statistic question
glangsing
RefertothefollowingtableforQuestions1,2,and3.
Thetableshowstemperaturesonthefirst12daysofOctoberina smalltowninMaryland.
Date | Temperature | Date | Temperature | Date | Temperature |
Oct1 | 73 | Oct5 | 53 | Oct9 | 66 |
Oct2 | 65 | Oct6 | 52 | Oct10 | 49 |
Oct3 | 65 | Oct7 | 62 | Oct11 | 52 |
Oct4 | 70 | Oct8 | 55 | Oct12 | 57 |
1. | Determinethefive-numbersummaryforthisdata. |
|
2. | Determinethemeantemperature. |
|
3. | Determinethemode(s),ifany. |
|
RefertothefollowingfrequencydistributionforQuestions4,5,6,and7.
Thefrequencydistributionbelowshowsthedistributionforcheckouttime(inminutes)in
UMUCMiniMartbetween3:00and4:00PMonaFridayafternoon.
CheckoutTime(inminutes) | Frequency |
1.0-1.9 | 6 |
2.0-2.9 | 7 |
3.0-3.9 | 2 |
4.0-4.9 | 3 |
5.0-5.9 | 2 |
4. | Whatpercentageofthecheckouttimeswasat least4minutes? |
|
5. | Calculate themeanofthisfrequencydistribution. |
|
6. Calculate thestandarddeviationofthisfrequencydistribution.
7. Assumethatthesmallestobservationinthisdatasetis1.2 minutes.Supposethis observationwereincorrectlyrecordedas 0.12insteadof1.2.Will themeanincrease, decrease,orremainthesame?Willthemedianincrease,decreaseorremainthesame? Explainyouranswers.
RefertothefollowinginformationforQuestions8 and9.Showallwork.
A6-faceddieisrolledtwotimes.LetAbetheeventthatthe outcomeofthefirstrollis greaterthan
4.LetBbetheeventthattheoutcomeofsecondrollis anoddnumber.
8. Whatistheprobabilitythatthe outcomeofthesecondrollisanoddnumber,giventhatthefirst rollisgreaterthan4?
9. AreAandBindependent?Whyorwhynot?
Refertothefollowingdatatoanswerquestions10and11.Showall work.
ArandomsampleofSTAT200weeklystudytimesinhoursisasfollows:
414151720
10. Findthestandarddeviation.
11. Areanyofthesestudytimesconsideredunusualinthesenseofourtextbook?Explain.
Doesthisdifferwithyourintuition?Explain.
RefertothefollowinginformationforQuestions12and 13.
Thereare 1500juniorsina college.Amongthe1500juniors,200studentsaretaking
STAT200,and100studentsaretakingPSYC300.Thereare50juniorstakingbothcourses.
12. Whatistheprobabilitythata randomlyselectedjuniorisinat least oneofthetwo courses?
13. Whatistheprobabilitythata randomlyselectedjuniortakesonlyoneofthetwocourses?
)
RefertothefollowinginformationforQuestions14,and 15.Showallwork.
Aboxcontains10chips.Thechipsarenumbered1 through10.Otherwise,thechipsareidentical. Fromthisbox,wedrawonechipatrandom,andrecorditsvalue.Wethenputthechipbackinthe box.Werepeatthisprocesstwomoretimes,makingthreedrawsinallfromthisbox.
14. | Howmanyelementsareinthesamplespaceofthisexperiment? |
|
15. | Whatistheprobabilitythatthethreenumbersdrawnare allmultiplesof5? |
|
Questions16and17 involvetherandomvariablex withprobabilitydistributiongivenbelow.
Showallwork.Justtheanswer,withoutsupportingwork,will receivenocredit.
x | 1 | 2 | 3 | 4 | 5 |
P(x) | 0.1 | 0.2 | 0.3 | 0.1 | 0.3 |
16. | Determinetheexpectedvalueof x. |
|
17. | Determinethestandarddeviationof x. |
|
ConsiderthefollowingsituationforQuestions18,19and20.
Mimijuststartedhertennisclassthreeweeksago.Onaverage,sheisabletoreturn15%of
heropponent’sserves.LetrandomnumberX bethenumberofservesMimireturns.As
weknow,thedistributionofXis a binomialprobabilitydistribution.Ifheropponentserves
10times,pleaseanswerthefollowingquestions:
18. Whatisthenumberoftrials(n),probabilityofsuccesses(p)andprobabilityoffailures(q),
| respectively? |
|
19. | Findtheprobabilitythatshereturnsatmost8 ofthe10servesfromheropponent. |
|
20. | Findthe meanandstandarddeviationfortheprobabilitydistribution. |
|
RefertothefollowinginformationforQuestions21,22,and23.Showallwork.
Theheightsofpecantreesarenormallydistributedwitha meanof10feet andastandarddeviationof 2 feet.
21. | Whatistheprobabilitythata randomlyselectedpecanisbetween8 and12feettall? |
|
22. | Findthe 80thpercentileofthepecantreeheightdistribution. |
|
23. Ifa randomsampleof 64pecantreesisselected,whatisthestandarddeviationofthesample
mean?
24. Arandomsampleof 625SATscoreshasameanof1500.AssumethatSATscoreshave
a populationstandarddeviationof250.Constructa 95%confidenceintervalestimateofthemean
SATscores.Showallwork.Justtheanswer,withoutsupportingwork,will receivenocredit.
25. Givena samplesize of 81,withsamplemean730andsamplestandarddeviation90,we performthefollowinghypothesistest atthea=0.05level.
H0:m=750
H1:m<750
(a) Determinethetest statistic. Showallwork;writingthecorrectteststatistic,without supportingwork,will receivenocredit.
(b)Determinethecritical value.Showall work;writingthecorrectcriticalvalue, withoutsupportingwork,will receivenocredit.
(c) Whatisyourconclusionofthetest?Pleaseexplain.
26. Considerthehypothesistest givenby
H0:m=530
H1:m¹530.
Ina randomsampleof 225subjects,thesamplemeanisfoundto be populationstandarddeviationiss=25.
x=525.Also,the
(a) Determinethetest statistic. Showallwork;writingthecorrectteststatistic,without supportingwork,will receivenocredit.
(b)DeterminetheP-valueforthistest. Showallwork;writingthecorrectP-value,
withoutsupportingwork,will receivenocredit.
(c) Istheresufficientevidencetojustifytherejectionof
H0 at thea=0.01level?
Explain.
27. Acertainresearcherthinksthattheproportionofwomenwhosay thattheearthisgetting warmerisgreaterthantheproportionofmen.Theresearchconducteda survey,and foundthefollowingresult:
Ina randomsampleof 250women,70%saidthattheearthisgettingwarmer. Ina randomsampleof200men,67%saidthattheearthisgetting warmer.
Assume wewant to usea0.05 significancelevelto test theclaim.
(a) Identifythenullhypothesisandthealternative hypothesis.
(b)Determinethetest statistic. Showallwork;writingthecorrectteststatistic,without supportingwork,will receivenocredit.
(c) Determinethecritical value.Showallwork;writingthecorrectcriticalvalue,
withoutsupportingwork,will receivenocredit.
(d)Istheresufficientevidencetosupporttheclaimthattheproportionofwomen saying theearthisgettingwarmerishigherthantheproportionofmensayingtheearthis gettingwarmer?Justifyyourconclusion. (25pts)
RefertothefollowingdataforQuestions28and29.
:
x | 0 | – 1 | 1 | 2 | 4 |
y | 3 | – 2 | 4 | 6 | 8 |
28. Findanequationoftheleastsquaresregressionline. Showallwork;writingthecorrect equation,withoutsupportingwork,will receivenocredit.
29. Basedontheequationfrom# 28,whatisthepredictedvalueofyifx =3?Showallwork andjustifyyouranswer.
30. TheUMUCDailyNewsreportedthatthecolordistributionforplainM&M’swas: 35% brown,20%yellow,20%orange,15%green,and10%tan. Eachpieceofcandyina randomsampleof100plainM&M’swasclassifiedaccordingto color,andtheresultsare listedbelow.
Color | Brown | Yellow | Orange | Green | Tan |
Number | 42 | 21 | 15 | 9 | 13 |
Assumewewantto usea 0.10significancelevel to test theclaimthatthepublishedcolor distributioniscorrect.
(a) Identifythenullhypothesisandthealternative hypothesis.
(b)Determinethetest statistic. Showallwork;writingthecorrectteststatistic,without supportingwork,will receive nocredit.
(c) Determinethecritical value.Showallwork;writingthecorrectcriticalvalue,
withoutsupportingwork,will receivenocredit.
(d)Istheresufficientevidencetosupporttheclaimthatthepublishedcolordistribution
12 years ago
Purchase the answer to view it
stastics_solutions.docx
