STAT 200 Final Examination
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Refertothefollowing frequencydistributionforQuestions1, 2,3, and4. Showallwork.Just the answer,withoutsupportingwork,willreceivenocredit.
Thefrequencydistribution belowshows thedistributionforcheckouttime(in minutes)in
UMUCMiniMartbetween 3:00 and4:00PMon aFriday afternoon.
Checkout Time (in minutes) | Frequency |
1.0 -‐ 1.9 | 5 |
2.0 -‐ 2.9 | 6 |
3.0 -‐ 3.9 | 4 |
4.0 -‐ 4.9 | 3 |
5.0 -‐ 5.9 | 2 |
1. Whatpercentageofthecheckout times waslessthan 3minutes? (5 pts)
2. Calculatethe meanofthisfrequencydistribution. (5 pts)
3. Calculatethestandarddeviation ofthisfrequencydistribution. (10 pts)
4. Assumethatthesmallestobservationinthisdatasetis1.2 minutes. Suppose this observationwereincorrectlyrecordedas0.12instead of1.2.Willthemeanincrease, decrease,orremainthe same?Will themedianincrease,decreaseorremainthe same? Explain youranswers. (5 pts)
RefertothefollowinginformationforQuestions5and6. Showallwork. Justtheanswer, without supporting work, willreceiveno credit.
A6-faced die isrolled twotimes.LetAbe theeventthatthe outcomeofthefirstrollisgreater than
4. LetBbetheeventthatthe outcomeofsecond roll isan odd number.
5. Whatistheprobabilitythattheoutcomeof thesecondrollisan odd number,giventhat thefirst rollisgreaterthan4? (10 pts)
6. AreA and Bindependent?Whyorwhynot? (5 pts)
Refertothefollowingdatato answerquestions 7and 8. Showallwork. Justtheanswer, without supporting work, willreceiveno credit.
Arandomsample ofSTAT200weeklystudy timesin hoursisasfollows:
4 14 15 17 20
7. Find thestandarddeviation. (10 pts)
8. Areanyofthesestudytimes consideredunusualin thesenseofourtextbook? Explain.
Does thisdifferwith yourintuition? Explain. (5 pts)
RefertothefollowingtableforQuestions9, 10,and 11. Showallwork. Justtheanswer, without supporting work, willreceiveno credit.
The tableshowstemperaturesonthefirst12daysofOctober ina smalltownin Maryland.
Date | Temperature | Date | Temperature | Date | Temperature |
Oct1 | 73 | Oct5 | 53 | Oct9 | 66 |
Oct2 | 66 | Oct6 | 52 | Oct10 | 49 |
Oct3 | 65 | Oct7 | 62 | Oct11 | 53 |
Oct4 | 70 | Oct8 | 55 | Oct12 | 57 |
9. | Determinethefive-numbersummaryfor thisdata. | (10 pts) |
10. | Determinethe meantemperature. | (3 pts) |
11. | Determinethemode(s), ifany. | (2 pts) |
RefertothefollowinginformationforQuestions 12and 13. Showallwork.Just theanswer, withoutsupporting work,willreceivenocredit.
Thereare1000studentsin theseniorclassatacertain high school. Thehighschooloffers twoAdvancedPlacementmath/statclassestoseniorsonly:APCalculusandAPStatistics. Therosterof theCalculusclassshows100 people;theroster of theStatisticsclassshows80 people.Thereare 45 overachievingseniorsonbothrosters.
12. Whatistheprobabilitythata randomlyselectedseniorisinat leastoneofthetwoclasses
? (10 pts)
13. Whatistheprobabilitythata randomlyselectedseniortakesonlyone class? (10 pts)
Refertothefollowinginformation forQuestions14,and 15. Showallwork.Just theanswer, withoutsupporting work,willreceivenocredit.
Aboxcontains10 chips.Thechipsarenumbered1 through10.Otherwise,thechipsareidentical. Fromthisbox,wedrawonechipatrandom,and record itsvalue. Wethen put thechip backin the box. We repeat thisprocess twomoretimes,makingthreedrawsin allfromthisbox.
14. | Howmanyelementsare inthe samplespaceof thisexperiment? | (5 pts) |
15. | Whatistheprobabilitythatthethreenumbersdrawn areallmultiplesof3? | (10 pts) |
Questions16 and 17 involve therandomvariablexwith probabilitydistribution given below.
Showallwork.Justtheanswer, withoutsupporting work, willreceiveno credit.
x | 2 | 3 | 4 | 5 | 6 |
P(x) | 0.1 | 0.2 | 0.3 | 0.1 | 0.3 |
16. | Determinethe expectedvalue ofx. | (10 pts) |
17. | Determinethestandarddeviationof x. | (10 pts) |
Considerthefollowing situation forQuestions18, 19and 20. Showallwork.Justtheanswer, withoutsupporting work,willreceivenocredit.
Mimijuststarted hertennisclass threeweeksago.On average,sheisabletoreturn15%of heropponent’sserves. LetrandomnumberXbe thenumberofservesMimireturns. As
weknow,thedistribution ofXisa binomialprobability distribution.Ifheropponentserves
10 times, pleaseanswer thefollowing questions:
18. Whatisthenumberoftrials (n), probabilityofsuccesses (p)and probabilityoffailures(q),
| respectively? | (5 pts) |
19. | Find theprobabilitythatshe returnsatleast2 of the10servesfromheropponent. | (10pts) |
20. | Find themean andstandarddeviation fortheprobabilitydistribution. | (10 pts) |
Refertothefollowinginformation forQuestions21,22, and 23.Showallwork.Justtheanswer, withoutsupporting work,willreceivenocredit.
The heightsofpecan treesarenormallydistributed with amean of10feetand astandard deviationof2 feet.
21. | Whatistheprobabilitythata randomlyselectedpecanisbetween10and12feettall? | (10 pts) |
22. | Find the90thpercentile of thepecan treeheightdistribution. | (5 pts) |
23. Ifa randomsampleof25 pecantreesisselected,whatisthestandarddeviationofthesample
mean? (5 pts)
24. Arandomsampleof225SATscoreshasameanof1500.Assume thatSATscoreshave
apopulationstandard deviationof300. Constructa95%confidence intervalestimateof themean
SATscores. Showallwork.Justtheanswer, withoutsupporting work, willreceiveno credit.
(15 pts)
25. Givena samplesizeof100,withsamplemean 730 andsamplestandard deviation80,we
performthefollowinghypothesistestattheD
0.05level.
H 0:P
750
H1:P 750
(a) Determinetheteststatistic.Showallwork;writingthecorrectteststatistic, without supporting work, willreceiveno credit.
(b)Determinethe criticalvalue.Showallwork;writingthecorrectcriticalvalue, withoutsupporting work,willreceivenocredit.
(c) Whatisyourconclusionofthetest? Pleaseexplain. (20 pts)
26. Considerthehypothesistestgiven by
H 0:P
530
H1:Pz530.
In a randomsampleof81 subjects,thesamplemean isfoundto bex
524.Also, the
population standarddeviation isV
27.
(a) Determinetheteststatistic.Showallwork;writingthecorrectteststatistic,without supporting work, willreceiveno credit.
(b)Determinethe P-valuefor thistest. Showallwork;writingthe correctP-value,
withoutsupporting work,willreceivenocredit.
(c) Is theresufficientevidencetojustifythe rejectionofH0 attheD
0.01level?
Explain. (20 pts)
27. Acertainresearcherthinksthattheproportion ofwomen who saythattheearthis getting warmer isgreater than theproportion ofmen. The researchconductedasurvey,and foundthefollowingresult:
Inarandomsampleof250women, 70%said thatthe earthisgettingwarmer. In a randomsampleof200men, 67%saidthattheearth isgettingwarmer.
Assume we want to usea0.05significancelevel to test the claim.
(a) Identifythenullhypothesisand thealternativehypothesis.
(b)Determinetheteststatistic.Showallwork;writingthecorrectteststatistic,without supporting work, willreceiveno credit.
(c) Determinethe criticalvalue.Showallwork;writingthecorrectcriticalvalue, withoutsupporting work,willreceivenocredit.
(d)Is theresufficientevidenceto supporttheclaimthattheproportionofwomen saying
the earthisgettingwarmer ishigher thantheproportion ofmen saying theearthis gettingwarmer?Justify yourconclusion. (25 pts)
RefertothefollowingdataforQuestions28 and 29.
:
x | 0 | – 1 | 1 | 2 | 3 |
y | 3 | – 2 | 5 | 6 | 8 |
28. Find anequation ofthe leastsquaresregressionline. Showall work;writing thecorrect equation, withoutsupporting work, willreceivenocredit. (15 pts)
29. Based ontheequation from# 28, whatis thepredicted valueofyifx =4? Showallwork and justifyyouranswer. (10 pts)
30. TheUMUC DailyNews reported thatthecolordistribution forplainM&M’swas:40% brown, 20%yellow, 20%orange, 10%green, and 10%tan. Eachpieceofcandyina randomsampleof100plainM&M’swasclassifiedaccordingtocolor,andtheresultsare listedbelow.
Color | Brown | Yellow | Orange | Green | Tan |
Number | 42 | 21 | 15 | 9 | 13 |
Assumewewant tousea0.10 significanceleveltotestthe claimthatthe publishedcolor distributioniscorrect.
(a) Identifythenullhypothesisand thealternativehypothesis.
(b)Determinetheteststatistic.Showallwork;writingthecorrectteststatistic, without supporting work,willreceivenocredit.
(c) Determinethe criticalvalue.Showallwork;writingthecorrectcriticalvalue,
withoutsupporting work,willreceivenocredit.
(d)Is theresufficientevidencetosupportthe claimthatthepublished colordistribution
iscorrect?Justify your answer. (25 pts)
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