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Color Smart 5000
Course: ACCOUTNING 550, Spring 2012School: DeVry Houston
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Word Count: 381
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ThemanufactureroftheColorSmart5000televisionsetclaimsthat95percentofitssets lastatleastfiveyearswithoutneedingasinglerepair.Inordertotestthisclaim,a consumergrouprandomlyselects400consumerswhohaveownedaColorSmart5000 televisionsetforfiveyears.Ofthese400consumers,316saythattheirColorSmart5000 televisionsetsdidnotneedrepair,while84saythattheirColorSmart5000televisionsets didneedatleastonerepair. A....
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ThemanufactureroftheColorSmart5000televisionsetclaimsthat95percentofitssets
lastatleastfiveyearswithoutneedingasinglerepair.Inordertotestthisclaim,a
consumergrouprandomlyselects400consumerswhohaveownedaColorSmart5000
televisionsetforfiveyears.Ofthese400consumers,316saythattheirColorSmart5000
televisionsetsdidnotneedrepair,while84saythattheirColorSmart5000televisionsets
didneedatleastonerepair.
A. LettingpbetheproportionofColorSmart5000televisionsetsthatlastfiveyears
withoutasinglerepair,setupthenullandalternativehypothesesthattheconsumer
groupshouldusetoattempttoshowthatthemanufacturersclaimisfalse.
B. Userejectionpointsandthepreviouslygivensampleinformationtotestthe
hypothesesyousetupinpartabysettingaequalto.10,.05,.01,and.001.Howmuch
evidenceistherethatthemanufacturersclaimisfalse?
C. Doyouthinktheresultsoftheconsumergroupssurveyhavepractical
importance?Explainyouropinion.
Solution:Wefollowthesetofformulaegivenbelow:
Largesampletestofhypothesisaboutapopulationproportion
ONETAILEDTEST
TWOTAILEDTEST
H0:p=p0
H0:p=p0
Ha:p>p0(orHa:p<p0)
Ha:p TheHypothesesare:H0:p=0.95versusHA:p<0.95
(b) p0
Teststatistic:
Rejectionregion:
Rejectionregion:
z>z(orz<z)
z<z/2(orz>z/2)
whereq0=1p0
whereq0=1p0
Assumption:Theinterval
doesnotcontain0and1.
Herep0=95%=0.95
(a) TestStatistic:
Here,,p0=0.95,q0=0.05
z=
Levelofsignificance=
Rejectionrule:Rejectthenullhypothesisifz<
Thefollowingtableshowsthevalueofforcorrespondingvaluesof.
z
0.1 1.28155
0.05 1.64485
0.01 2.32635
0.001 3.09023
Observation:Forallthesevaluesof,thecalculatedvalueofz=14.68fallsinthe
rejectionregion.
Conclusion:Rejectthenullhypothesis.Thereissufficientevidencetoconcludethat
themanufacturersclaimthat95%ofitsColorSmart5000televisionsetlastatleast
fiveyearswithoutneedingasinglerepairisfalseatalltheabovelevelsof
significance.
Theresultoftheconsumergroupsurveyhasvalidpracticalimportance.The
televisionsetmanufacturershouldupgradeitsmanufacturingproceduresandensure
greaterqualitycontroltojustifyhisclaim.Alternatively,theconsumersmaydecideto
takethemanufacturertocourtforfalseandmisleadinginformation.
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