Solution manual for statistical methods 3rd edition rudolf freund donna mohr william wilson

Solution Manual forÂ

Statistical Methods, 3rd Edition, Rudolf Freund, Donna Mohr William Wilson

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CHAPTER7: SAMPLEPROBLEMSFORHOMEWORK,CLASSOREXAMS

These problems are designed to be done without access to a computer, but they may require a calculator.

1. Youare readingaresearchpaperthatdescribesastudyofY=meanclassscoreonarithmetic examversusX=numberofarithmetichomeworkproblemsperweekassignedintheclass.Since thedatasetissmall,withonlyn=10classes,youperformtheregressiononascientific calculator.Thescreenoutputstates;

Y = ax + b

a = 1.4

b = 2.1

r = 0.71

a. Interpretthecoefficients,anddescribetherelationshipinsimplelanguage.

b. Istheresignificant evidenceofalinearrelationship,using  =5%?

c. Givea95%confidenceintervalfortheexpectedchangeinY,ifoneadditionalhomework problemisassignedperweek.(Hint:solveforthe t statisticfortheslope.)

2. Youare readingaresearchpaperthatdescribesaregressionofY=fruitsugarcontentonthe independentvariableX=lowtemperatureatharvesttimeindegreesCelsius.Thedataconsisted ofasampleof16observations.Theauthorsprovidethefollowingsummaryinformation:

Intercept 14.26 X -0.35

MSE=0.11

a. Insimplelanguage,describetherelationshipbetweenfruitsugarcontentandlowtemperature.

b. Giveapointestimateoftheexpectedfruitsugarcontentwhenthelowtemperatureis10C.

c. AssumethatthevaluesofXinthedatahadasamplemeanof12Candasamplestandard deviationof4C. Givea95%confidenceintervalfortheexpectedfruitsugarcontentwhenthe lowtemperatureis10C.

3.Inasampleof25observations,thesamplecorrelationbetweensystolicbloodpressureand bodymassindexis0.29. Istheresignificant evidenceofalinearrelationshipbetweenthesetwo variables,using  =5%?

4.Youare researchingtherelationshipbetweensurvivaltimeforlivertransplantpatientswith particularemphasisonthepossiblerelationwithage.Inanarticleinamedicaljournal,youfind thefollowingstatement.

The correlation between age and log(survival time) was -0.65 (p value = 0.094).

a.Describetheapparentrelationshipbetweenageandlog(survivaltime)in simplelanguage.

b. Whatisthemostlikelyreasonforstatingthecorrelationintermsofthelogarithmsratherthan thesurvivaltimes?

c. Thepresenceofthe p valueimpliesahypothesiswastested.Whathypothesiswasmostlikely tested,andwhatconclusionwouldyoureachifyouuse  =5%?

d. Howcouldacorrelationcoefficientwithsuchalarge absolutevaluehavesuchahigh p value?

5. Aresearcharticlestatesthat ThefittedregressionofY=ln(asphaltstrength)onX=ln(sandcontent) was

Assumethisregressioncamefromasampleof15observationswherethesamplemeanofXwas ln(20).Whatcanyousayaboutthetypicalvalueofasphaltstrengthswhensandcontentis20? Usea95%confidenceinterval,andbespecificwithregardtotheparameterforwhichyouare givinganinterval.

6. Autilitycompanyisattemptingtopredictsummerdailydemandforelectricityusingthetwodayaheadweatherforecastfortheday’shigh.(Usingthetwo-dayaheadforecastgivestheutility companytimetoprepare.)Aregressionisdoneusingrecordsfor40randomlyselectedsummer daysduringthepasttwoyears.Demandisinmegawatts. Partoftheprintoutisshownbelow.

a. Fillintheblanksintheprintout.

b. Givea95%confidenceintervalforthedifferenceinexpectedelectricity consumptionfortwo days,oneofwhichis5degreeshotterthantheotherday.

c. Considertwodayswithexactlythesamepredictedhightemperature.Writethesymbolic expression(intermsof 01 , and )forthedifferenceintheiractualelectricityconsumption. Knowingwhatwehavediscussedregardingindependentrandomvariables,usetheinformation abovetogivearough95%confidenceintervalfortheamountbywhichthesetwodayscould differintheir actualelectricityconsumption.[Thisisastretch-your-brainproblem,doasmuch asyoucan.]

7. Youaremodelingvehiclecarbonemissionsasafunctionofethanolcontentoffuel.Eachof theresidualplotsbelowisforsometransformofthedependentandindependentvariables.For each,saywhatisthemostobviousviolationoftheassumptions,andsuggesttheremedy(e.g. non-normalresiduals,transformY). Ifthemodelappearsacceptable,sayso.

8. Youhavedataonarandomsampleof15fifth-gradeclasseswhereY=meanscoreonstandardized readingtestandX=percentofstudentswhoseparentsarenotnativespeakersofEnglish.Hereisa portionoftheregressionprintout:

Givea95%confidenceintervalforthemeanscoreinanindividualclasswhere20percentofthestudents haveparentswhoarenotnativespeakersofEnglish.

A.

B.

C.

SOLUTIONS

1. a. Asnumberofhomeworkproblemsincreases,themeanscoretendstoincrease.Foreachextra homeworkproblemperweek,theclassmeanisexpectedtoincreaseby1.4points.If0homework problemsareassigned,theclassmeanisexpectedtobe2.1.

b. F= 2 2 8(0.71) 8.13 (10.71)  with1and8df.Thecriticalvalueat  =5%is5.32.Thereissignificant evidenceofarelationship.

c. 1.4

2a.Asthelowtemperatureincreases(thatis,weatheriswarmer),thefruitsugarcontentdeclines.

b. 10.76

c. 2 14 10.762.14480.1110.760.20(10.56,10.96) 16 15(4)

3. 2 2 23(0.29) 2.11 (10.29) F  with1and23df.Thecriticalvalueat  =5%is4.28. Thereisno significantevidenceofarelationshipbetweensystolicbloodpressureandbodymassindex.

4. a. Asageincreases,log(survivaltime)tendstodecline.

b.Therelationshipofageandsurvivaltimeismostlikelynonlinear.

c. Ho: 0   where  isthepopulationcorrelationbetweenageandlog(survivaltime).Sincethep valueis0.094,wecannotrejectHo.Thereisnosignificantevidenceofalinearrelationbetweenageand log(survivaltime).

d.Musthavebeenasmallsample,orFwouldhavebeenlarge.

5. MustremembertotransformSandContent=20toX=ln(20). Pointestimateformeanln(asphaltstrength)is3.42–0.49*ln(20)=1.952. SincevalueofXforwhichthe predictionisdesiredisatthesamplemean,donotneedthesumsofsquaresfortheXvalues.

Notethatthisisaconfidenceintervalforthemeanofln(asphaltstrength)whenSandContentis20. To obtainastatementabouttypicalAsphaltStrength,mustexponentiate.

Withconfidence95%,medianAsphaltStrengthisbetween5.64and8.80whenSandContentis20.

b. 5(0.3502.03(0.0149))(1.6,1.9) 

Withconfidence95%,theexpecteddifferenceisbetween1.6and1.9.

c. ForDay1, 1011 YX andforDay2, 2012

. Thedifferenceintheiractual consumptionis 12 . Sincetheerrorsareindependentwithvariance 2  thedifferencehasmean0

andvariance 2 2 . Hence,aroughconfidenceintervalforthedifferencewouldbe 2 2222(8.132)8.07

7. A. nonconstantvariance,transformtheYvariable

B. Looksgood

C. Nonlinearity,butnostrongchangeinvariance. TransformtheXvariable.

8. pointestimate

Solution Manual for Statistical Methods, 3rd Edition, Rudolf Freund, Donna Mohr William Wilson