The normal distribution curve is always symmetric to its mean

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  1. TrueorFalse.Justifyfor fullcredit. (10pts)

 

 

    1. Thenormaldistributioncurve is alwayssymmetricto itsmean.

 

    1. If the variancefroma datasetis zero,thenalltheobservations inthisdatasetareidentical.

    2. P(AANDAc) = 1, where Ac is the complement of A.

 

 

  1. In a hypothesistesting,ifthep-value islessthanthesignificancelevelα, wedo nothavesufficientevidenceto rejectthenullhypothesis.

 

  1. The volume ofmilkin ajugof milkis 128 oz.Thevalue 128isfroma discretedataset.

 

 

 

Refertothefollowingfrequencydistribution forQuestions2, 3,4, and5. Showallwork.Justtheanswer, withoutsupportingwork,willreceive nocredit.

 

Arandomsampleof 25customerswas chosen in UMUCMiniMartbetween3:00 and 4:00PMon aFridayafternoon.Thefrequencydistributionbelowshowsthedistribution forcheckouttime(in minutes).

 

CheckoutTime(inminutes)

Frequency

RelativeFrequency

1.0-1.9

2

2/25

2.0-2.9

8

8/25

3.0-3.9

=25-(2+8+5) = 10

10/25

4.0-5.9

5

5/25

Total

25

 

 

 

  1. Completethefrequencytablewithfrequencyand relativefrequency. (1pt)

  2. Whatpercentage ofthecheckouttimeswaslessthan 3minutes? (1pt)

  3. Inwhatclassinterval mustthe medianlie?Explainyouranswer. (1pt)

 

 

  1. Assume thatthelargestobservation inthisdatasetis5.8.Supposethisobservationwereincorrectlyrecordedas8.5insteadof5.8.Willthemeanincrease,decrease,orremain thesame?Willthe medianincrease,decreaseorremain thesame?Why? (1pt)

 

 

  1. A randomsampleofSTAT200weeklystudytimes in hours is asfollows:2 15 15 1830

 

 

 

RefertothefollowinginformationforQuestions7,8, and 9. Show allwork.Justtheanswer,withoutsupportingwork,willreceive nocredit.

 

Afaircoinistossed 4times.

 

  1. How manyoutcomes aretherein thesamplespace? (5 pts)

 

 

  1. Whatistheprobabilitythatthethirdtossisheads,giventhatthefirst tossis heads? (5pts)

 

 

  1. Let Abetheeventthatthefirst tossis heads,and Bbethe eventthatthethirdtossis heads.AreA

andBindependent?Whyor whynot? (5 pts)

 

 

 

 

RefertothefollowingsituationforQuestions10,11, and 12.

 

Theboxplotsbelowshowtherealestatevaluesofsingle familyhomesin twoneighboringcities, inthousandsofdollars.

 

Foreach question,giveyouransweras one ofthefollowing:(a)Tinytown;(b)BigBurg;(c)Bothcitieshavethesamevaluerequested;(d)It isimpossible totellusingonlythegiveninformation.Then explain youranswerin each case. (5 ptseach)

 

  1. Whichcityhas greatervariabilityin realestatevalues?

 

 

  1. Whichcityhasthe greaterpercentage ofhouseholdswithvalues$85,000and over?

 

 

  1. Whichcityhasa greaterpercentage ofhomeswithrealestatevaluesbetween$55,000and $85,000?

 

 

 

RefertothefollowinginformationforQuestions13and 14. Show allwork.Justtheanswer,withoutsupportingwork,willreceive nocredit.

 

Thereare 1000juniorsina college.Amongthe1000juniors,200studentsaretakingSTAT200, and100 studentsaretakingPSYC300.Thereare50studentstakingbothcourses.

 

 

  1. Whatistheprobabilitythata randomlyselectedjunior is takingatleastone ofthesetwocourses? (5pts)

 

  1. Whatistheprobabilitythata randomlyselectedjunior is takingPSYC300,given thathe/sheistakingSTAT200? (5pts)

 

 

 

  1. UMUCStatClubissendinga delegateof 2 memberstoattendthe2015JointStatisticalMeetingin Seattle.Thereare 10qualifiedcandidates.How manydifferentwayscanthedelegatebeselected? (5 pts)

 

 

 

 

  1. Imagineyou are ina gameshow.Thereare4prizeshidden ona game board with10spaces.Oneprize is worth$100, anotheris worth$50,and twoareworth $10.Youhave to pay

$20 tothehostifyourchoiceis not correct.Lettherandomvariable xbethewinning.Show allwork.Just the answer,withoutsupportingwork,willreceive nocredit.

 

 

(a)

Whatis yourexpectedwinningin this game?

 

 

(5 pts)

 

 

 

 

 

 

 

 

 

 

 

 

  1. Mimijuststartedhertennisclassthreeweeksago.Onaverage, sheis abletoreturn 20%of heropponent’sserves.Assume her opponentserves 8 times.Show allwork.Just the answer,withoutsupportingwork,willreceive nocredit.

 

(a) LetXbethenumberofreturnsthatMimigets. Asweknow, the distributionof Xis a binomialprobabilitydistribution. What isthe numberoftrials(n),probabilityofsuccesses(p) and

 

 

probabilityof failures(q),respectively?

(5 pts)

(b)

Findtheprobabilitythat thatshereturnsatleast1ofthe8 servesfromheropponent.

(5pts)

(c)

How manyserves can sheexpecttoreturn?

(5 pts)

 

RefertothefollowinginformationforQuestions18,19, and 20.Show allwork.Justtheanswer,withoutsupportingwork,willreceive nocredit.

 

The IQ scoresarenormallydistributedwith amean of100 anda standarddeviation of 15.

 

18.

Whatistheprobabilitythata randomly personhas an IQ between85 and 115?

(5pts)

19.

Findthe90thpercentile of theIQ distribution.

(5 pts)

  1. If a randomsample of100peopleisselected,whatisthestandarddeviationofthesamplemean?

(5 pts)

 

 

 

  1. Arandomsample of100lightbulbshasa meanlifetimeof3000 hours.Assumethatthepopulationstandarddeviationofthelifetime is500hours.Constructa 95%confidenceinterval

  2.  

  3.  

  4. estimate ofthe meanlifetime.Showallwork.Just theanswer, without supportingwork,willreceiveno credit. (5pts)

  5.  

  7.  

  8. Considerthe hypothesistestgiven by

  9.  

  1. H0 :p H1:p

  2. 0.5

  3. 0.5

  1.  

  1.  

     

    In a randomsample of225subjects, the sampleproportionisfound tobepˆ

  2. 0.51.

  1.  

    1. Determinetheteststatistic.Show allwork;writingthecorrectteststatistic,withoutsupportingwork,willreceive no credit.

    2. Determinethep-valueforthistest.Show allwork;writingthe correctP-value,withoutsupportingwork,willreceive nocredit.

    1. Isthere sufficientevidencetojustifytherejectionofH0atthe

    2. level?

    1. Explain. (5pts)

    3.  

  1. Anew prepclasswasdesigned toimproveAPstatisticstest scores.Fivestudentswereselectedatrandom.Thenumbers of correctanswersontwopracticeexamswererecorded;onebeforetheclassandone after.The datarecordedin thetablebelow.Wewanttotest ifthenumbersof correctanswers,onaverage, are higheraftertheclass.

    1.  

        1. Numberof CorrectAnswers

        1. Subject

        1. Before theclass

        1. Aftertheclass

        1. 1

        1. 12

        1. 14

        1. 2

        1. 15

        1. 18

        1. 3

        1. 9

        1. 11

        1. 4

        1. 12

        1. 10

        1. 5

        1. 12

        1. 12

    3. Is there evidenceto suggestthatthemeannumberofcorrectanswersafter theclassexceedsthe meannumberofcorrectanswersbeforetheclass?

    4.  

    5. Assumewewanttousea 0.01significanceleveltotesttheclaim.

    6. Identifythe nullhypothesisand thealternativehypothesis.

    7. Determinetheteststatistic.Show allwork;writingthecorrectteststatistic,withoutsupportingwork,willreceive no credit.

    8. Determinethep-value.Show allwork;writingthecorrectcritical value,withoutsupportingwork,willreceive no credit.

    9. Is there sufficientevidence to supporttheclaimthatthemeannumberofcorrectanswersaftertheclassexceedsthemeannumberofcorrectanswersbeforetheclass?Justifyyourconclusion. (10pts)

    1.  

    3.  

    5.  

  1. Arandomsample of4 professionalathletesproducedthefollowingdatawhere x is thenumberof endorsementstheplayerhasand yistheamountofmoneymade (in millionsofdollars).

    1.  

        1. x

        1. 0

        1. 1

        1. 3

        1. 5

        1. y

        1. 3

        1. 2

        1. 3

        1. 8

  1. Find anequationoftheleastsquaresregressionline.Show allwork;writingthecorrectequation,without supportingwork,willreceive nocredit. (5pts)

  2. Based ontheequationfrompart(a),whatisthepredictedvalueofyifx = 4?Show allwork andjustifyyouranswer. (5pts)

    2.  

    4.  

  1. Randomlyselectednonfataloccupationalinjuriesandillnessesarecategorizedaccordingto the dayofthe weekthattheyfirstoccurred, andtheresultsarelistedbelow.Usea 0.05significancelevelto testtheclaimthatsuchinjuriesandillnesses occur withequalfrequencyonthe differentdays oftheweek.Show allwork andjustifyyouranswer.

    2.  

        1. Day

        1. Mon

        1. Tue

        1. Wed

        1. Thu

        1. Fri

        1. Number

        1. 22

        1. 22

        1. 20

        1. 19

        1. 17

    5.  

    6. Identifythe nullhypothesisand thealternativehypothesis.

    7. Determinetheteststatistic.Show allwork;writingthecorrectteststatistic,withoutsupportingwork,willreceive no credit.

    8. Determinethep-value.Show allwork;writingthecorrectcritical value,withoutsupportingwork,willreceive no credit.

    9. Is there sufficientevidenceto supporttheclaimthatsuchinjuries andillnessesoccurwithequalfrequencyon thedifferentdays ofthe week?Justifyyouranswer.

    10. (5pts)

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