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STAT200(Wiesner)–Exam1–PracticeTestSolutions
1. C–Stratifiedrandomsamplebecausestudentsweredividedintogroups.
Thenarandomsamplewastakenfromthegroupselected.
2. C–Yes,becausetheresultisbasedonanexperiment.Youknowtheproblem
isdescribinganexperimentbecausetreatmentsarerandomlyassignedto
participants.Itispossibletodrawcauseandeffectconclusionsfrom
experiments;however,itisnotpossibletodrawcauseandeffectconclusions
fromobservationalstudies.
3. B–Switchtodoor#3becausethereisa2/3probabilitytheprizeisbehind
door#3andthereisonlya1/3probabilitytheprizeisbehinddoor#1.This
exampleiseasiertoconceptualizeifyouthinkaboutthesamescenario;
however,insteadofjustthreedoorsthereare100doors.Ifyourandomly
pickonedoor,thereisa1/100chanceyoupickedthecorrectdooranda
99/100thecorrectdoorisoneofthedoorsyoudidn’tpick.Ifthegameshow
hostopens98ofthedoorsyoudidn’tpickandshowsyoutheyareempty,it
meansthereisa99/100chancetheprizeisbehindthedooryoudidn’tpick
anda1/100chancetheprizeisbehindthedooryoudidpick.Thusyou
shouldalwaysswitchdoorsinthisscenariotoincreasethechancesyouwin
theprize.
4. C–1dividedbythesquarerootof64
CMoE=1/ 𝑛 = 1/ 64
5. C–NotindependentbecauseP(CHEM110)timesP(MATH140)doesnot
equalP(CHEM110andMATH140).
Independencerule=P(AandB)=P(A)*P(B)
P(CHEM110)=0.7
P(MATH140)=0.8
P(CHEM110andMATH140)=0.60
0.60≠(0.7)(0.8)
6. A–Youknowthisisanexperimentbecausetreatmentswererandomly
assignedtoparticipants.
7. B–Nonresponsebias
8. A–Mutuallyexclusive
Theeventsaremutuallyexclusivebecauseitisnotpossibleforthembothto
happenatthesametime.
Iftwoeventsaremutuallyexclusive,youknowP(OandB)=0.The
independencerulesaysthatifthetwoeventsareindependentthefollowing
willholdtrue.
P(OandB)=P(O)*P(B)
P(0)=4/6=2/3
P(B)=2/6=1/3
0≠(2/3)(1/3)
Sincetheindependenceruledoesnothold,weknowtheeventsarenot
independent.
9. A–TheweightofPennStatestudents
10. C–Samplesurvey
11. C–Orange,orange,orangebecauseorangeisthemostlikelyeventtooccur
eachtimethedieisrolled.
12. D–18.17becauseitrepresentsQ3inthefivenumbersummary.
13. A–1/3becausetherearethreeevennumbersonthedie,2,4,and6.
14. B–80and3becausethecurvewillincreasethemean,butitwillnotaffect
thestandarddeviation.
15. B–No,iftwoeventsareindependent,knowingthateventBoccurredwillnot
affecttheprobabilitythateventAoccurs.
16. C–Fatconsumption(explanatoryvariable)“explains”heartfunction
(responsevariable).
17. D–Onlytheviewerwhovotedinthisparticularpollbecausethiswasaselfselectedsample,whichonlygivesyouinformationabouttheparticipantsin
thesample.
18. B–Astudycanonlybeclassifiedasanexperimentifthetreatmentsare
randomlyassignedtoparticipants.However,astudycanstillbean
experimentevenifparticipantsarenotrandomlyselected.
19. C–10.21to18.17becausethisanswerchoicerepresentstheIQR.
20. D–Positive2
𝑧=
𝑂𝑏𝑠𝑒𝑟𝑣𝑒𝑑𝑣𝑎𝑙𝑢𝑒 − 𝑀𝑒𝑎𝑛 82 − 76
=
= 2
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
3
21. D–Thenumberoftimesperweekanindividualeatsfastfoodisnotalurking
variableinthisexamplebecauseitisavariableusedinthestudy.
22. A–67
Observedvalue − Mean
z=
Standarddeviation
𝑥 − 76
−3 =
3
x=67
23. B–Notrepresentativebecausethenumberofhoursofsleepastudentgets
thenightbeforeabigexamisnotrepresentativeoftheaveragenumberof
hoursastudentsleepseachnight.
24. A–Histogrambecausewearedealingwithquantitativevariables.
25. A–AllregisteredPAvoters.
26. B–13.45becausethemedianisthemiddlenumberinafivenumber
summary.
27. D–Itispossibletodrawacauseandeffectconclusioninarandomized
experiment;however,itisnotpossibleforanobservationalstudy.
28. C–Sidbysideboxplotsbecausesalaryisaquantitativevariableandwewant
tocomparetwodistinctgroupsthroughavisualdisplay.
29. A–Representative
30. B–Observationalstudybecausetreatmentswerenotrandomlyassigned.
31. D–18.17to37becauseintervalonlyrepresents25%ofthesalaries.This
intervalisfromQ3tothemaximumvalue.
32. C–70to82becausetheempiricalruletellsusthat95%ofallvaluesfall
within2standarddeviationsofthemean.
33. A–Ifthesamplesizeincreases,themarginoferrordecreases.Thesample
sizedoesnotaffectresponsebias.
34. B–Morethan13.45becausewhendataispositivelyskewed(skewedtothe
right)meanisgreaterthanthemedian.13.45isthemediansoweknowthe
meanmustbegreaterthan13.45.
35. A–35/45
Totalfemale=45
Totalfemaleinstate=35
Probability=35/45
36. A–Yes,becausetheyaredependentevents
37. A–Yes,because0.2*0.8=0.16whichmakestheeventsindependent.
38. D–Eachanswerchoiceisequallylikelybecausethereisanequalchanceof
thedielandingonorangeorblue.
39. C–1/2becausethereisa50%chancethenumberis1anda50%chancethe
numberis2.
40. C–Stratifiedbecausethepopulationisdividedintogroupsandthenasimple
randomsampleistakenfromeachgroup.
41. C–Piechartbecausewearegraphingquantitativevariablesandpiecharts
areusedtographcategoricalvariables.
42. A–Yes,becausewheneventsaredependentknowingthatoneevent
occurredchangestheprobabilitythattheothereventoccurs.
43. D–Eachanswerchoiceisequallylikelybecausethereisanequalchanceof
landingonorangeorblue.
44. B–Themedianformethod2issmallerthanitisformethod1.Youcansee
fromtheside-by-sideboxplotsthatmethod2hasalargermedianthan
method1.
45. A–Categorical.Theexplanatoryvariableinthisexampleisgender,whichisa
categoricalvariable.
46. B–Quantitativeandcontinuous.Theresponsevariableisheightininches,
whichisaquantitativeandcontinuousvariable.
47. B–Themedianislargerformales.Thelineinthemiddleofthe“box”portion
oftheboxplotrepresentsthemedian.Youcanseethatthemedianformales
islargerthanthemedianforfemales.
48. C–Bothdatasetsareskewed;however,theyareskewedinopposite
directions.Themedianformalesisclosertothetopofthebox,soweknowit
isskewedtotheleft.Themedianforfemalesisclosertothebottomofthe
box,soweknowitisskewedtotheright.
49. C–Mean<Median.Thisdatasetwillbeskewedtotheleftbecausethe
salariesofthethreeadministrativeassistantsaremuchlowerthanthe
salariesofthelawyers.Thesmallersalariesoftheadministrativeassistants
willhaveagreatereffectonthemeanthantheywillonthemedianbecause
ofthedifferenceinthewaythetwovaluesarecalculated.Themeanwill
alwaysbelessthanthemedianwhenadatasetisskewedtotheleft.
50. A–Continuousrandomvariable.Weightisacontinuousrandomvariable
becauseitcantakealargenumberofvalueswithinagiveninterval.
51. A–Right-skewed.ThemedianisclosertoQ1thanitistoQ3.
52. B–160pounds.ThevaluesfromQ1tothemaximummakeupapproximately
75%oftheobservations.
53. D–75%.ThevaluesfromtheminimumtoQ3makeupapproximately75%of
theobservations.
54. B–Themiddle50%ofthedataspans30pounds.TheIQRistherangeofdata
betweenQ1andQ3.TheIQRmakesupthemiddle50%ofthedata.
55. B–BoxplotBmatchesthevaluesgiveninthefive-numbersummary.
56. D–Genderistheexplanatoryvariableandgenderisacategoricalvariable.
Thetemperatureistheresponsevariable.Temperateisaquantitative
variable
57. A–Themedianformalesislessthanthemedianforfemales.Youcantell
thisbecausethelinethroughthemiddleoftheboxesrepresentsthemedian.
58. B–TheIQRformalesislargerthantheIQRforfemales.Youcantellthis
becausethesizeofthegreyboxrepresentstheIQR.
59. A–Theboxportionoftheboxplotshowsthattheshapeforthefemale
sampledifferentthanthemalesample.Thelocationofthemedianlinein
theboxportionoftheboxplottellsyouabouttheshapeofthesample.
60. B–Therearefeweroutliersinthemalesamplethanthefemalesample.The
outliersarerepresentsbythe*intheboxplots.
61. D–Thefemalesamplehasthesamemaximumandminimumvaluesasthe
malesample.Theminimumvaluesarerepresentedbythe*at0degreesfor
bothsamples.Themaximumvaluesarerepresentedbywherethetailsofthe
boxplotsend.
62. A–Theprobabilitythatthetestisnegativewhenthepersondoeshavethe
disease.Itisonlypossibletohaveafalsenegativeresultifyoudohavethe
disease.Ifyouhaveadisease,youwilleithergetacorrectresultthatyou
havethedisease,oryouwillgetafalsenegativesayingyoudonothavethe
disease.
63. D–Oneminusspecificity.Specificityisfoundbytakingoneminusthe
probabilityofafalsepositive.Thustheprobabilityofafalsepositiveisone
minusspecificity.
64. D–Theprobabilityofanegativetestresultwhenyoudonothavethe
disease.
65. B–(4425+4428–4200)/4685.Wehavetosubtract4200oncebecausethe
valueisincludedinboththetotalthatactuallyhavethediseaseandthetotal
ofnegativeresults.Ifwedon’tsubtractit,wewillbecountingthevaluetwice.
66. D–28/260.Thenumberofpeoplewhohavethediseasebutgetanegative
resultdividedbythetotalnumberofpeoplewhoactuallyhavethedisease.
67. D–90%ofpeoplewhodonothavekidneystoneswilltestnegative.
68. D–Theslowesttimeof47minutesisanoutlier.Anasteriskinaboxplot
representsanobservationthatisclassifiedasanoutlier.
69. A–0.99becausespecificityisfoundbytakingoneminusthefalsepositive
rateindecimalform.
70. C–0.999becausesensitivityisfoundbytakingoneminusthefalsenegative
rateindecimalform.
71. A–Yes,allofthebinomialconditionsaremet
72. A–0.025
𝑧=
𝑂𝑏𝑠𝑒𝑟𝑣𝑒𝑑𝑣𝑎𝑙𝑢𝑒 − 𝑀𝑒𝑎𝑛 $220 − $180
=
= 2
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
$20
Wearenotgivenaz-tabletosolvethisproblem;however,weknowthat95%
ofobservationswillfallwithintwostandarddeviationsofthemeanvalue.
Thismeansthat2.5%ofobservationswillbetotheleftof–2and2.5%ofthe
observationswillbetotherightof+2.Thisproblemisaskingaboutthearea
totherightof+2.
73. C–Discretebecausethevariablehasacountablelistofdistinctpossibilities
74. D–Continuousbecausetemperatureissomethingthatismeasured,andwe
canalwaystakeamoreprecisemeasurementoftemperature
75. B–2.8
E(X)=1(0.25)+2(0.20)+3(0.15)+4(0.30)+5(0.10)=2.8
76. D–0.55
0.15+0.30+0.10=0.55
77. B–Discretebecausethenumberofpuppiessoldisacountablelistofdistinct
possibilities.
78. D– (100)(0.85)(1 − 0.85)
p=85/100=0.85
σ= 𝑛𝑝(1 − 𝑝) = (100)(0.85)(1 − 0.85) = 3.57
79. C–Findthecumulativeprobabilityfor6successforabinomialvariablewith
n=10andp=1/4.Youwantthecumulativeprobabilitybecauseproblem
asksfortheprobabilityof6orfewer.Youwantn=10becausethatisthesize
ofthesample.Youknowp=1/4becausethatistheprobabilityofgettingany
givenquestioncorrect.
80. C–ThenumberofquestionsaPennStatestudentgotcorrectonanexam.
81. B–Usethez-tabletofindtheprobabilityofgettingaz-scoregreaterthan
negative1.5.Youknowyouwanttofindthegreaterthanprobability
becausetheproblemwantstoknowtheprobabilityastudentspendsmore
than$120atJimmyJohns.
𝑧=
𝑂𝑏𝑠𝑒𝑟𝑣𝑒𝑑𝑣𝑎𝑙𝑢𝑒 − 𝑀𝑒𝑎𝑛 $120 − $150
=
= −1.5
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
$20
82. C–Apiechartisusedtodisplayqualitative(categorical)data.
83. A–Howmanypairsofsandalsyouhaveinyourcloset