Problem2(Unit1).SaudiArabiisamajorexporterofcrudeoilintheworld.ThefollowingtablereportstheexporttoChina,India,SouthKorea,Japan,USA,andothercountriesin2021.

China($38.3billion),	India($15.8billion),	SouthKorea($18.5billion),
Japan($21.9billion),	USA($7.76billion),	Othercountries($35.74billion)

A. Constructthefrequencydistributiontableforthesedata.Makesurethatthetableincludesthefrequency,relativefrequency,andsliceofthepie.Showyourwork.

B. Drawabarchart.Showyourwork.

C. Drawapiechart.Showyourwork.

D. Whatinformationisconveyedbyeachchart?Clearlyexplain.

Problem3(Unit1).AQIstandsfortheAirQualityIndex,anditrangesfrom0to500.AnAQIvalueof 50 or lower represents good air quality (or low level of air pollution). The government of largecountry claims that the AQI value for all of its cities is 50. To test this claim, the AQI value isdetermined for 20 randomly selected cities. The random sample yields an average AQI value of53,withastandarderror of2.Now,answerthefollowingquestions.

A. Whatkindofdescriptivemeasurearewedealingwithhere(mean,variance,orproportion)?

B. Whatisthepopulationinthisexample?

C. Whatisthesampleinthisexample?

D. Whatdoes"20"representinthisexample?

E. Whatisthenotationforthepopulationparameterinthisexample?

F. Whatisthenotationforthesamplestatisticinthisexample?

G. Whatdoes"50"representinthisexample?

H. Whatdoes"53"representinthisexample?

I. Doyoureject(orfailtoreject)theclaim?Showyourcalculations.

Problem4(Unit2).LetthevariableXbe households'income(inthousandsofdollars)inalarge city.Forarandomsampleoftenhouseholds,X={20,85,65,40,32,72,28,60,23,35}.

A. Findthesamplemeanandmedian.Showyourwork.

B. Isthedistributionofthedataskewedorapproximatelysymmetricinthisexample?Explain.

C. Isthemeanormediananappropriatemeasureofcentraltendencyinthisexample?Explain.

D. Findandinterpretthe25^thpercentile(Q1),50^thpercentile(Q2),and75^thpercentile(Q3).Showyourwork.

E. Findtherangeandinterquartilerange.Showyourwork.

F. Istherangeorinterquartilerangeanappropriatemeasureofvariationinthisexample?Explain.

Problem 5 (Unit 2).The average number of years of schooling of individuals in a large city isestimated to be 12 years (that is, = 12) with a standard deviation of S= 2 years. In answering thefollowingquestions,use Chebyshev'stheoremandtheempirical rule(whereappropriate).

A. Whatfractionofindividualshasbetween8and16yearsofschooling?Notethatnoinformationis givenabouttheshapeofthedistribution.Showyourwork.

B. Howdoesyouranswer topart(a)changeifthedistributionisbell-shaped?Showyourworkbydrawing abell-shapeddistributionthatincludesyouranswer.

C. Whatfractionofindividualshasbetween 10and14yearsofschooling ifthedistributionisbell-shaped?Showyourworkbydrawingabell-shapeddistributionthatincludesyouranswer.

D. Whatfractionofindividualshasmore than18yearsofschoolingifthedistributionisbell-shaped?Showyourworkbydrawingabell-shapeddistributionthatincludesyouranswer.

Problem6(Unit3).Studiesindicatethatthereisastrongassociationbetweenlaborproductivity(X)andrealwages(Y).Forarandomsampleof100workersinalargeindustry,_xy=.70withastandarderrorof.08.AcriticclaimsthatthetruecorrelationcoefficientbetweenYandXis.85.Nowanswerthefollowingquestions.

1. Whatkindofdescriptivemeasurearewedealingwithhere(mean,variance,proportion,orcorrelationcoefficient)?
2. Whatisthenotationforthepopulationparameterinthisexample?
3. Whatisthenotationforthesamplestatisticinthisexample?
4. Whatdoes.70representinthisexample?Clearlyexplain.
5. Whatdoes.85 representinthisexample?Clearlyexplain.
6. Whatdoes_xy=.70revealabouttherelationshipbetweenXandY?Clearlyexplain.
7. Testthevalidityoftheclaim.Doyoureject(orfailtoreject)theclaim?Showyourcalculations.

Problem7(Units1,2&3).Asmallcardealershiphasthefollowing dataoncarpricesandonthenumberofcarssoldfor2017-2023.

Year	Numberofcarssold(Y)	Pricepercarinthousandsofdollars(X)	.
2017	25	10
2018	21	12
2019	20	15
2020	17	17
2021	14	15
2022	12	21
2023	10	22

A. Arethedatacross-sectionalortime-series?Explainclearly.

B. Usingtimeplots,displaythebehaviour ofthepriceandthebehaviorofsalesfor2017-2023.Comment onyourresults.

C. Whichvariableisthedependentvariable,andwhichistheindependentvariableinthisexample?Explain.

D. Usingthescatterdiagram, investigatetherelationshipbetweenYandX.Istherelationshipperfectorimperfect?Istherelationshippositiveornegative? Explainclearly.

E. Findthemeanpriceinadditiontothestandarddeviation.Showyourwork.

F. Findthemeannumberofcarssoldinadditiontothestandarddeviation.Showyourwork.

G. FindboththecovarianceandcorrelationcoefficientbetweenYandX.Showyourwork.

H. Usingyourresultsinpart(g),whatcanyousayaboutthedirectionandstrengthoftheassociationbetweenXandY?Explain clearly.

Problem8(Unit3).Americanshavedifferent politicalviews.Ingeneral,conservativeAmericansvote Republican, and liberal Americans vote Democratic. Conservatives tend to live in smalltowns, while liberals tend to live in large cities.To investigate whether there is an associationbetween"location"and"politicalviews," wefocusonasample of400Americansasfollows:

• 200conservatives:130liveinsmalltownsand70liveinmajorcities

• 200liberals:50liveinsmalltownsand150liveinmajorcities

A. Constructthefrequency table.Showyourwork.

B. Constructtherowrelative frequencytable.Isthereanassociationbetween"location"and"politicalviews"?Clearlyinterpret yourresults.Showyourwork.

C. Constructthecolumnrelative frequencytable.Isthereanassociationbetween"location"and"politicalviews"?Clearlyinterpret yourresults.Showyourwork.

Note: these Questions are complete from all aspects.