461
10.11Lab:HypothesisTestingforTwoMeansandTwoProportions
13
ClassTime:
Names:
10.11.1StudentLearningOutcomes:
 Thestudentwillselecttheappropriatedistributionstouseineachcase.
 Thestudentwillconducthypothesistestsandinterprettheresults.
10.11.2Supplies:
 Thebusinesssectionfromtwoconsecutivedays’newspapers
 3smallpackagesofM&Ms®
 5smallpackagesofReese’sPieces®
10.11.3IncreasingStocksSurvey
Lookatyesterday’snewspaperbusinesssection. Conductahypothesistesttodetermineiftheproportion
ofNewYorkStockExchange(NYSE)stocksthatincreasedisgreaterthantheproportionofNASDAQstocks
thatincreased.Asrandomlyaspossible,choose40NYSEstocksand32NASDAQstocksandcompletethe
followingstatements.
1. H
o
2. H
a
3. Inwords,definetheRandomVariable.____________=
4. Thedistributiontouseforthetestis:
5. Calculatetheteststatisticusingyourdata.
6. Drawagraphandlabelitappropriately.Shadetheactuallevelofsignificance.
a. Graph:
13
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462
CHAPTER10. HYPOTHESISTESTING:TWOMEANS,PAIREDDATA,TWO
PROPORTIONS
Figure10.8
b. Calculatethep-value:
7. Doyourejectornotrejectthenullhypothesis?Why?
8. Writeaclearconclusionusingacompletesentence.
10.11.4DecreasingStocksSurvey
Randomlypick8stocksfromthenewspaper. Usingtwoconsecutivedays’businesssections,testwhether
thestockswentdown,onaverage,forthesecondday.
1. H
o
2. H
a
3. Inwords,definetheRandomVariable.____________=
4. Thedistributiontouseforthetestis:
5. Calculatetheteststatisticusingyourdata.
6. Drawagraphandlabelitappropriately.Shadetheactuallevelofsignificance.
a. Graph:
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463
Figure10.9
b. Calculatethep-value:
7. Doyourejectornotrejectthenullhypothesis?Why?
8. Writeaclearconclusionusingacompletesentence.
10.11.5CandySurvey
BuythreesmallpackagesofM&Msand5smallpackagesofReese’sPieces(samenetweightastheM&Ms).
Testwhetherornotthemeannumberofcandypiecesperpackageisthesameforthetwobrands.
1. H
o
:
2. H
a
:
3. Inwords,definetherandomvariable.__________=
4. Whatdistributionshouldbeusedforthistest?
5. Calculatetheteststatisticusingyourdata.
6. Drawagraphandlabelitappropriately.Shadetheactuallevelofsignificance.
a. Graph:
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CHAPTER10. HYPOTHESISTESTING:TWOMEANS,PAIREDDATA,TWO
PROPORTIONS
Figure10.10
b. Calculatethep-value:
7. Doyourejectornotrejectthenullhypothesis?Why?
8. Writeaclearconclusionusingacompletesentence.
10.11.6ShoeSurvey
Testwhetherwomenhave,onaverage,morepairsofshoesthanmen.Includeallformsofsneakers,shoes,
sandals,andboots.Useyourclassasthesample.
1. H
o
2. H
a
3. Inwords,definetheRandomVariable.____________=
4. Thedistributiontouseforthetestis:
5. Calculatetheteststatisticusingyourdata.
6. Drawagraphandlabelitappropriately.Shadetheactuallevelofsignificance.
a. Graph:
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465
Figure10.11
b. Calculatethep-value:
7. Doyourejectornotrejectthenullhypothesis?Why?
8. Writeaclearconclusionusingacompletesentence.
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CHAPTER10. HYPOTHESISTESTING:TWOMEANS,PAIREDDATA,TWO
PROPORTIONS
SolutionstoExercisesinChapter10
SolutiontoExample10.2,Problem1(p.433)
twomeans
SolutiontoExample10.2,Problem2(p.433)
unknown
SolutiontoExample10.2,Problem3(p.433)
student’s-t
SolutiontoExample10.2,Problem4(p.433)
X
A
X
B
SolutiontoExample10.2,Problem5(p.433)
 H
o
:m
A
m
B
 H
a
:m
A
>m
B
SolutiontoExample10.2,Problem6(p.433)
right
SolutiontoExample10.2,Problem7(p.433)
0.1928
SolutiontoExample10.2,Problem8(p.433)
Donotreject.
SolutiontoExample10.4,Problem(p.436)
Theproblemasksforadifferenceinproportions.
SolutiontoExample10.6,Problem(p.440)
means;Ata5%levelofsignificance,fromthesampledata,thereisnotsufficientevidencetoconcludethat
thestrengthdevelopmentclasshelpedtomaketheplayersstronger,onaverage.
SolutiontoExample10.7,Problem(p.441)
H
0
m
d
equals0; H
a
m
d
doesnot equal0; ; Do o notreject thenull; Ata5%significance level, fromthe
sampledata,thereisnotsufficientevidencetoconcludethatthemeandifferenceindistancesbetweenthe
children’sdominantversusweakerhandsissignificant(thereisnotsufficientevidencetoshowthatthe
childrencouldpushtheshot-putfurtherwiththeirdominanthand).Alphaandthep-valueareclosesothe
testisnotstrong.
SolutionstoPractice1:HypothesisTestingforTwoProportions
SolutiontoExercise10.7.1(p.443)
Proportions
SolutiontoExercise10.7.2(p.443)
a.
H
0
:
PN
=
PND
a.
H
a
:
PN
>
PND
SolutiontoExercise10.7.3(p.443)
right-tailed
SolutiontoExercise10.7.6(p.443)
Normal
SolutiontoExercise10.7.8(p.443)
3.50
SolutiontoExercise10.7.10(p.444)
0.0002
SolutiontoExercise10.7.11(p.444)
a. Rejectthenullhypothesis
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467
SolutionstoPractice2:HypothesisTestingforTwoAverages
SolutiontoExercise10.8.1(p.445)
Means
SolutiontoExercise10.8.2(p.445)
a. H
0
:m
W
=m
NW
b. H
a
:m
W
6=m
NW
SolutiontoExercise10.8.3(p.445)
two-tailed
SolutiontoExercise10.8.4(p.445)
X
W
X
NW
SolutiontoExercise10.8.5(p.445)
Thedifferencebetweenthemeanlifespansofwhitesandnonwhites.
SolutiontoExercise10.8.8(p.445)
5.42
SolutiontoExercise10.8.10(p.446)
0.0000
SolutiontoExercise10.8.11(p.446)
a. Rejectthenullhypothesis
SolutionstoHomework
SolutiontoExercise10.9.1(p.447)
A
SolutiontoExercise10.9.3(p.447)
B
SolutiontoExercise10.9.5(p.447)
A
SolutiontoExercise10.9.7(p.447)
D
SolutiontoExercise10.9.9(p.447)
C
SolutiontoExercise10.9.11(p.448)
d. t
68.44
e. -1.04
f. 0.1519
h. Decision:Donotrejectnull
SolutiontoExercise10.9.13(p.448)
StandardNormal
e. z=2.14
f. 0.0163
h. Decision:Rejectnullwhena=0.05;Donotrejectnullwhena=0.01
SolutiontoExercise10.9.15(p.449)
e. 0.73
f. 0.2326
h. Decision:Donotrejectnull
SolutiontoExercise10.9.17(p.449)
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468
CHAPTER10. HYPOTHESISTESTING:TWOMEANS,PAIREDDATA,TWO
PROPORTIONS
e. -7.33
f. 0
h. Decision:Rejectnull
SolutiontoExercise10.9.19(p.450)
d. t
7
e. -1.51
f. 0.1755
h. Decision:Donotrejectnull
SolutiontoExercise10.9.21(p.450)
d. t
9
e. t1.86
f. 0.0479
h. Decision:Rejectnull,butrunanothertest
SolutiontoExercise10.9.23(p.451)
d. t
108
e. t0.82
f. 0.2066
h. Decision:Donotrejectnull
SolutiontoExercise10.9.25(p.451)
d. t
7
e. t=2.9850
f. 0.0102
h. Decision: Rejectnull;Thereissufficientevidencetoconcludethatthemeandifferenceismorethan2
minutes.
SolutiontoExercise10.9.27(p.452)
e. 0.22
f. 0.4133
h. Decision:Donotrejectnull
SolutiontoExercise10.9.29(p.452)
e. z=2.50
f. 0.0063
h. Decision:Rejectnull
SolutiontoExercise10.9.31(p.453)
e. -4.82
f. 0
h. Decision:Rejectnull
SolutiontoExercise10.9.33(p.453)
d. t
20.32
e. -4.70
f. 0.0001
h. Decision:Rejectnull
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469
SolutiontoExercise10.9.35(p.453)
d. t
40.94
e. -5.08
f. 0
h. Decision:Rejectnull
SolutiontoExercise10.9.37(p.453)
e. -0.9223
f. 0.1782
h. Decision:Donotrejectnull
SolutiontoExercise10.9.39(p.454)
D
SolutiontoExercise10.9.40(p.454)
B
SolutiontoExercise10.9.41(p.454)
B
SolutiontoExercise10.9.42(p.455)
A
SolutiontoExercise10.9.43(p.455)
C
SolutiontoExercise10.9.44(p.456)
B
SolutiontoExercise10.9.45(p.456)
C
SolutiontoExercise10.9.46(p.456)
A
SolutiontoExercise10.9.47(p.457)
A
SolutiontoExercise10.9.48(p.457)
D
SolutiontoExercise10.9.49(p.457)
D
SolutiontoExercise10.9.50(p.457)
B
SolutiontoExercise10.9.51(p.458)
D
SolutiontoExercise10.9.52(p.458)
C
SolutionstoReview
SolutiontoExercise10.10.1(p.459)
77
100
SolutiontoExercise10.10.2(p.459)
12
42
SolutiontoExercise10.10.3(p.459)
a. False
b. False
c. True
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470
CHAPTER10. HYPOTHESISTESTING:TWOMEANS,PAIREDDATA,TWO
PROPORTIONS
d. False
SolutiontoExercise10.10.4(p.459)
N(180,16.43)
SolutiontoExercise10.10.5(p.459)
A
SolutiontoExercise10.10.6(p.459)
C
SolutiontoExercise10.10.7(p.460)
N
2,
.25
p
16
SolutiontoExercise10.10.9(p.460)
0.5000
SolutiontoExercise10.10.10(p.460)
7.6
SolutiontoExercise10.10.11(p.460)
5
SolutiontoExercise10.10.12(p.460)
0.9431
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