Revision Exercises on ttests and nonparametricsolution.docx

Revision Exercises on ttests and nonparametricsolution.docx

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RevisionExercisesonttestsandnonparametricsolution

REVISIONEXERCISESONT-TESTSANDNON-PARAMETRICTESTS

Question1

File:

Country

Thefollowingresultsistotestthenullhypothesisthattheaveragelifeexpectancyformalesisthesameastheaveragelifeexpectancyforfemales（variables:

lifeexpmandlifeexpf）.

Interprettheresults.

Ho:

µdiff=0

Ha:

µdiff=0

µdiff:

meandifferencebetweenmaleandfemalelifeexpectancy

Sig.=0.000.Resultsaresignificantatthe0.1%level.Femalelifeexpectancyissignificantlyhigher（mean=66.31）thanmalelifeexpectancy（mean=61.9）

Question2

File:

gss

Interprettheresultsabove.

Age

Ho:

µ1=µ2

Ha:

µ1≠µ2

Whereµ1andµ2aremeanageforpeoplewhobeliefanddon’tbeliefinlifeafterdeath

Sig.=0.338.Resultsarenotsignificant.Thereisnosignificantdifferenceinmeanageforpeoplewhobeliefanddon’tbeliefinlifeafterdeath.

Education

Ho:

µ1=µ2

Ha:

µ1≠µ2

Whereµ1andµ2aremeanyearsofeducationforpeoplewhobeliefanddon’tbeliefinlifeafterdeath

Sig.=0.551.Resultsarenotsignificant.Thereisnosignificantdifferenceinmeanyearsofeducationforpeoplewhobeliefanddon’tbeliefinlifeafterdeath.

Question3

File:

Salary

Thefollowingisanon-parametrictesttotesttherelationshipbetweenyearsonthejobbetweenmalesandfemalesforclericalworkers.Interprettheresults.

Ho:

Thereisnodifferenceinthejobseniorityofmalesandfemales

Ha:

Thereissignificantdifferenceinthejobseniorityofmalesandfemales

Sig.=0.725.Resultsarenotsignificant.Thereisnosignificantdifferenceinthejobseniorityofmalesandfemales

Question4

File:

gss

Thefollowingdataisrestrictedtohusbandsandwives,bothofwhomareemplyedfulltime（wrkstat=1;spwrksta=1）.Anon-parametrictestwasperformedtoseeifhusbandsandwivesworkthesamenumberofhoursaweek（husbhrandwifehr）.Interpretyourresults.

Interprettheresults

Ho:

Thereisnodifferenceinthehoursworkedofhusbandsandwives

Ha:

Thereisasignificantdifferenceinthehoursworkedofhusbandsandwives

Sig.=0.000.Resultsaresignificantatthe0.1%level.Husbandsworklongerhoursthanwives.

Question5

BelowaretwoboxplotsonhomepricesintheNortheastRegion（NE=Yes）andotherregions（NE=Non）inAlbuquerque.Thedottedlinesrepresentthemeanvalues.

a）Whatcanyousayaboutthevariationinthetwogroups?

Whatstatisticalmeasureisusedtomeasurethisvariationandwhataspectoftheboxplotdepictsthismeasure?

Nametwoothermeasuresofvariation.

b）Commentonthedistributionofpriceforthetwogroups.Whatistheimplicationofthisintermsofthechoiceofstatisticaltests?

c）Wouldthemeanormedianbeabettermeasuretocomparethepriceofhousesbetweenthetwogroups?

Why?

d）Whatisyourcommentonthepricesofhousesinthetwoareas?

e）Giveoneadvantageofusingtheboxplotoverthehistogram.

f）Stateatestthatwouldbesuitabletoanalysethedifferenceinhomepricesbetweenthetworegions.

a）Thevariationinthetwogroupsaredifferent.TheNortheastsectorhasahighervariationthantheothersectors.（1m）Thestatisticalmeasureusedtomeasurethevariationistheinterquartilerangeanditisrepresentedbythelengthoftheboxplot.（2m）.Othermeasuresofvariationaresuchasthestandarddeviationandthecoefficientofvariation.（1m）

b）FortheNortheastsector,thepriceisslightlypositivelyskewed,forotherregions,thepriceisslightlynegativelyskewed.Thisimpliesthatthetypesoftestchosenshouldbenon-parametrictests.（3m）

c）Themedianwouldbeabettermeasurebecausethedistributionisskewed.（2m）

（d）TheboxplotshowsthatthepriceofhousesisapproximatelyequalbutthevariationinpriceishigherforNortheastregionscomparedtootherregions.（2m）

（e）Theboxplotshowsthemeasuresofcentraltendencyandvariationwhereasthebarchartonlyshowsthemeasuresofcentraltendencyandnotvariation.（1m）.

f）MannWhitney

Question6

ThefollowingoutputisobtainedfromadatasetcontainingarandomsampleofnursinghomescollectedbytheDepartmentofHealthandSocialServicesinNewMexico.You’vebeenaskedtoexaminethedataanddeterminewhetherthereisadifferenceinrevenuegeneratedbyruralandnon-ruralnursinghomes.Yougeneratedthefollowingoutput.

a）Didyouusepooled（equalvar）orunspooled（unequal）varianceforthet-test?

Explain.

b）Interpretthetesttodeterminewhetherthereisadifferenceinrevenuegeneratedbyruralandnon-ruralnursinghomes.Includeinyourinterpretation,thenullandalternativehypothesis.

a）

Ho:

Equalvarianceassumed

Ha:

Equalvariancenotassumed

Sig.=0.445>5%DonotrejectHo.EqualvarianceassumedUsepooledvariance

（2m）

b）Ho:

µ1=µ2

Ha:

µ1≠µ2（1m）

Where:

µ1andµ2arethemeanrevenueofruralandnonruralareasrespectively.

（1m）

Resultsaresignificantatthe5%level.（1m）Thisshowsthatthereisasignificantdifferenceinthemeanrevenuebetweenruralandnon-ruralnursinghomes.Therevenuefornon-ruralhomesishigherthanruralhomes.（2m）.

Question7

Determinewhetherthefollowingtestsarepairedorindependent.

a）Aneconomistwishestodeterminewhetherthereisadifferenceinmeanfamilyincomeforhouseholdsin2socioeconomicgroups.

b）You’reamarketingresearchanalyst.Youwanttocompareaclient’scalculatortoacompetitor’s.Yousample8retailstores.

a）independent

b）paired

Question8

Forthefollowingstudies,indicatewhetheranindependent-samplesorpairedt-testisappropriate:

（i）Youwanttostudythegenderdifferencesinthespendinghabitsofyoungadults.Youselect400malesand300femalestostudytheirspendingbehaviour.

（2marks）

（ii）ConsumerpreferencesforPizzaHut’snew“HawaiianX-traPersona”pizzawereobtainedon7-pointLikertscale.Thesameconsumerswerethenshownacommercialaboutthisnewpizza.Afterthecommercial,consumer’spreferenceforthenewpizza,weremeasured.Hasthecommercialbeensuccessfulininducingachangeinpreference?

（2marks）

i）Independent

ii）paired

Question9

Atrainerhasdevelopedanewmethodforimprovingthesalesofsalespersons.Toevaluatethenewmethod,hecomparedthesalesofeachof10salespersonsbeforeandafterthetraining.ThefollowingSPSSoutputwasproduced:

PairedSamplesTest

Paireddifferences

t

df

Sig.

（2-tailed）

Mean

Std.Deviation

Std.Error

Mean

Pairaftertraining-

1beforetraining

4.30

3.401

1.075

3.998

9

.003

Interprettheresults

（4marks）

H0mdiff=0

H1mdiff≠0

Wheremdiffisthemeandifferenceinsalesbeforeandaftertraining.Sig.=0.003.Resultsaresignificantatthe1%level.Meansaleshassignificantlyincreasedbyanaverageof4.3aftertraining.

Question10

AresearcherwantstostudythegenderdifferencesinthecurrentsalariesofemployeesinamarketingdivisionofMars&VenusLtdatthe5%significancelevel.HeobtainedthefollowingoutputswhenusingSPSS:

GroupStatistics

CurrentSalary

Gender

N

Mean

Std.Deviation

Std.Error

Mean

Female

216

$26031.9

$7,558.021

$514.258

Male

258

$41441.8

$19,499.214

$1,213.968

IndependentSamplesTest

Levene’sTestforEqualityof

Variances

t-testforEqualityofMeans

F

Sig.

t

df

Sig.

（2-tailed）

Mean

Difference

Current

Salary

Equalvariancesassumed

119.67

.000

-10.95

472

.000

-$15,409.86

Equalvariancesnotassumed

-11.69

344.26

.000

-$15,409.86

Interprettheresults

Ho:

µ1=µ2

Ha:

µ1≠µ2

Whereµ1andµ2aremeansalaryformalesandfemales

Sig.=0.000.Resultsaresignificantatthe0.1%level.Themeansalaryofmalesissignificantlyhigher（mean=41441）thanfemales（mean=26031）.

Question11

Indicatewhichnon-parametrictest（Mann-WhitneyUTest,Wilcoxonmatched-pairssigned-rankstest,andKruskal-WallisTest）youwoulduseineachofthefollowingsituations.Writethenullandalternativehypothesesforeachexample.

i）Youareinterestedincomparingthesatisfactionrankingsgivenbymaleandfemalepurchasersofanewproduct.

ii）Youareinterestedincomparingthefamilyincomesofpurchasersoffourdifferenttypesofproducts.

iii）Youareinterestedinwhetherproductratingsdifferbeforeandafteruse.

（9marks）

i）MannWhitney

ii）KruskalWallis

iii）Wilcoxon

Question12

Atruckmanufacturerkeepsalogofdieselconsumptionof20trucksoverasix-monthperiod.Fromapreviousstudy,theaverageconsumptionoftrucksinMalaysiawasfoundtobe4800litrespermonth.Heasksyoutointerpretthefollowingresults:

InterprettheresultsobtainedinTables10aand10b.

（5marks）

Ho:

m=4800

Ha:

m¹4800

m:

meandieselconsumption

p-value<5%.Resultsaresignificantatthe5%sig.level.Theaveragediesel

consumptionoftrucksissignificantlylessthan4800（mean=4215）.

Itcanbeseenthattheaveragedieselconsumptionis4215litrespermonth

（1m）

between3737.62and4692.35litrespermonth（95%confidenceintervalfor

populationmean）.（1m）

Question13

Aresearcherwishestoexaminetheeffectoftemperatureonpilotperformance.Arandomsampleof15pilotswasrecordedfollowingparticipationinanairstimulationtask,incockpitsofdifferingtemperatures（20degreesCelsiusand35degreesCelsius）.Anon-parametrictestwasconductedwiththefollowingresults.

Table10

Table11

（i）Statethesituationinwhichthenon-parametrictestswouldhavebeensuitable.

（3marks）

（ii）Whatnon-parametrictestwasusedtogenerateTables10and11?

（2marks）

（iii