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.
ItisaviolationoftheAcademicDishonestyandPlagiarismpolicy
touse unauthorizedmaterialsorworkfromothers.
Answerall20questions.Makesureyouranswersareascompleteaspossible. Show
allofyoursupportingworkandreasoning.Answersthatcomestraight fromcalculators,programsorsoftwarepackages
withoutanyexplanationwillnot
beaccepted.Ifyouneedtouse
technology(forexample,Excel,onlineorhand-
heldcalculators,statisticalpackages)toaid
inyourcalculation,you mustcitethe
sourcesandexplainhowyougettheresults.
Recordyouranswersandworkontheseparateanswersheetprovided.
Thisexamhas100totalpoints;
5pointsforeachquestion.
Youmustinclude
theHonorPledgeonthetitlepageofyoursubmittedfinal
exam. ExamssubmittedwithouttheHonorPledgewillnotbeaccepted.
1.
True orFalse.Justifyforfullcredit.
(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.
2. Choosethe bestanswer.
Justifyforfullcredit.
(a)
Astudywasconducted atalocalcollege to
analyze theaverage
GPA
ofstudents graduated fromin
2015.100students graduatedfromin 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,
News Club organized
anexitpollin which specific polling stations were randomlyselectedand
allvoters
were surveyed as theyleftthose
pollingstations. Thistypeofsamplingiscalled:
(i) cluster
(ii)
convenience (iii)
systematic (iv)
stratified
3.
Choosethe bestanswer.
Justifyforfullcredit.
(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
10 programs.
Whatstatisticalapproachshould
beused? (i)
t-test
(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
(iv) F-test
4. Arandomsample of100 students waschosen fromSTAT200
classes.The
frequency distributionbelowshowsthe
distribution
forstudytime
eachweek(inhours).(Showallwork.
Just
theanswer, withoutsupporting work,
willreceiveno
credit.)
|
Study Time(inhours) |
Frequency |
RelativeFrequency |
|
0.0– 4.9 |
5 |
|
|
5.0-9.9 |
13 |
|
|
10.0- 14.9 |
0.22 |
|
|
15.0-19.9 |
42 |
|
|
20.0–24.9 |
||
|
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?
5.
The five-numbersummary
belowshows the
gradedistribution ofaSTAT200 quizfora
sample of1000 students.
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
(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.)
(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)?
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.
(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?
(b)
Mimiplans
onbringingthreeofthesix
books with herin aroadtrip. Howmanydifferentways can the twobooksbe selected?
10. Assume randomvariablexfollows aprobabilitydistribution shown
inthetable
below.
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 |
11.
Mimijoined basketball teamsincesummer2016.On average,
she
is
abletoscore30%
of the field goals.Assumeshetries15 field goalsin a game.
(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?
(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.
(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.
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.
(b)
Determinetheteststatistic. Showallwork;writingthecorrectteststatistic, withoutsupporting
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 studentswaschosen.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 |
Assume wewant
to usea0.05 significancelevel
to test the claim.
(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.
(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.
(c) DeterminetheP-value for thistest.
Showallwork;writingthe correctP-value,without
supporting work, willreceiveno credit.
(d)
Is there sufficientevidencetosupportthe
researcher’sclaim? Explain.
19. The 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.
(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
score is95?Show allworkand justify
your answer.
