. • $23$23 Thatiscorect! $$23 MATH 225N Week 4 Statistics Quiz – Question and Answers AnswerExplanation Corectanswers: TofindthenumberofstudentsinMs.James'scl ass,findtheheightsofthebarsforthat classandad them.Inthiscase,wefinditis11+12=23. QUESTI ON26 0/1POIN TS Thelinegraphshownbelowrepresentsthenu mberofTVsinahousebysquare fo tage(inhundredsofet).Acordingtotheinf ormationabove,whichofthefolowing isanap ropriateanalysisofsquarefo tageandTVs? That'snotright. MATH 225N Week 4 Statistics Quiz – Question and Answers Alinegraphhasanx-axislabeledSquareFo tage(inhundredsofet)inincrementsof one,anday- axislabeledNumberofTV'sinincrementsofo ne.Begin ingathepoint startparentheses6,2endparentheses,alin eincreasestothepointstartparentheses 8.5,3endparentheses.Thelineremainscons tantothepointstartparentheses10,3 endparentheses.Thelinethenincreases,pa ssingthroughthepointstartparentheses 12,5end parenthesesandcontinuesincreasinguntil itreachesthepointstart parentheses16,6endparentheses. From thedata,thenumberofTVsdoubledfrom asquarefotageof8.5 and10. From • $\text{median=}26\text{ thousands of dollars}$median=26 thousands of dollars Thatiscorect! $$median=26 thousands of dollars MATH 225N Week 4 Statistics Quiz – Question and Answers Rememberthathemeanisthesum ofthenumbersdividedbythenumberof numbers.Thereare5 numbersinthelist.Sowefindthathemeanboxessold is QUESTI ON28 1/1POIN TS Giventhefolowinglistofprices(inthousandsofdo lars)ofrandomlyselectedtrucksat acardealership,findthemedian. 20,46,19,14,42,26,33 AnswerExplanation Corectanswers: Ithelpstoputhenumbersinorder. 14,19,20,26,33,42,46 Now,becausethelisthaslength7,whichisod ,weknowthemediannumberwilbe themid lenumber.Inotherwords,wecancountoitem 4 inthelist,whichis26.So themedianprice(inthousandsofdolars)ofr andomlyselectedtrucksatacar dealershipis26. QUESTI ON29 1/1POIN TS Eachpersoninagroupshufflesadeckofcardsan dke psselectingacarduntila que nap ears.Findthemodeofthefolowingnumberofc ardsdrawnfrom adeckuntil aque nap ears. Thatiscorect! MATH 225N Week 4 Statistics Quiz – Question and Answers 3,12,3,11,5,5,3,10,12 • $\text{mode=}3\text{ cards}$mode=3 cards $$mode=3 cards MATH 225N Week 4 Statistics Quiz – Question and Answers AnswerExplanation Corectanswers: Ifwecounthenumberoftimeseachvalueap earsinthelist,wegethefolowing frequencytable: Value Frequency 3 3 5 2 10 1 11 1 12 2 Notethat3 ocurs3 times,whichisthegreatestfrequency,so3 isthemodeofthe numberofcardsdrawnfrom adeckuntilaque nap ears. QUESTI ON30 1/1POIN TS Giventhefolowinghistogram,decideifthedatais skewedorsymmetrical. MATH 225N Week 4 Statistics Quiz – Question and Answers Corectanswer: Thedataaresymmetric. Notethathehistogram ap earstoberoughlysymmetric.Sothedataare symmetric. QUESTI ON31 1/1POIN TS Whichofthedatasetsrepresentedbythefolowingb oxandwhiskerplotshasthe smaleststandarddeviation? Fourhorizontalbox-and- whiskerplotsshareaverticalaxiswiththec lassesD,C,B,and Aandahorizontalaxisfrom 0to120inincrementsof20.Thebox-and- whiskerplot abovetheclasslabelAhasthefolowingfive- numbersummary:4 ,69,7 ,82,and1 2. MATH 225N Week 4 Statistics Quiz – Question and Answers Thebox-and- whiskerplotabovetheclasslabelBhasthe folowingfive-number summary:19,64,78,87,and121.Thebox-and- whiskerplotabovetheclasslabelC hasthefolowingfive- numbersummary:60,72,75,80,and92.Thebo x-and-whisker Thatiscorect! MATH 225N Week 4 Statistics Quiz – Question and Answers plotabovetheclasslabelDhasthefolowingfive- numbersummary:2,63,7 ,92,and 138.Alvaluesareap roximate. A B C D AnswerExplanation Corectanswer: C Rememberthathestandarddeviationisamea sureofhowspreadouthedatais.Ifthe valuesareconcentratedaroundthemean,th enadatasethasalowerstandard deviation. Aboxandwhiskerplotwithshortwhiskersandashort boxhasvaluesthatareless spreadout,andhencehasasmalerstandarddeviati on. QUESTI ON32 1/1POIN TS Thegraphbelowshowsthegraphsofseveralnor maldistributions,labeledA,B,andC, onthesameaxis.Determinewhichnormaldistr ibutionhasthesmaleststandard deviation. Thatiscorect! MATH 225N Week 4 Statistics Quiz – Question and Answers 1/1POINTS Braydentossesacoin500 times.Ofthose500 times,heobservesheadsatotal of416 times.Calculationsshowthatheprobabilit yofthisocurringbychanceisless than0.01,assumingthecoinisfair.Determin ethemeaningofthesignificancelevel. Weexpecthat416 ofevery500 cointosseswilresultinheads. Athe0.01 levelofsignificance,thecoinislike lynotafaircoin. Thereiscertaintythathecoinisnota faircoin. Theresultsarenotstatisticalysignificantathe0.0 5 levelofsignificance. AnswerExplanation Corectanswer: Athe0.01 levelofsignificance,thecoinislikelynotafairco in. Theresultsoftheexperimentaresignificantathe0. 01 levelofsignificance.This meanstheprobabilitythatheoutcomewastheresul tofchanceis0.01 orless. Becauseofthis,wecanbefairlyconfident,butnotc ertain,thathecoinisnotafair coin. QUESTI ON34 1/1POIN Thatiscorect! MATH 225N Week 4 Statistics Quiz – Question and Answers TS Isthestatementbelowtrueorfalse? Independentisthepropertyoftwoeventsinwhicht heknowledgethatoneoftheevents ocurreddoesnotaffecthechancetheotherocurs. Thatiscorect! MATH 225N Week 4 Statistics Quiz – Question and Answers True False AnswerExplanation Corectanswer: True Independentisdefinedasthepropertyoftwoe ventsinwhichtheknowledgethatoneof theeventsocurreddoesnotaffecthechancet heotherocurs. QUESTI ON35 1/1POIN TS Ofthefolowingpairsofevents,whichpairhasmutu alyexclusiveevents? rolingasum greaterthan7 from tworolsofastandarddieandrolinga4 forthefirst throw drawinga2 anddrawinga4 withreplacementfrom astandarddeckofcards rolingasum of9 from tworolsofastandarddieandrolinga2 forthefirstrol drawingaredcardandthendrawingablackc ardwithreplacementfrom astandard deckofcards AnswerExplanation Corectanswer: rolingasum of9 from tworolsofastandarddieandrolinga2 forthefirstrol • $\left(0.10,\ 0.18\right)$(0.10, 0.18) • $\left(67,\ 87\right)$(67, 87) Thatiscorect! $$(0.10, 0.18) MATH 225N Week 4 Statistics Quiz – Question and Answers AnswerExplanation Corectanswers: Aconfidenceintervalisanintervalofvalues,cent eredonapointestimate,oftheform (pointestimate−marginof error,pointestimate+marginof error) Usingthegivenpointestimateforthemean,x¯=77 andmarginoferror10,the confidenceintervalis: (77−10,77+10)(67,87) QUESTI ON38 1/1POIN TS Arandom sampleofadultswereaskedwhethertheypre fereadingane-bo kovera printedbo k.Thesurveyresultedinasampleproportio nofp′=0.14,withasampling standarddeviationofσp ′=0.02,whopreferredreadingane-bo k. Usetheempiricalruletoconstructa95% confidenceintervalforthetrueproportiono f adultswhoprefere-bo ks. AnswerExplanation Corectanswers: BytheEmpiricalRule,a95% confidenceintervalcorrespondstoaz-scoreofz=2. Substitutingthegivenvaluesp′=0.14 andσp ′=0.02,aconfidenceintervalis MATH 225N Week 4 Statistics Quiz – Question and Answers (p′−z⋅σp′,p′+z⋅σp′)(0.14−2⋅0.02,0.14+2⋅0.02) (0.14−0.04,0.14+0.04)(0.10,0.18) • $14\text{ dog heights}$14 dog heights Thatiscorect! $$14 dog heights MATH 225N Week 4 Statistics Quiz – Question and Answers QUESTI ON39 1/1POIN TS Thepopulationstandarddeviationfor theheightsofdogs,ininches,inacity is3.7 inches.Ifwewantobe95% confidenthathesamplemeanis within2 inchesofthetruepopulationmean,whatisthemini mum samplesizethatcan betaken? z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576 Usethetableaboveforthez- score,andbesuretorounduptothenearestinteger . AnswerExplanation Corectanswers: Theformulaforsamplesizeisn=z2σ2EBM2.Inthisformul a,z=zα2=z0.025=1.96, becausetheconfidencelevelis95%.From theproblem,weknow thatσ=3.7 andEBM=2.Therefore,n=z2σ2EBM2=(1.96)2(3.7)222≈13.1 5. Usen=14 toensurethathesamplesizeislargeenoug h. Also,thesamplesizeformulashownaboveissometi meswritenusinganalternate formatofn=(zσE)2.Inthisformula,Eisusedtodenote marginoferrorandtheentire parenthesesisraisedtotheexponent2. Therefore,themarginoferrorforthemeanca nbedenotedby"EBM"orby"E".Either MATH 225N Week 4 Statistics Quiz – Question and Answers 11 14 12 12 13 8 14 3 15 1 16 1 • • 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 MATH 225N Week 4 Statistics Quiz – Question and Answers • AnswerExplanation 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 Rememberthatdataareleftskewedifthereisamain concentrationoflargevalueswith severalmuchsmalervalues.Similarly,rightskew eddatahaveamainconcentrationof smalvalueswithseveralmuchlargervalues.Weca nse thathefolowingisleft skewedbecauseoftheconcentrationoflargevalue swithmanysmalervalues: Value Frequency 12 1 13 1 14 3 15 6 MATH 225N Week 4 Statistics Quiz – Question and Answers 16 23 17 29 18 19 19 15 20 3 Andthefolowingisrightskewedbecauseofitsconc entrationofsmalvalueswithmany largervalues: Value Frequency 0 5 1 16 2 23 3 19 4 22 5 9 6 4 7 2 Theotherfrequencytablesaremorebalancedandsy mmetrical. Youranswer: 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 Theresultsarestatisticalysignificantat he0.05 levelofsignificanceinshowingthat theproportionofpeopleinruralareaswhowa Thatiscorect! MATH 225N Week 4 Statistics Quiz – Question and Answers Theresultsarestatisticalysignificantathe0.05 levelofsignificanceinshowingthat theproportionofpeopleinruralareaswhowanthed efendingchampionstowinthe gameisdifferenthantheproportionofpeopleinurba nareas. Thedataisnotstatisticalysignificantathe0.05 levelofsignificanceinshowingthat theproportionofpeopleinruralareaswhowanthed efendingchampionstowinthe gameisdifferenthantheproportionofpeopleinurba nareas. AnswerExplanation Corectanswer: Theprobabilityvaluecalculatedis0.03.Thisisles sthan0.05,soweconcludethat thedataarestatisticalysignificantinshowingth atheproportionofpeopleinruralareas whowanthedefendingchampionstowinthegameisdi fferenthantheproportionof peopleinurbanareas. QUESTI ON42 1/1POIN TS Inapsychologicalstudyaimedatestingadrugthat reducesanxiety,theresearcher groupedtheparticipantsinto2 groupsandgavetheanxiety- reductionpiltoonegroup andaninertpiltoanothergroup.Whichgrouprecei vestheplacebo? thegroupthatreceivedt heanxiety- reductionpil MATH 225N Week 4 Statistics Quiz – Question and Answers thepsychologicalstudy althepeopleinthestudy thegroupthatreceivedtheinertpil AnswerExplanation Afitnesscenterclaimsthathemeanamountof timethatapersonspendsathegym pervisitisfewerthan38 minutes. Thatiscorect! MATH 225N Week 4 Statistics Quiz – Question and Answers Corectanswer: thegroupthatreceivedtheinertpil Whentheexperimentalunitsarepeople,ap lyingtreatmentsthatshouldbeinertcan actualyhaveeffects.Sothegroupthatreceivedth einertpilreceivedtheplacebo. QUESTI ON43 1/1POIN TS Whichofthefolowingresultsinthenulhyp othesisμ≥38 andalternative hypothesisμ<38? Afitnesscenterclaimsthathemeanamountoftimeth atapersonspendsathegym pervisitisatmost38 minutes. Afitnesscenterclaimsthathemeanamountoftimeth atapersonspendsathegym pervisitisfewerthan38 minutes. Afitnesscenterclaimsthathemeanamounto ftimethatapersonspendsathegym pervisitis38 minutes. Afitnesscenterclaimsthathemeanamountoftimeth atapersonspendsathegym pervisitismorethan38 minutes. AnswerExplanation Corectanswer: Considereachoftheoptions.Thescenario inoptionBhasthenul hypothesisμ≥38 basedonthewords"fewerthan"andthefac thathenul hypothesisisalwaysstatedwithsomeform ofequality. QUESTION4 MATH 225N Week 4 Statistics Quiz – Question and Answers contingencytable.Forexample,lo kingathesecondrowinthetable,weknow Thatiscorect! MATH 225N Week 4 Statistics Quiz – Question and Answers that33 ad edtotheunknownnumberinthemid leis67,sothatunknownnumber is34.Continuinginthisway,wecanfilintheentiret able: StudentsplaysportsdonotplaysportsTotalplayaninstrument273 360donotplayaninstrument353469Total6267129 From this,wecanse thathenumberofstudentswhobothdonotplaysport sanddo notplayaninstrumentis34. QUESTI ON46 1/1POIN TS Theanswerchoicesbelowrepresentdiffere nthypothesistests.Whichofthechoices areleft-tailedtests? Selectalcorectanswers. • H0:X=17.3,Ha:X≠17.3 • • H0:X≥19.7,Ha:X<19.7 • • H0:X≥11.2,Ha:X<11.2 • H0:X≥19.7,Ha:X<19.7 H0:X≥11.2,Ha:X<11.2 Thatiscorect! MATH 225N Week 4 Statistics Quiz – Question and Answers • H0:X=13.2,Ha:X≠13.2 • • H0:X=17.8,Ha:X≠17.8 • AnswerExplanation Corectanswer: Remembertheformsofthehypothesistests. • Right-tailed:H0:X≤X0,Ha:X>X0. • Left-tailed:H0:X≥X0,Ha:X<X0. • Two-tailed:H0:X=X0,Ha:X≠X0. Sointhiscase,theleft-tailedtestsare: • H0:X≥11.2,Ha:X<11.2 • H0:X≥19.7,Ha:X<19.7 QUESTI ON47 1/1POIN TS Assumethenulhypothesis,H0,is:Jacobearnsenoug hmoneytoaffordaluxury apartment.FindtheTypeIerrorinthisscenario. Thatiscorect! MATH 225N Week 4 Statistics Quiz – Question and Answers AnormalbelcurvelabeledUp erAandanormalelongatedcurvelabeledUp erBare centeredathesamepoint.NormalcurveUp erBisnarrowerandabovenormalcurve Up erA. • A hasthelargermean. • • B hasthelargermean. • • ThemeansofA andB areequal. • • A hasthelargerstandarddeviation. • • B hasthelargerstandarddeviation. • ThemeansofA andB areequal. A hasthelargerstandarddeviation. MATH 225N Week 4 Statistics Quiz – Question and Answers • ThestandarddeviationsofA andB areequal. • AnswerExplanation Corectanswer: Rememb rthathemeanofanorm ldistributionisth ex-valueofitscentralpoint(the topofthe"hil").Therefore,adistributionwitha largermeanwilbecenteredfartherto therighthanadistributionwithasmalermean. BecauseA andB arecenteredathesamepoint,theirmeansareequa l. Rememberthathestandarddeviationtelshowsprea douthenormaldistributionis.So ahighstandarddeviationmeansthegraphwilbesho rtandspreadout.Alowstandard deviationmeansthegraphwilbetalandskiny. BecauseA isshorterandmorespreadouthanB,wefindt hatA hasthelarger standarddeviation. QUESTI ON49 1/1POIN TS Hugoaverages72 wordsperminuteonatypingtestwithast andarddeviation of12 wordsperminute.Sup oseHugo'swordsperminuteonatypingte stare normalydistributed.LetX= thenumberofwordsperminuteonatyping test. Then,X∼N(72,12). Sup oseHugotypes54 MATH 225N Week 4 Statistics Quiz – Question and Answers wordsperminuteinatypingtestonWednesda y.Thez-score whenx=54 is . Thisz- scoretelsyouthatx=54 is standard deviationstothe (right/left)ofthemean, .