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Stat 200 Final Exam Done on 16 Dec 2016
Question
STAT 200
OL4 / US2 Sections
Final Exam
Fall2016
Thefinalexamwillbepostedat12:01amonDecember16,andit
isdueat11:59pmonDecember18,2016.EasternTimeisour
referencetime.
Thisisanopen-bookexam.Youmayrefer
toyourtextandothercoursematerials as youworkontheexam,andyou mayuseacalculator.Youmustcompletethe exam individually.Neither
collaborationnorconsultationwithothersisallowed.
ItisaviolationoftheUMUCAcademicDishonestyandPlagiarismpolicy
touse unauthorizedmaterialsorworkfromothers.
Answerall20questions.Makesureyouranswersareascompleteaspossible. Show
allofyoursupportingworkandreasoning.Answersthatcomestraight
fromcalculators,programsorsoftwarepackages withoutanyexplanationwillnot
beaccepted.Ifyouneedtouse
technology(forexample,Excel,onlineorhand- heldcalculators,statisticalpackages)toaid
inyourcalculation,you mustcitethe sourcesandexplainhowyougettheresults.
Thisexamhas100totalpoints; 5pointsforeachquestion.
Youmustinclude
theHonorPledgeonthetitlepageofyoursubmittedfinal exam. ExamssubmittedwithouttheHonorPledgewillnotbeaccepted.
.gif">
(a) Ais anevent, and Acis thecomplementofA, then P(AAND Ac)= 0.
(b)If the variance ofa datasetis 0,then all the observations in
thisdatasetmustbezero.
(c) Ifa 95%confidence intervalforapopulation mean contains 1,then the
90%confidence intervalforthesame parametermustcontain 1
(d)When plotted onthe same graph, a distribution withamean of40 anda
standarddeviation of10 will lookmorespreadoutthana distribution witha mean of50
and standard deviation of5.
(e) In a two-tailedtest,thevalue ofateststatisticis2.Theteststatistic
follows adistribution withthe distributioncurveshown below.Ifwe knowthe
shaded areais 0.03,thenwehave sufficientevidencetorejectthe nullhypothesis
at0.05levelofsignificance.
.gif">.jpg">
(a) Astudywasconducted atalocalcollege to analyze theaverage GPA
ofstudents graduated fromUMUCin 2015.100students graduatedfromUMUCin 2015were randomlyselected,
and the average GPA for the group is3.5.The value3.5 is a
(i) statistic
(ii) parameter
(iii) cannotbe determined
(b) Thehotelratings are usuallyon a scale from0 star to5stars.The
levelofthis measurementis
(i) interval
(ii) nominal (iii) ordinal (iv) ratio
(c) On the Election Day, UMUC News Club organized anexitpollin which
specific polling stations were randomlyselectedand allvoters were surveyed as
theyleftthose pollingstations. Thistypeofsamplingiscalled:
(i) cluster
.gif">(ii) convenience (iii)
systematic (iv) stratified
(a) Astudyof10differentweight lossprograms involved 500 subjects. Eachofthe 10
programs had 50 subjects in it.The subjects werefollowed for12 months. Weightchange
for each subjectwasrecorded.Youwantto testtheclaimthatthe mean weight lossisthesame for
the
(ii) linearregression
(iii) ANOVA
(iv) confidenceinterval
(b) ASTAT200instructorteaches twoclasses. She wantsto
test if the variancesofthe score distributionforthe two classesaredifferent. Whattype
ofhypothesistestshouldsheuse? (i) t-test for twoindependentsamples
(ii) t-test formatchedsamples
(iii) z-test for twosamples
.gif">(iv) F-test
4. Arandomsample of100 students waschosen fromUMUCSTAT200 classes.The frequency
distributionbelowshowsthe distribution forstudytime eachweek(inhours).(Showallwork. Just
theanswer, withoutsupporting work, willreceiveno credit.)
|
Study
Time(inhours)
|
Frequency
|
RelativeFrequency
|
|
5
|
||
|
13
|
||
|
0.22
|
||
|
42
|
||
|
Total
|
100
|
(a) Complete the frequencytable with frequencyandrelative frequency.Expressthe
relative frequencytothreedecimalplaces.
(b) What percentage ofthestudy timeswasatleast15 hours?
(c) Does this distributionhavepositiveskew or negative skew?
Whyorwhynot?
.gif">
5. The five-numbersummary belowshows the gradedistribution ofaSTAT200
quizfora sample of1000 students.
.jpg">Answereach questionbased on the
given information,andexplainyouranswerineach case. (a) What
istheinterquartilerange in the gradedistribution?
(b) Which scorebandhasthefeweststudents? (i)20-60
(ii)60-75
(iii)75 -90
(iv)Cannotbedetermined
.gif">(c) Howmanystudents arein the
score band between75 and 100?
6. Considerselectingone cardatatime froma 52-card deck. Whatisthe
probabilitythat the first cardisfromthesuitofheartsand the secondcard isalso
fromthesuitofhearts? (Note:There are 13 cardsfromthesuitofhearts ina
deckofcards) (Showallwork. Justtheanswer, without supporting
work, willreceiveno credit.)
.gif">(a) Assumingthe card selection
is withoutreplacement. (b) Assumingthecardselection is withreplacement.
7. Thereare1000students in a high school. Amongthe1000
students,150 studentstake AP Statistics, and 300studentstake APFrench.100studentstake
both AP courses.LetS bethe event thatarandomlyselected student takesAP
Statistics,andF be the eventthata randomly selected student takesAP French. Showallwork. Just the answer, withoutsupporting
work, willreceivenocredit.
(a) Provide awritten description ofthe complementeventof (SORF). (b) What
istheprobability ofcomplementeventof (SORF)?
.gif">.gif">.gif">8. Considerrollingafair6-faced die twice.LetAbe the
event thatthesumofthetworollsisat most6, and B betheevent thatthefirstone is
anevennumber.
(a) What istheprobabilitythatthesumof thetwo rollsisatmost6 given
thatthe firstoneisan even number?Showallwork. Just
the answer, withoutsupporting work, willreceiveno credit.
.gif">(b) Are eventAand
eventBindependent?Explain.
9. Thereare6 books in the“StatisticsisFun”series.(Showallwork.Just
the answer, without supporting work, willreceiveno credit).
(a) Howmanydifferentways canMimiarrange the6books in herbookshelf?
.gif">(b) Mimiplans
onbringingthreeofthesix books with herin aroadtrip. Howmanydifferentways
can the twobooksbe selected?
Determinethe mean andstandarddeviation of x.Showallwork. Just the answer,without supporting
work, willreceiveno credit.
|
x
|
-2
|
-1
|
0
|
1
|
2
|
|
P(x)
|
0.1
|
0.4
|
0.1
|
0.1
|
0.3
|
(a) LetXbethenumberoffield goalsthatMimiscores inthe game. As we know,
thedistribution ofX isa binomialprobabilitydistribution.Whatis
thenumberoftrials(n), probabilityof successes (p)and probabilityof
failures(q),respectively?
(b) Find the probabilitythatMimiscoresatleast2 ofthe 15 field goals. (round the
answer to3 decimalplaces)Showallwork.Justthe answer, withoutsupporting work,
willreceive nocredit.
12. Aresearchconcludes thatthe numberofhours ofexerciseperweek for adults is
normally distributed with a mean of3.5 hours anda standarddeviationof3hours. Showall work. Just the answer,
withoutsupportingwork, willreceivenocredit.
(a) Find the 75thpercentile forthe distributionofexercisetime perweek. (round the
answerto 2 decimal places)
(b) What istheprobabilitythata randomlyselectedadulthasmore than5
hoursofexerciseperweek?
.gif">(round the answerto
4decimalplaces)
13. Assume theSATMathematicsLevel2 testscoresare normallydistributed with
amean of500 anda standard deviationof 100. Showallwork.Just the answer, withoutsupporting work,
will receiveno credit.
.gif">.gif">.gif">
(a) Considerallrandomsamplesof 100testscores.Whatis the
standarddeviationofthesample means?
(b) What istheprobabilitythat100 randomlyselectedtestscoreswillhave amean
testscorethatis between490and510?
14. An insurance companychecks policerecords on1200randomlyselectedauto
accidentsand notesthatteenagers were at the wheelin180 ofthem.Constructa90%confidence
interval estimate oftheproportionofauto accidents thatinvolve teenage drivers. Showall work. Justthe answer, withoutsupportingwork,
willreceivenocredit.
.gif">15. Acitybuilta new parking garage in a businessdistrict. For
arandomsample of100 days, daily feescollected averaged $1,800, with a standard
deviation of $500. Constructa 90%confidence intervalestimateofthemean dailyincome
thisparking garage generates. Showall
work. Just the answer,
withoutsupporting work, willreceiveno credit.
16. ABC Companyclaims that the proportion of itsemployees investingin
individualinvestment accountsis higherthannationalproportion of50%.Asurveyof100
employeesinABC Companyindicated that58of themhave investedin
anindividualinvestmentaccount.
AssumeMimiwantsto use a 0.10 significanceleveltotest the claim. (a) Identifythe
nullhypothesisand the alternative hypothesis.
work, willreceive nocredit.
(c) DeterminetheP-value for thistest. Showallwork;writingthe
correctP-value,without supporting work, willreceiveno credit.
(d) Is there sufficientevidencetosupportABC Company’sclaimthat the
proportionofits
employees investingin individualinvestmentaccountsis
higherthan50%?Explain.
17. Mimiwascuriousifregularexcisereallyhelps weightloss, henceshedecidedto
performa hypothesis test. Arandomsample of5 UMUCstudentswaschosen.The
studentstooka 30- minute exerciseeverydayfor6 months.The weightwas
recordedforeachindividualbefore and afterthe exercise regimen. Doesthedata
belowsuggest thatregularexercisehelpsweight loss?
|
Weight(
Before
160
170
190
165
200
|
pounds)
|
|
|
Subject
|
After
|
|
|
1
2
3
4
5
|
120
168
175
165
190
|
(a) Identifythe nullhypothesisand the alternative hypothesis.
(b)Determinetheteststatistic. Showallwork;writingthecorrectteststatistic,
without supporting work, willreceiveno credit.
(c) Determinethe p-value.Showallwork;writing
the correctcriticalvalue, without supporting work, willreceiveno credit.
.gif">(d)Is there sufficientevidentto
supporttheclaimthatregularexercisehelps weightloss?
Justify yourconclusion.
18. In apulse rateresearch,asimple randomsample of120 men resultsin a mean
of 80 beats per minute, anda standard deviation of11 beats per minute. Basedon the
sample results,the researcherconcludesthat the pulseratesofmen have
astandarddeviation greater than 10 beats perminutes.Usea 0.10significancelevelto
test the researcher’sclaim.
(a) Identifythe nullhypothesisand alternative hypothesis.
(b) Determinetheteststatistic.Showallwork;writingthecorrect
teststatistic, without supporting work, willreceiveno credit.
(d) Is there sufficientevidencetosupportthe researcher’sclaim? Explain.
19. TheUMUC DailyNews reported that the colordistribution forplain M&M’s
was:40% brown, 20% yellow, 20%orange, 10% green,and 10%tan. Each pieceofcandyin a random sample of100 plainM&M’s was classified
accordingto color,and the results are listed below. Use a 0.05significancelevelto
testtheclaimthat thepublished colordistributionis correct. Showallworkandjustify your answer.
|
Color
|
Brown
|
Yellow
|
Orange
|
Green
|
Tan
|
|
Number
|
45
|
21
|
11
|
8
|
15
|
(a) Identifythe nullhypothesisand the alternative hypothesis.
(b)Determinetheteststatistic. Showallwork;writingthecorrectteststatistic,
without supporting work, willreceiveno credit.
(c) Determinethe p-value.Showallwork;writing
the correctcriticalvalue, without supporting work, willreceiveno credit.
.gif">(d)Is there
sufficientevidenceto supportthe claimthatthe published colordistribution is
correct?Justify youranswer.
20. ASTAT200instructorbelieves
that the average quiz scoreisa good predictorof finalexam score.Arandomsample
of 10 studentsproducedthefollowingdata where xis the average quiz score andyis the
finalexamscore.
|
x
|
80
|
50
|
60
|
100
|
70
|
85
|
40
|
65
|
75
|
90
|
|
y
|
72
|
60
|
55
|
90
|
60
|
85
|
35
|
60
|
78
|
95
|
(a) Find anequation of the leastsquares regressionline. Showall work;writing the correct equation,
withoutsupporting work, willreceivenocredit.
(b) Based ontheequation frompart (a), whatis the predictedfinalexamscoreifthe
average quiz
|
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