Tutorial 8Two Sample Test and OneWay ANOVAAnswerWord格式文档下载.docx
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Tutorial 8Two Sample Test and OneWay ANOVAAnswerWord格式文档下载.docx
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”,so
H0:
µ
1=u2;
H1:
1≠u2;
ThisisatwotailZTest.
Step4:
ChecktheZcriticalvalue:
Sinceα=0.05thus
Step5:
CalculateZstat:
Becausebothpopulationstandarddeviationsareknownso:
Checktheprobabilitydensitychart:
Because0.3904islocatedintheacceptancearea,sodonothaveenoughevidencetorejectthenullhypothesis.
So,noenoughevidencetosayhasnoticeabledifferenceaboutthelifeexpectancyofbulbswhichproducedbythattwotypesofmachines.
Solutiontob)
TocalculatetheP-value,needtocalculatetheZstat
Accordingtothesolutiona),Zstat=0.3904,checktheaccumulativestandarddistributionprobabilitytable,theP-valueis:
P=P(Z<
-0.3904)+P(Z>
0.3904)=0.3483+0.3483=0.6966,soitisgreaterthanα=0.05
SinceP≥α,thuswedonothaveenoughevidencetorejectthenullhypothesis.
Thatmeansnoenoughevidencetosayhasnoticeabledifferenceaboutthelifeexpectancyofbulbswhichproducedbythattwotypesofmachines
Pooled-VariancetTestforthedifferencebetweenTwoMeans
Question2:
AlocalPizzarestaurantclosetoacollegecampusadvertisesthattheirdeliverytimetoacollegedormitoryislessthanforalocalbranchofanationalpizzachain.Inordertodeterminewhetherthisadvertiseisvalid,youandyourfrienddecidetoorder10pizzasfromthenationalchain,allatdifferenttimes.ThedeliverytimeinminutesPIZZATIMEareshowinfollowingtable:
PIZZATIME
Local
Chain
16.8
22.0
11.7
15.2
15.6
18.7
16.7
17.5
20.8
18.1
19.5
14.1
17.0
21.8
13.9
16.5
24.0
Atthe0.05significancelevel,isthereevidencethatthemeandeliverytimeislowerforthelocalpizzarestaurantthanforthenationalpizzachain?
Answertoquestion2:
SincethequestioniswanttoknowwhetherthemeanislowerforalocalpizzarestaurantthanforthenationalchainPizzachain,sothisisaone-tailtestwiththefollowingnullandalternativehypothesis:
1≥u2;
(ThemeantimeofLocalpizzarestaurantisequalorhigherthanforthenationalPizzachain)
1<
u2;
(ThemeantimeofLocalpizzarestaurantislessthanforthenationalPizzachain)
Restaurants
X1
X2
0.1
0.01
22
3.12
9.7344
-5
25
-3.68
13.5424
-1.1
1.21
-0.18
0.0324
-3.28
10.7584
0.8
0.64
1.92
3.6864
1.4
1.96
0.62
0.3844
-2.6
6.76
17
-1.88
3.5344
5.1
26.01
-2.8
7.84
-2.38
5.6644
4.1
16.81
24
5.12
26.2144
Sum
167
86.24
188.8
73.936
Average=
18.88
Thepopulationstandarddeviationsareunknownsupposetheyareequalwitheachother.Thetdistributiontestmodelmustbeapplied:
Calculatethepooled-varianceforthesamples:
Thetstatistics:
Checkthecriticaltvalue:
Sinceα=0.05,andaccordingtothenullhypothesisthisisaonetailtest:
Because
thusdonotrejectthenullhypothesis.Basedonthisanalysis,thereisinsufficientevidenceforthelocalpizzarestauranttomaketheadvertisingclaimthattheyhavealowerdeliverytime.
Theconfidenceintervalof
is:
Withsignificancelevelof0.05,thedifferenceofthedeliverytimeis:
Computingthemeansoftworelatedpopulation:
Question3:
Thesoftwareapplicationcompanyisdevelopinganewfinancialapplicationpackage.Becausecomputing-processtimeisanimpotentdecisioncriteria,thedeveloperwantsthenewpackagetohavethesamefeaturesandcapacitiesasthecurrentmarketleaderwhileprovidingresultsfasterthanthecurrentleadingpackage.Ifthenewfinancialpackageiseffective,itwillprovidethesameresultsasthecurrentleaderbutwilluselessprocessingtime.
Theresultsdisplayedinthefollowingtableareforasampleofn=10financialapplicationsprojectsusedintheexperimentCOMPTIME.
ProcessingTimes(inseconds)
Applicationprojects
BycurrentmarketLeader
(X1i)
BynewSoftwarePackage
(X2i)
Difference
(Di=X1i-X2i)
1
9.98
9.88
0.10
2
9.86
0.02
3
9.84
9.75
0.09
4
9.99
9.80
0.19
5
9.94
9.87
0.07
6
7
-0.01
8
10.12
0.26
9
9.90
9.83
10
9.91
0.05
0.84
Giventhesignificancelevelis0.05andassumingthedifferencebetweentwopackagesisnormallydistributed.
Whetherthenewsoftwarepackageisfaster?
AnswertoQuestion3:
Accordingtothegiveninformationandtherequirementofthisquestionsetthehypothesisasbelow:
µ
D≤0;
(meanprocessingtimeforthecurrentpackageislessthanorthesameasthatforthenewpackage)
D>
0;
(meanprocessingtimeforthecurrentpackageisgreaterthanthatforthenewpackage)
Thisisaone-tailttest
Checkthetcriticalvalue:
Ift>
rejectH0,otherwiseacceptH0;
Forthen=10differences,thesamplemeandifferenceis:
And
Becauset=3.15>
sorejectthenullhypothesis.
Thereisevidencethatthemeanprocessingtimeishigherforthecurrentmarketleaderthanforthenewpackage.
FtestforthedifferencebetweenTwoVariance:
Question4:
TotherearetwogroupstudentsofCDUTE-Businessdepartment,theteacherswanderingwhetherthevarianceoftheheightofthesetwogroupstudentsissameornot.
Givenlevelofsignificanceisα=0.05.Resultsdisplayinthefollowingtableisthesampleofthistwogroupstudents.
HeightofStudentsHeightTable
(incm)
ID
Group2
Group1
158
160
164
162
168
165
166
175
170
155
11
Answertoquestion4:
HeightofStudentsHeightTable(cm)
(X2)
(X1)
-8.44
71.30864
-5.90909
34.91736
0.56
0.308642
1.090909
1.190083
-2.44
5.975309
-3.90909
15.28099
1.56
2.419753
2.090909
4.371901
-1.44
2.08642
0.090909
0.008264
-0.44
0.197531
8.56
73.19753
9.090909
82.64463
4.090909
16.73554
-10.9091
119.0083
1498
158.2222
1825
2.84E-14
282.9091
Mean=
166.4444
17.58025
165.9091
25.71901
(S1mustgreaterthanS2)
Accordingtothequestionsetthenullandalternativehypothesisas:
(Varianceofbothpopulationswithoutnoticeabledifference)
(Varianceofbothpopulationswithnoticeabledifference)
ChecktheFCriticalvalue:
So,thereareinsufficientevidencestorejectthenullhypothesis.Thevariancesofbothgroupstudentsarewithoutnoticeabledifference.
One-WayANOVA
Question5:
Anadvertisingagencyhasbeenhiredbyamanufacturerofopentodevelopmentanadvertisingcampaignfortheupcomingholidayseason.Toprepareforthisprojecttheresearchdirectordecidestoinitiateastudyoftheeffectofadvertisingonproductperception.Anexperimentisdesignedtocompare5differentadvertisements.AdvertisementAgreatlyundersellsthepen’scharacteristics.AdvertisementBslightlyundersellsthepen’scharacteristics.AdvertisementCslightlyoversellsthepen’scharacteristics.AdvertisementDgreatlyundersellsthepen’scharacteristics.AdvertisementEattemptcorrectlystatethepen’scharacteristics.Asampleof30adultrespondentstakenfromalargefocusgroup,israndomlyassignedtothefiveadvertisements(sothereare6respondentstoeach).Afterreadingtheadvertisementanddevelopingasenseof“productexpectation,”allrespondentsunknowinglyreceivethesamepentoevaluate.Therespondentsarepermittotestpenandplausibilityoftheadvertisingcopy.Therespondentsarethentoratethepenfrom1to7ontheproductcharacteristicscalesofappearance,durability,andwritingperformance.T
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