Download 1. C – 70 ± 2x5. You were told that this dataset has a normal shape

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STAT200–Buchanan–Exam1–PracticeExamSolutions
1. C–70±2x5.Youweretoldthatthisdatasethasanormalshape.The
empiricalruletellsusthatapproximately95%ofvalueswillfallwithin2
standarddeviationsofthemeanwhendealingwithanormaldistribution.
2. A–Principle2.Thisstatisticmakesitsoundlikethemajorityofpeopleliving
inFloridawillbediagnosedwithskincancer.Whenreadingstatisticslike
this,youneedtoalsokeepinmindtheprobabilityofgettingdiagnosedwith
skincancer.Theprobabilityofgettingdiagnosedwithskincancerisstill
prettylow,evenforpeoplelivinginFlorida.Makesuretonotethatyoumay
berequiredtoknowwhichprinciplesrelatetowhichnumberstobeableto
answerproblemslikethis.
3. B–Randomizedexperiment.Themethods,ortreatments,wererandomly
assignedtoparticipants.
4. B–Thetrainingmethodused.Thetrainingmethodexplainsthetimeittook
theemployeestocompletetheroutinetasksafterthetrainingwascomplete.
5. C–Thetimeittooktheemployeetocompletethetasksafterthetraining.
Thetimeittooktheemployeetocompletethetasksaftertrainingisa
responsetothemethodoftrainingused.
6. A–Itispossibletodrawacause-and-effectconclusionbasedonthe
informationprovided.Itisgenerallypossibletodrawacause-and-effect
conclusionwhendealingwithrandomexperiments;however,itisgenerally
notpossibletodrawacause-and-effectconclusionfromanobservational
study.
7. B–Themedianformethod2issmallerthanitisformethod1.Youcansee
fromtheside-by-sideboxplotsthatmethod2hasalargermedianthan
method1.
8. D–.9810.Theempiricalruletellsusthatforanormaldistributionthereisa
95%chanceavaluewillbe±2standarddeviationsfromthemeanandthere
isa99.7%chanceavaluewillbe±3standarddeviationsfromthemean.This
problemasksfortheprobabilitythatavaluewillbebetween–2.5and2.2
standarddeviationsfromthemean.Because.9810istheonlyvaluebetween
.9500and.9970,.9810istheonlylogicalanswer.
9. B–Thevariationinthemiddle50%ofthedataspans4hoursperday.The
IQRisfrom2hoursperdayto6hoursperday,sothemiddle50%ofthedata
spans4hoursperday.
10. D–75%.Approximately75%ofthevalueswillfallbetweenQ1andthe
maximumvalue.
11. D–75%.Approximately75%ofthevalueswillfallbetweentheminimum
andQ3.
12. B–2hoursperday.Approximately75%ofthevalueslieaboveQ1.
13. D–140.Valuesthatfallthefarthestfromthemeanwillhavethegreatest
effectonstandarddeviation.
14. C–4.Aboxplotshowsyouthevaluesfortheminimum,Q1,themedian,Q3,
andthemaximum;however,youonlyneedfourunitsofdatatocreatea
boxplot.Ifthereareonlyfourunitsofdata,themedianiscalculatedbytaking
anaverageofthemiddletwonumbers.
15. B–3581113141519.Thecount,orfrequency,isthe
numberoftimesavaluefallswithineachcategory.AnswerBistheonly
answerchoicethatmatcheswiththetableprovided.
16. A–Observational.Inthisexample,theresearchersaremerelyobservingthe
participants.Theresearchersarenotrandomlyassigningparticipants
treatmentsastheydoinrandomizedexperiments.
17. B–Itisnotpossibletodrawacause-and-effectconclusionbasedonthe
informationprovided.Itgenerallyisnotpossibletodrawcause-and-effect
conclusionsaboutobservationalstudies;however,itisgenerallypossibleto
drawcause-and-effectconclusionsaboutrandomizedexperiments.
18. A–s=5points.Inthisexample,yourscorewasabovethemean.Sinceyou
scoredhigherthanthemean,youwanttobeasmanystandarddeviations
abovethemeanaspossible.Ifthestandarddeviationis5points,youwould
be2standarddeviationsabovethemean;however,ifthestandarddeviation
is10points,youwouldonlybe1standarddeviationabovethemean.
19. MultipleSelect–Sampleestimate,statistic
20. A–Bargraph:Jobpreferenceaftergraduation:(Accountant,consultant,
investmentbanker)
B–Histogram:(NumberofdaysitissunnyinthemonthofMarch)
C–Boxplot:(HoursperdayspentwatchingTV)and(agegroup)
21. C–Standarddeviationaccuratelymeasuresspreadregardlessoftheshapeof
thedata.Thisstatementisfalsebecausestandarddeviationaccurately
measuresspreadonlywhendealingwithastandardnormaldistribution.
22. A–Categorical.Theexplanatoryvariableinthisexampleisgender,whichisa
categoricalvariable.
23. B–Quantitativeandcontinuous.Theresponsevariableisheightininches,
whichisaquantitativeandcontinuousvariable.
24. B–Themedianislargerformales.Thelineinthemiddleofthe“box”portion
oftheboxplotrepresentsthemedian.Youcanseethatthemedianformales
islargerthanthemedianforfemales.
25. C–Bothdatasetsareskewed;however,theyareskewedinopposite
directions.Themedianformalesisclosertothetopofthebox,soweknowit
isskewedtotheleft.Themedianforfemalesisclosertothebottomofthe
box,soweknowitisskewedtotheright.
26. C–Mean<Median.Thisdatasetwillbeskewedtotheleftbecausethe
salariesofthethreeadministrativeassistantsaremuchlowerthanthe
salariesofthelawyers.Thesmallersalariesoftheadministrativeassistants
willhaveagreatereffectonthemeanthantheywillonthemedianbecause
ofthedifferenceinthewaythetwovaluesarecalculated.Themeanwill
alwaysbelessthanthemedianwhenadatasetisskewedtotheleft.
27. A–P(Z<–9)=1.0.Weknowthatapproximately99.7%ofvalueshavezscoresbetween–3and+3.AnswerchoiceAissaying100%ofvalueswill
haveaz-scoreoflessthan–9wheninfact0%ofvaluesshouldhaveaz-score
oflessthan–9.AnswerCiscorrectbecause100%ofvalueswillhaveazscorelessthan+9.AnswerBiscorrectbecausez-scoresrepresent
continuousrandomvariables,sotheprobabilitythataz-scorewillequalan
exactvaleisalways0%.Aswithallcontinuousrandomvariables,weexpress
z-scoresashavingaprobabilityoffallingwithinaspecificrange.
28. A–Methods1and2havethesamestandarddeviation.Itiseasytoseeinthe
dotplotthatmethods2and3willbothhaveameanof150.Youcanalsotell
thatmethods1and3willhavethesamestandarddeviationbecauseofthe
spacingoftheirvalues.However,methods1and2willhavedifferent
standarddeviationsbecausethevaluesformethod1aremorespreadout
thanthevaluesformethod2.Thus,answerAisfalse.
29. C–11to15apps.Inthisproblem,youarelookingtofindthemiddlevalueof
thisdatasetbasedonthefrequency.
30. D–TheIQRisusedtoquantifytheamountofvariationinthemiddle68%of
thesample.AnswerDisfalsebecausetheIQRisusedtoquantifytheamount
ofvariationinthemiddle50%ofthesample.
31. B–s=10points.Sinceyourscorewasbelowthemean,youwanttobe
withinasfewstandarddeviationsofthemeanaspossible.Astandard
deviationof5pointswouldmeanyouscored2standarddeviationsbelow
themean;however,astandarddeviationof10pointswouldmeanyouonly
scored1standarddeviationbelowthemean.
32. C–220to280.Whendealingwithabell-shapeddistribution,approximately
99.7%ofallobservationswillfallwithin±3standarddeviationsofthemean.
33. F–BothBandC.Valuesthatarefarthestfromthemeanhavethegreatest
effectonthestandarddeviation.Thisalsomeansthatvaluesclosesttothe
meanwillhavetheleasteffectonthestandarddeviation.
34. D–70inches.AnswerDrepresentsthe77.8thpercentilebecause77.8%of
observationsfallbetween58and70inches.
35. B–22.2%.AnswerBiscorrectbecause22.2%ofobservationsfallbetween
70and76inches.
36. C–Wearelookingforthegraphthatdisplaystheprobabilityofhavingazscoregreaterthan2.32.Weknowthereisalowprobabilityofhavingazscoregreaterthan2.32.Withoutdoinganycalculations,youknowthat.0102
isamorelogicalprobabilityforthisvaluethan.9898.
37. A–Discrete–binomial:Numberofstudentswhohaveblondehair
B–Discrete–nonbinomial(waiting-timevariable):Numberofdaysinthe
semesteruntilyourfirstexam
C–Discrete–nonbinomial(notwaiting-timevariable):Numberofclasses
withweeklyquizzes
D–Continuous:Amountoftimeittakestogethomefromcampus
38. A–Continuousrandomvariable.Weightisacontinuousrandomvariable
becauseitcantakealargenumberofvalueswithinagiveninterval.
39. A–Right-skewed.ThemedianisclosertoQ1thanitistoQ3.
40. B–160pounds.ThevaluesfromQ1tothemaximummakeupapproximately
75%oftheobservations.
41. D–75%.ThevaluesfromtheminimumtoQ3makeupapproximately75%of
theobservations.
42. B–Themiddle50%ofthedataspans30pounds.TheIQRistherangeofdata
betweenQ1andQ3.TheIQRmakesupthemiddle50%ofthedata.
43. B–BoxplotBmatchesthevaluesgiveninthefive-numbersummary.
44. A–AllAmericanadults
45. B–Categorical
46. B–Principle3.Principle3statesthatarepresentativesampleofonlya
thousand,oreveninsomecasesonlyafewhundred,cangivereasonably
accurateinformationaboutapopulationofmanymillions.
47. D–Standarddeviationisanaccuratemeasureofspreadregardlessofthe
shapeofthedata
48. D–Genderistheexplanatoryvariableandgenderisacategoricalvariable.
Thetemperatureistheresponsevariable.Temperateisaquantitative
variable
49. A–Themedianformalesislessthanthemedianforfemales.Youcantell
thisbecausethelinethroughthemiddleoftheboxesrepresentsthemedian.
50. B–TheIQRformalesislargerthantheIQRforfemales.Youcantellthis
becausethesizeofthegreyboxrepresentstheIQR.
51. B–Theboxportionoftheboxplotshowsthattheshapeforthefemale
sampledifferentthanthemalesample.Thelocationofthemedianlinein
theboxportionoftheboxplottellsyouabouttheshapeofthesample.
52. B–Therearefeweroutliersinthemalesamplethanthefemalesample.The
outliersarerepresentsbythe*intheboxplots.
53. D–Thefemalesamplehasthesamemaximumandminimumvaluesasthe
malesample.Theminimumvaluesarerepresentedbythe*at0degreesfor
bothsamples.Themaximumvaluesarerepresentedbywherethetailsofthe
boxplotsend.
54. D–4±(2)(0.6)becausetheempiricalruletellsusthat95%ofvalueswillfall
withintwostandarddeviationsofthemeanwhenvaluesarenormally
distributed.
55. B–Continuous
56. C–1,000becausevaluesclosesttothemeanwillhavetheleasteffecton
standarddeviation.1,000isthesamplemeanso1,000wouldalsobethe
closestvaluetothesamplemean.
57. C–Mean<Medianbecausethemeanisasensitivestatisticwhilethemedian
isaresistantstatistic.
58. D–Becausethisstatementsaidmedianinsteadofmean.
59. A–100becauseitisthevaluethatfallfurthestfromthemean.Valuesthat
fallfurthestfromthemeanhavethemostimpactonthevalueofstandard
deviation.
60. B–Gender
61. B–TheIQRislargerforthefemalesamplethanthemalesamplebecause
IQRisrepresentedbythesizeoftheboxportionoftheboxplot.
62. Cthemedianisthesameforthefemaleandmalesamples.Thelinegoing
throughtheboxportionoftheboxplotrepresentsthemedian.
63. Thenumberofoutliersaresmallerforthefemalesamplethanthemale
samplebecausetheoutlierarerepresentedbythenumberof*.
64. B–Theboxportionoftheboxplotshowsthattheshapeforthefemale
sampledifferentthanthemalesample.Thelocationofthemedianlinein
theboxportionoftheboxplottellsyouabouttheshapeofthesample.
65. B–Themaximumvalueofthefemalesampleisdifferentthanthemale
samplebecausethelargestoutlierforfemalesisgreaterthanthelargest
outlierformales.Theminimumsarethesamebecausethelowertailsofthe
boxplotsallendinthesameplace.
66. C–Themedianbecauseitistheonlyresistantstatisticintheanswerchoices.
67. C–AnswerCisfalsebecauseageisacontinuousvariablebecausewecan
alwaystakeamoreprecisemeasurementofage.AnswerAistruebecauseQ3
isthe75thpercentile.AnswerBistruebecausestandarddeviationisa
sensitivestatisticanditisameasureofspread.AnswerDistruebecausethe
meanisgreaterthanthemedian.AnswerEistruebecausetheminimumis
18.0.
68. Levelsofmanagement–Categorical,ordinal
Amountofnoise–Quantitative
Students’opinions–Categorical,notordinal
69. E–StatisticalPrinciple4isappropriatetoexplaintheresultsfromthispoll.
ThesamplewasrepresentativeofthepopulationsoPrinciple4didnotapply.
70. C–Theobservationof900istheobservationthatcontributesthemosttothe
finalvalueofstandarddeviationisfalse.Thevaluethatfallsfurthestfrom
themeanisthevaluethatcontributesthemosttothefinalvalueofstandard
deviation.Forthisproblemtheobservationof100wouldcontributethe
mosttostandarddeviationbecauseitfallsthefurthestfromthesamplemean
of600.
71. μ=3.1
x=3.3
σ=0.52
s=0.55
72. D–Xisadiscreterandomvariableisfalsebecausebatterylifeinminutesis
acontinuousrandomvariable.
73. D– M. E. = 1/ 𝑛 = 1/ 1,420
74. Cholesterol–Quantitative
StudentIDNumber–Categorical,notordinal
MovieTicketClassification–Categorical,ordinal