Ecologistsconductedastudytoinvestigatethepotentialecological impactofgolfcourses.Investigatorsmonitoredthereproductive successofbluebirdsinbirdhousesatninegolfcoursesandten similarbirdhousesatnongolfsites.Dataonnestsinbirdhouses occupiedonlybybluebirdsareshowninthetable.ObservedNumberofNestsperBirdhousebyLocation 0nests1nest2or3 nestsTotalGolf3042880Nongolf405822120Total7010030200 Iftheproportionsofnestsoccupiedisthesameforgolfandnongolf sites,whatwouldbetheexpectedcountofbirdhouseswith1nestin nongolflocations?60 Afisheriesbiologistcollectedarandomsampleoffishfromalake andconductedachi-squaregoodness-of-fittesttoseeifthe distributionoffishchangedovertime.Thetablebelowshowsthe distributionoffishthatwereputintothelakewhenitwas originallystocked.FishTypeTroutBassPerchSunfishCatfishPercent25%25%20%15%15% Thebiologistfoundevidencetorejectthenullhypothesisinfavor ofthealternativehypothesis.Whichofthefollowingrepresentsthe alternativehypothesisofthetest?Atleastoneofthefishproportionsisdifferentthanthe correspondingproportionwhenthelakewasoriginallystocked.10Must-HaveAccessoriesforSprucingUpYourCaravan Afactoryproducesbagsofrubberbands.Abagofrubberbandshas
fivedifferentsizes:extralarge(XL),large(L),medium(M),small
(S),andextrasmall(XS).Aqualitycontrolspecialistcollectsa randomsampleof450rubberbandsfromthebaggingmachineand calculatesachi-squaregoodness-of-fittesttoseeifthe frequenciesforeachsizeinthesamplematchthehypothesized distribution.Thequalitycontrolspecialistwilltesthissample againstthefollowingnullhypothesis Ho:pXL=0.10,pL=0.20,pM=0.40,pS=0.20,pXS=0.10Ho:pXL=0.10,pL= 0.20,pM=0.40,pS=0.20,pXS=0.10 Howmanymediumrubberbandsareexpectedintherandomsampleof450 rubberbands?
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Atacertaincompany,loanagentsarepaidbasedonthenumberof loanstheycloseinaday.Basedoncompanyrecords,thenumberof loansXthatarandomlyselectedloanagentclosesonarandomly selecteddayhastheprobabilitydistributionbelow.x1234567P(x)0.050.100.220.300.180.120.03 Atthecompany,thedailysalaryofaloanagentis$150plus$50per loanclosed.LetYrepresenttheamountofmoneymadebyarandomly selectedloanagentonarandomlyselectedday.Whichofthe followingstatementsisNOTtrue?Themeandailysalaryisgreaterthan$350perday.Anewspaperarticleindicatedthat43percentofcarswithblack seatsarewhite,46percentofcarswithblackseatsareblue,7 percentofcarswithblackseatsarered,and4percentofcarswith blackseatsareblack.Atestwasconductedtoinvestigatewhether thecolorofcarswithblackseatswasconsistentwiththenewspaper article.Arandomsampleofcarsofthesecolorswasselected,and thevalueofthechi-squareteststatisticwasχ2=8.2χ2=8.2.Which ofthefollowingrepresentsthep-valueforthetest?
P(χ2≥8.2)=0.04
NonnativespeakersofEnglishoftenhavecharacteristicsintheir handwritingthatdifferdependingonthespeaker'sfirstlanguage.HandwritingsamplesfromarandomsampleofChinese,Malay,and IndianchildreninaschoolinSingaporeweretakentoinvestigate thesedifferences.Onecharacteristicofinterestwasaroundingat thetopofthecapitalletterA.Dataforthetop-rounding characteristicforasampleof153childrenareshowninthetable.ObservedTopRoundingontheCapitalLetterA MalayIndianChineseTotalYes921838No423142115Total515250153 Ifchildrenfromthesecountriesexhibittoproundinginthesame proportions,whatistheexpectedcountforMalaychildrenwhoshow toprounding?
(153(38)(51))
LetXbearandomvariablewhosevaluesarethenumberofdotsthat appearontheuppermostfacewhenafairdieisrolled.Thepossible valuesofXare1,2,3,4,5,and6.ThemeanofXis7/2andthe varianceofXis35/12.LetYbetherandomvariablewhosevalueis thedifference(firstminussecond)betweenthenumberofdotsthat appearontheuppermostfaceforthefirstandsecondrollsofafair diethatisrolledtwice.WhatisthestandarddeviationofY?
3512+35121235+1235
notjusttheaddingone TheNationalParkServicewritesmaterialsforstudentstousewhile intheparks.Inastudyoftheeffectivenessofsomeofthese materials,arandomsampleofstudentswasselectedtotakeashort 2 / 3
quizaboutoaktreesafterusingthesematerials.Arandomsampleof parkprofessionalsalsotookthequiz.Investigatorscompared classifications(low,medium,andhigh)ofthecrownshapes—the generalshapesoftheleafypartsofthetrees—madebystudentsins 6through12withclassificationsmadebyprofessionals.Datafrom thestudyareshowninthetable.ProfessionalsStudentsTotalLow544397Medium483987High7916Total10991200 Iftheprofessionalsandthestudentsdonotdifferinthe distributionsoftheirresponses,whichofthefollowingisequalto theexpectednumberofstudentswhoclassifythecrownshapesas medium?
(200(87)(91))
Forwhichofthefollowingisachi-squaregoodness-of-fittestmost appropriate?Determiningwhetheracategoricalvariablehasasignificantly differentdistributionofproportionsthantheexpecteddistribution ArecentsurveyconcludedthattheproportionofAmericanteenagers whohaveacellphoneis0.27.Thetruepopulationproportionof Americanteenagerswhohaveacellphoneis0.29.Forsamplesofsize 1,000thatareselectedatrandomfromthispopulation,whatarethe meanandstandarddeviation,respectively,forthesampling distributionofthesampleproportionofAmericanteenagerswhohave acellphone?
0.29,1000(0.29)(0.71)theonewhereit'sdividedby1000 TypeofGrassSeedPercentFescue(F)55%Buffalograss(B)22%Bluegrama (BG)10%Indiangrass(I)7%Greenneedlegrass(NG)6% Aqualitycontrolspecialisttestssamplesoftheseedbeingpackaged andusesachi-squaregoodness-of-fittesttoseewhetherthe proportionsinthesamplesmatchwhatisclaimedbythecompany.Whichofthefollowingbestdescribesthenullhypothesisandthe alternativehypothesisforthetest?Ho:pF=0.55,pB=0.22,pBG=0.10,pI=0.07,pPNG=0.06Ho:pF=0.55,pB= 0.22,pBG=0.10,pI=0.07,pPNG=0.06 Ha:Ha:Atleastoneoftheproportionsisdifferent Eachpersoninarandomsampleofadultsindicatedhisorher favoritecolor.Theresults,showninthetablebelow,arereported byagegroupoftherespondents.Ifchoiceofcolorisindependentofagegroup,whichofthe followingexpressionsisequaltotheexpectednumberofrespondents whoareaged30to50,inclusive,andprefergreen?
314(99)(108)
Acompanyclaimstheyproducetheirmixedbagofcandiessothat,of thecandiesinthebag,20percentaredarkchocolate,60percentare
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