The Frequency Distribution for Small Town in Maryland
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The Frequency Distribution for Small Town in Maryland
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.
Thefrequencydistribution belowshowsthedistributionforcheckouttime(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.
- Calculate thestandarddeviationofthisfrequencydistribution.
- 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.
- Whatistheprobabilitythatthe outcomeofthesecondrollisanoddnumber,giventhatthefirst rollisgreaterthan4?
- AreAandBindependent?Whyorwhynot?
Refertothefollowingdatatoanswerquestions10and11.Showall work.
ArandomsampleofSTAT200weeklystudytimesinhoursisasfollows:
414151720
- Findthestandarddeviation.
- Areanyofthesestudytimesconsideredunusualinthesenseofourtextbook?Explain.
Doesthisdifferwithyourintuition?Explain.
RefertothefollowinginformationforQuestions12and 13.
Thereare 1500juniorsina college.Amongthe1500juniors,200studentsaretaking
STAT200,and100studentsaretakingPSYC300.Thereare50juniorstakingbothcourses.
- Whatistheprobabilitythata randomlyselectedjuniorisinat least oneofthetwo courses?
- Whatistheprobabilitythata randomlyselectedjuniortakesonlyoneofthetwocourses?
)
RefertothefollowinginformationforQuestions14,and 15.Showallwork.
Aboxcontains10chips.Thechipsarenumbered1 through10.Otherwise,thechipsareidentical. Fromthisbox,wedrawonechipatrandom,andrecorditsvalue.Wethenputthechipbackinthe box.Werepeatthisprocesstwomoretimes,makingthreedrawsinallfromthisbox.
14. Howmanyelementsareinthesamplespaceofthisexperiment? 15. Whatistheprobabilitythatthethreenumbersdrawnare allmultiplesof5?
The Frequency Distribution for Small Town in Maryland
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:
- 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.
- Ifa randomsampleof 64pecantreesisselected,whatisthestandarddeviationofthesample
mean?
- Arandomsampleof 625SATscoreshasameanof1500.AssumethatSATscoreshave
a populationstandarddeviationof250.Constructa 95%confidenceintervalestimateofthemean
SATscores.Showallwork.Justtheanswer,withoutsupportingwork,will receivenocredit.
- 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.
- 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.
- 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
- Findanequationoftheleastsquaresregressionline. Showallwork;writingthecorrect equation,withoutsupportingwork,will receivenocredit.
- Basedontheequationfrom# 28,whatisthepredictedvalueofyifx =3?Showallwork andjustifyyouranswer.
- 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
iscorrect?Justifyyouranswer.
The Frequency Distribution for Small Town in Maryland
RUBRIC
Excellent Quality
95-100%
Introduction 45-41 points
The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.
Literature Support
91-84 points
The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.
Methodology
58-53 points
Content is well-organized with headings for each slide and bulleted lists to group related material as needed. Use of font, color, graphics, effects, etc. to enhance readability and presentation content is excellent. Length requirements of 10 slides/pages or less is met.
Average Score
50-85%
40-38 points
More depth/detail for the background and significance is needed, or the research detail is not clear. No search history information is provided.
83-76 points
Review of relevant theoretical literature is evident, but there is little integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are included. Summary of information presented is included. Conclusion may not contain a biblical integration.
52-49 points
Content is somewhat organized, but no structure is apparent. The use of font, color, graphics, effects, etc. is occasionally detracting to the presentation content. Length requirements may not be met.
Poor Quality
0-45%
37-1 points
The background and/or significance are missing. No search history information is provided.
75-1 points
Review of relevant theoretical literature is evident, but there is no integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are not included in the summary of information presented. Conclusion does not contain a biblical integration.
48-1 points
There is no clear or logical organizational structure. No logical sequence is apparent. The use of font, color, graphics, effects etc. is often detracting to the presentation content. Length requirements may not be met
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