stst200 final exam done on 16 dec 2016

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.