商务与经济统计(原书第14版)选择题及答案 Chapter-12-Comparing-Multiple-Proportions-Test-of-Independence-and-Goodness-of-Fit

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Chapter12-ComparingMultipleProportions,TestofIndependenceandGoodnessofFit

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MultipleChoice

1.

Iftherearethreeormorepopulations,thenitis

a.

possibletotestforequalityofthreeormorepopulationproportions.

b.

impossibletotestforequalityofthethreepopulationproportions,becausechi-squaretestsdealwithonlytwopopulations.

c.

customarytouseatdistribution

totestforequalityofthethreepopulationproportions.

d.

reasonabletotestforequalityofmultiplepopulationproportionsusingchi-squarelowertailtests.

ANSWER:

a

2.

Apopulationwhereeachofitselement

isassignedtooneandonlyoneofseveralclassesorcategoriesisa_____population.

a.

multinomial

b.

Poisson

c.

normal

d.

binomial

ANSWER:

a

3.

Thesamplingdistributionforagoodnessoffittestisthe_____

distribution.

a.

Poisson

b.

t

c.

normal

d.

chi-square

ANSWER:

d

4.

Animportantapplicationofthechi-squaredistributionis

a.

makinginferencesaboutasinglepopulationvariance.

b.

testingforgoodnessoffit.

c.

testingfortheindependenceoftwocategoricalvariables.

d.

Allofthesealternativesarecorrect.

ANSWER:

d

5.

Thenumberofdegreesoffreedomassociatedwiththechi-squaredistributioninatestofindependenceisnumberof_____minus1.

a.

sampleitems

b.

populations

c.

rowsminus1timesnumberofcolumns

d.

populationsminusnumberofestimatedparameters

ANSWER:

c

6.

Astatisticaltestconductedtodeterminewhethertorejectornotrejectahypothesizedprobabilitydistributionforapopulationisknownasa_____test.

a.

comparison

b.

probability

c.

goodnessoffit

d.

normality

ANSWER:

c

7.

Thedegreesoffreedomforadatatablewith10rowsand10columnsis

a.

100.

b.

81.

c.

18.

d.

20.

ANSWER:

b

8.

Thedegreesoffreedomforatablewith7rowsand4columnsis

a.

28.

b.

11.

c.

9.

d.

18.

ANSWER:

d

9.

Thedegreesoffreedomforadatatablewith10rowsand11columnsis

a.

100.

b.

110.

c.

21.

d.

90.

ANSWER:

d

10.

Marascuiloprocedureisusedtotestforasignificantdifferencebetweenpairsofpopulation

a.

proportions.

b.

means.

c.

variances.

d.

standarddeviations.

ANSWER:

a

11.

Whenindividualsinasampleof150wereaskedwhetherornottheysupportedcapitalpunishment,thefollowinginformationwasobtained.

Doyousupport

capitalpunishment?

Numberof

individuals

Yes

45

No

55

NoOpinion

50

​

Weareinterestedindeterminingwhetherornottheopinionsoftheindividuals(astoYes,No,andNoOpinion)areuniformlydistributed.

Theexpectedfrequencyforeachgroupis

a.

.333.

b.

.50.

c.

1/3.

d.

50.

ANSWER:

d

12.

Whenindividualsinasampleof150wereaskedwhetherornottheysupportedcapitalpunishment,thefollowinginformationwasobtained.

Doyousupport

capitalpunishment?

Numberof

individuals

Yes

45

No

55

NoOpinion

50

​

Weareinterestedindeterminingwhetherornottheopinionsoftheindividuals(astoYes,No,andNoOpinion)areuniformlydistributed.

Thecalculatedvaluefortheteststatisticequals

a.

2.

b.

-2.

c.

1.

d.

4.

ANSWER:

c

13.

Whenindividualsinasampleof150wereaskedwhetherornottheysupportedcapitalpunishment,thefollowinginformationwasobtained.

Doyousupport

capitalpunishment?

Numberof

individuals

Yes

45

No

55

NoOpinion

50

​

Weareinterestedindeterminingwhetherornottheopinionsoftheindividuals(astoYes,No,andNoOpinion)areuniformlydistributed.

Thenumberofdegreesoffreedomassociatedwiththisproblemis

a.

150.

b.

149.

c.

2.

d.

3.

ANSWER:

c

14.

Whenindividualsinasampleof150wereaskedwhetherornottheysupportedcapitalpunishment,thefollowinginformationwasobtained.

Doyousupport

capitalpunishment?

Numberof

individuals

Yes

45

No

55

NoOpinion

50

​

Weareinterestedindeterminingwhetherornottheopinionsoftheindividuals(astoYes,No,andNoOpinion)areuniformlydistributed.

The

p-valueis

a.

lessthan.01.

b.

largerthan.1.

c.

between.01and.05.

d.

between.05and.1.

ANSWER:

b

15.

Whenindividualsinasampleof150wereaskedwhetherornottheysupportedcapitalpunishment,thefollowinginformationwasobtained.

Doyousupport

capitalpunishment?

Numberof

individuals

Yes

45

No

55

NoOpinion

50

​

Weareinterestedindeterminingwhetherornottheopinionsoftheindividuals(astoYes,No,andNoOpinion)areuniformlydistributed.

Theconclusionofthetestatthe5%levelofsignificanceisthatthe

a.

distributionisuniform.

b.

nullhypothesiscannotberejected.

c.

distributionmighthavebeennormal.

d.

Marascuiloprocedureismoreapplicable.

ANSWER:

a

16.

Lastschoolyear,thestudentbodyofalocaluniversityconsistedof30%freshmen,24%sophomores,26%juniors,and20%seniors.Asampleof400studentstakenfromthisyear'sstudentbodyshowedthefollowingnumberofstudentsineachclassification.

Freshmen

113

Sophomores

98

Juniors

115

Seniors

74

​

Weareinterestedindeterminingwhetherornottherehasbeenasignificantchangeintheclassificationsbetweenthelastschoolyearandthisschoolyear.

Theexpectednumberoffreshmenis

a.

120.

b.

96.

c.

113.

d.

10.

ANSWER:

a

17.

Lastschoolyear,thestudentbodyofalocaluniversityconsistedof30%freshmen,24%sophomores,26%juniors,and20%seniors.Asampleof400studentstakenfromthisyear'sstudentbodyshowedthefollowingnumberofstudentsineachclassification.

Freshmen

113

Sophomores

98

Juniors

115

Seniors

74

​

Weareinterestedindeterminingwhetherornottherehasbeenasignificantchangeintheclassificationsbetweenthelastschoolyearandthisschoolyear.Theexpectedfrequencyofseniorsis

a.

120.

b.

96.

c.

80.

d.

74.

ANSWER:

c

18.

Lastschoolyear,thestudentbodyofalocaluniversityconsistedof30%freshmen,24%sophomores,26%juniors,and20%seniors.Asampleof400studentstakenfromthisyear'sstudentbodyshowedthefollowingnumberofstudentsineachclassification.

Freshmen

113

Sophomores

98

Juniors

115

Seniors

74

​

Weareinterestedindeterminingwhetherornottherehasbeenasignificantchangeintheclassificationsbetweenthelastschoolyearandthisschoolyear.Thecalculatedvaluefortheteststatisticequals

a.

.54.

b.

.65.

c.

2.063.

d.

2.664.

ANSWER:

c

19.

Lastschoolyear,thestudentbodyofalocaluniversityconsistedof30%freshmen,24%sophomores,26%juniors,and20%seniors.Asampleof400studentstakenfromthisyear'sstudentbodyshowedthefollowingnumberofstudentsineachclassification.

Freshmen

113

Sophomores

98

Juniors

115

Seniors

74

​

Weareinterestedindeterminingwhetherornottherehasbeenasignificantchangeintheclassificationsbetweenthelastschoolyearandthisschoolyear.

The

p-valueis

a.

lessthan.005.

b.

between.025and.05.

c.

between.05and.1.

d.

greaterthan.1.

ANSWER:

d

20.

Lastschoolyear,thestudentbodyofalocaluniversityconsistedof30%freshmen,24%sophomores,26%juniors,and20%seniors.Asampleof400studentstakenfromthisyear'sstudentbodyshowedthefollowingnumberofstudentsineachclassification.

Freshmen

113

Sophomores

98

Juniors

115

Seniors

74

​

Weareinterestedindeterminingwhetherornottherehasbeenasignificantchangeintheclassificationsbetweenthelastschoolyearandthisschoolyear.

Ata.01levelofsignificance,thenullhypothesis

a.

shouldnotberejected.

b.

shouldberejected.

c.

wasdesignedwrong.

d.

cannotbetested.

ANSWER:

a

21.

Inthepast,35%ofthestudentsatABCUniversitywereintheBusinessCollege,35%ofthestudentswereintheLiberalArtsCollege,and30%ofthestudentswereintheEducationCollege.Toseewhetherornottheproportionshavechanged,asampleof300studentsfromtheuniversitywastaken.NinetyofthesamplestudentsareintheBusinessCollege,120areintheLiberalArtsCollege,and90areintheEducationCollege.Thisproblemisanexampleofa

a.

ztestforproportions.

b.

testforindependence.

c.

Marascuiloprocedure.

d.

multinomialpopulation.

ANSWER:

d

22.

Inthepast,35%ofthestudentsatABCUniversitywereintheBusinessCollege,35%ofthestudentswereintheLiberalArtsCollege,and30%ofthestudentswereintheEducationCollege.Toseewhetherornottheproportionshavechanged,asampleof300studentsfromtheuniversitywastaken.NinetyofthesamplestudentsareintheBusinessCollege,120areintheLiberalArtsCollege,and90areintheEducationCollege.TheexpectedfrequencyfortheBusinessCollegeis

a.

.3.

b.

.35.

c.

90.

d.

105.

ANSWER:

d

23.

Inthepast,35%ofthestudentsatABCUniversitywereintheBusinessCollege,35%ofthestudentswereintheLiberalArtsCollege,and30%ofthestudentswereintheEducationCollege.Toseewhetherornottheproportionshavechanged,asampleof300studentsfromtheuniversitywastaken.NinetyofthesamplestudentsareintheBusinessCollege,120areintheLiberalArtsCollege,and90areintheEducationCollege.Thecalculatedvaluefortheteststatisticequals

a.

.01.

b.

.75.

c.

4.29.

d.

4.38.

ANSWER:

c

24.

Inthepast,35%ofthestudentsatABCUniversitywereintheBusinessCollege,35%ofthestudentswereintheLiberalArtsCollege,and30%ofthestudentswereintheEducationCollege.Toseewhetherornottheproportionshavechanged,asampleof300studentsfromtheuniversitywastaken.NinetyofthesamplestudentsareintheBusinessCollege,120areintheLiberalArtsCollege,and90areintheEducationCollege.Thehypothesisistobetestedatthe5%levelofsignificance.Thecriticalvaluefromthetableequals

a.

7.378.

b.

9.348.

c.

5.991.

d.

7.815.

ANSWER:

c

25.

Inthepast,35%ofthestudentsatABCUniversitywereintheBusinessCollege,35%ofthestudentswereintheLiberalArtsCollege,and30%ofthestudentswereintheEducationCollege.Toseewhetherornottheproportionshavechanged,asampleof300studentsfromtheuniversitywastaken.NinetyofthesamplestudentsareintheBusinessCollege,120areintheLiberalArtsCollege,and90areintheEducationCollege.Usingα=.05,theconclusionofthetestisthatthe

a.

nullhypothesiscannotberejected.

b.

proportionshavenotchangedsignificantly.

c.

proportionsfollownormaldistribution.

d.

Marascuiloprocedureismoreapplicable.

ANSWER:

b

26.

Thetablebelowgivesbeveragepreferencesforrandomsamplesofteensandadults.

Teens

Adults

Total

Coffee

55

200

255

Tea

100

150

250

SoftDrink

195

200

395

Other

50

50

100

400

600

1000

​

Weareaskedtotestforindependencebetweenage(i.e.,adultandteen)anddrinkpreferences.Witha.05levelofsignificance,thecriticalvalueforthetestis

a.

5.991.

b.

7.815.

c.

14.067.

d.

15.507.

ANSWER:

b

27.

Thetablebelowgivesbeveragepreferencesforrandomsamplesofteensandadults.

Teens

Adults

Total

Coffee

55

200

255

Tea

100

150

250

SoftDrink

195

200

395

Other

50

50

100

400

600

1000

​

Weareaskedtotestforindependencebetweenage(i.e.,adultandteen)anddrinkpreferences.Theexpectednumberofadultswhoprefercoffeeis

a.

153.

b.

255.

c.

150.

d.

200.

ANSWER:

a

28.

Thetablebelowgivesbeveragepreferencesforrandomsamplesofteensandadults.

Teens

Adults

Total

Coffee

55

200

255

Tea

100

150

250

SoftDrink

195

200

395

Other

50

50

100

400

600

1000

​

Weareaskedtotestforindependencebetweenage(i.e.,adultandteen)anddrinkpreferences.Theteststatisticforthistestofindependenceis

a.

0.

b.

8.4.

c.

62.5.

d.

54.7.

ANSWER:

d

29.

TheownerofacarwashwantstoseeifthearrivalrateofcarsfollowsaPoissondistribution.InordertotesttheassumptionofaPoissondistribution,arandomsampleof150ten-minuteintervalswastaken.Youaregiventhefollowingobservedfrequencies:

NumberofCarsArriving

ina10-MinuteInterval

Frequency

0

3

1

10

2

15

3

23

4

30

5

24

6

20

7

13

8

8

9ormore

4

150

​

CalculatemeanandusePoissonprobabilities.

Theexpectedfrequencyofexactly3carsarrivingina10-minuteintervalis

a.

.1533.

b.

.1743.

c.

23.

d.

26.145.

ANSWER:

d

30.

TheownerofacarwashwantstoseeifthearrivalrateofcarsfollowsaPoissondistribution.InordertotesttheassumptionofaPoissondistribution,arandomsampleof150ten-minuteintervalswastaken.Youaregiventhefollowingobservedfrequencies:

NumberofCarsArriving

ina10-MinuteInterval

Frequency

0

3

1

10

2

15

3

23

4

30

5

24

6

20

7

13

8

8

9ormore

4

150

​

Thecalculatedvaluefortheteststatisticequals

a.

3.11.

b.

.18.

c.

1.72.

d.

2.89.

ANSWER:

d

31.

TheownerofacarwashwantstoseeifthearrivalrateofcarsfollowsaPoissondistribution.InordertotesttheassumptionofaPoissondistribution,arandomsampleof150ten-minuteintervalswastaken.Youaregiventhefollowingobservedfrequencies:

NumberofCarsArriving

ina10-MinuteInterval

Frequency

0

3

1

10

2

15

3

23

4

30

5

24

6

20

7

13

8

8

9ormore

4

150

Thep-valueis

a.

greaterthan.1.

b.

between.05and.1.

c.

between.025and.05.

d.

lessthan.01.

ANSWER:

a

32.

TheownerofacarwashwantstoseeifthearrivalrateofcarsfollowsaPoissondistribution.InordertotesttheassumptionofaPoissondistribution,arandomsampleof150ten-minuteintervalswastaken.Youaregiventhefollowingobservedfrequencies:

NumberofCarsArriving

ina10-MinuteInterval

Frequency

0

3

1

10

2

15

3

23

4

30

5

24

6

20

7

13

8

8

9ormore

4

150

​

Atthe.05levelofsignificance,theconclusionofthetestisthatthe

a.

nullhypothesiscannotberejected.

b.

arrivalofcarsdoesnotfollowaPoissondistribution.

c.

10-minuteintervalsfollowaPoissondistribution.

d.

arrivalofcarshasnodistribution.

ANSWER:

a

33.

Youwanttotestwhetherornotthefollowingsampleof30observationsfollowsanormaldistribution.Themeanofthesampleequals11.83andthestandarddeviationequals4.53.

2

3

5

5

7

8

8

9

9

10

11

11

12

12

12

12

13

13

13

14

15

15

15

16

16

17

17

18

18

19

​

Thenumberofintervalsorcategoriesusedtotestthehypothesisforthisproblemis

a.

4.

b.

5.

c.

6.

d.

10.

ANSWER:

c

34.

Youwanttotestwhetherornotthefollowingsampleof30observationsfollowsanormaldistribution.Themeanofthesampleequals11.83andthestandarddeviationequals4.53.

2

3

5

5

7

8

8

9

9

10

11

11

12

12

12

12

13

13

13

14

15

15

15

16

16

17

17

18

18

19

​

Theexpectedfrequencyinthe3rdintervalis

a.

3.

b.

4.

c.

5.

d.

10.

ANSWER:

c

35.

Youwanttotestwhetherornotthefollowingsampleof30observationsfollowsanormaldistribution.Themeanofthesampleequals11.83andthestandarddeviationequals4.53.

2

3

5

5

7

8

8

9

9

10

11

11

12

12

12

12

13

13

13

14

15

15

15

16

16

17

17

18

18

19

​

Thecalculatedvaluefortheteststatisticequals

a.

0.

b.

1.67.

c.

2.

d.

6.

ANSWER:

c

36.

Youwanttotestwhetherornotthefollowingsampleof30observationsfollowsanormaldistribution.Themeanofthesampleequals11.83andthestandarddeviationequals4.53.

2

3

5

5

7

8

8

9

9

10

11

11

12

12

12

12

13

13

13

14

15

15

15

16

16

17

17

18

18

19

​

Thep-valueis

a.

greaterthan.1.

b.

between.05and.1.

c.

between.025and.05.

d.

lessthan.005.

ANSWER:

a

37.

Youwanttotestwhetherornotthefollowingsampleof30observationsfollowsanormaldistribution.Themeanofthesampleequals11.83andthestandarddeviationequals4.53.

2

3

5

5

7

8

8

9

9

10

11

11

12

12

12

12

13

13

13

14

15

15

15

16

16

17

17

18

18

19

​

Atthe5%levelofsignificance,theconclusionofthetestisthatthe

a.

nullhypothesiscannotberejected.

b.

datadoesnotfollowanormaldistribution.

c.

sampledatahasnoprobabilitydistribution.

d.

sampledataisincorrect.

ANSWER:

a

38.

Thefollowingtableshowsthenumberofindividualsinasampleof450whoindicatedtheysupportthenewtaxproposal.

PoliticalParty

Support

Democrats

150

Republicans

170

Independents

130

​

Weareinterestedindeterminingwhetherornottheopinionsoftheindividualsofthethreegroupsareuniformlydistributed.Theexpectedfrequencyforeachgroupis

a.

.333.

b.

.50.

c.

150.

d.

135.

ANSWER:

c

39.

Thefollowingtableshowsthenumberofindividualsinasampleof300whoindicatedtheysupportthenewtaxproposal.

PoliticalParty

Support

Democrats

150

Republicans

170

Independents

130

​

Weareinterestedindeterminingwhetherornottheopinionsoftheindividualsofthethreegroupsareuniformlydistributed.Thecalculatedvaluefortheteststatisticequals

a.

3.

b.

2.

c.

5.3.

d.

0.

ANSWER:

d

40.

Thefollowingtableshowsthenumberofindividualsinasampleof300whoindicatedtheysupportthenewtaxproposal.

PoliticalParty

Support

Democrats

100

Republicans

120

Independents

80

​

Weareinterestedindeterminingwhetherornottheopinionsoftheindividualsofthethreegroupsareuniformlydistributed.Thenumberofdegreesoffreedomassociatedwiththisproblemis

a.

2.

b.

3.

c.

300.

d.

299.

ANSWER:

a

41.

Theteststatisticforgoodnessoffithasachi-squaredistributionwithk

-1degreesoffreedomprovidedthattheexpectedfrequenciesforallcategoriesare​

a.

​5ormore.

b.

​10ormore.

c.

​kormore.

d.

​2k.

ANSWER:

a

42.

Thetestforgoodnessoffit​

a.

​isalwaysalowertailtest.

b.

​isalwaysanuppertailtest.

c.

​isalwaysatwo-tailedtest.

d.

​canbealoweroranuppertailtest.

ANSWER:

b

43.

Thenumberofcategoricaloutcomes

pertrialforamultinomialprobabilitydistributionis​

a.

​twoormore.

b.

​threeormore.

c.

​fourormore.

d.

​fiveormore.

ANSWER:

b

44.

Thetestforgoodnessoffit,testofindependence,andtestofmultipleproportionsaredesignedforusewith_____

data.

a.

categorical

b.

bivariate

c.

quantitative

d.

ordinal

ANSWER:

a

45.

Thepropertiesofamultinomialexperimentincludeallofthefollowingexcept​

a.

​theexperimentconsistsofasequenceofnidenticaltrials.

b.

​threeormoreoutcomesarepossibleoneachtrial.

c.

​theprobabilityofeachoutcomecanchangefromtrialtotrial.

d.

​thetrialsareindependent.

ANSWER:

c

SubjectiveShortAnswer

46.

Shopperswereaskedabouttheirregulargroceryshoppinglocations.Thetablebelowshowstheresponsesofthesampledshoppers.Weareinterestedindeterminingiftheproportionsoffemalesinthethreecategoriesaredifferentfromeachother.

​

Gender

Grocery

chain

Discount

store

Membershipwarehouse

Total

Female

230

80

100

410

Male

80

50

60

190

Total

310

130

160

600

​

​

​

​

​

​

​

a.

Providethenullandalternativehypotheses.

b.

Determinetheexpectedfrequencies.

c.

Computethesampleproportions.

d.

Computethecriticalvalues(CVij).

e.

Giveyourconclusionsbyprovidingnumericalreasoning.

ANSWER:

a.

H0:p1=p2=p3

Ha:Notallpopulationproportionsareequal

​

b.

GroceryChain

DiscountStore

MembershipWarehouse

Female

211.833

88.833

109.333

410

Male

98.167

41.167

50.667

190

310

130

160

600

​

c.

=

.7419

=

.6154

=

.6250

​

d.

CV12=

.12087

CV13=

.11170

CV23=

.14030

​

e.

Pairwisecomparison​

|

-|

CVij

Sig.if

|

-|>CVij

1Vs.2

.1266

.12087

Significant

1Vs.3

.1169

.11170

Significant

2Vs.3

.0096

.14030

Notsignificant

47.

Thefollowingtableshowstheresultsofastudyonsmokingandthreeillnesses.Weareinterestedindeterminingiftheproportionsofsmokersinthethreecategoriesaredifferentfromeachother.

​

Emphysema

Heartproblem

Cancer

Total

Smoker

150

70

100

320

Non-smoker

50

130

500

680

Total

200

200

600

1000

​

​

​

​

​

a.

Providethenullandalternativehypotheses.

b.

Determinetheexpectedfrequencies.

c.

Computethesampleproportions.

d.

Computethecriticalvalues(CVij).

e.

Giveyourconclusionsbyprovidingnumericalreasoning.

ANSWER:

a.

H0:p1=p2=p3

Ha:Notallpopulationproportionsareequal

​

b.

Emphysema

Heartproblem

Cancer

Total

Smoker

64

64

192

320

Non-smoker

136

136

408

680

Total

200

200

600

1000

​

​c.

.7500

.3500

.1667

​

d.

CV12

.11150

CV13

.08369

CV23

.09057

​

e.

PairwiseComparison

|

-|

CVij

Sig.if(|

-|)>

CVij

1Vs.2

.4000

.11150

Significant

1Vs.3

.5833

.08369

Significant

2Vs.3

.1833

.09057

Significant

48.

Priortothestartoftheseason,itwasexpectedthataudienceproportionsforthefourmajornewsnetworkswouldbeCBS-18.6%,NBC-12.5%,ABC-28.9%,andBBC-40%.Arecentsampleofhomesyieldedthefollowingviewingaudiencedata.

​

ObservedFrequencies(fi)

CBS

400

NBC

230

ABC

560

BBC

810

Total

2000

​

Wewanttodeterminewhetherornottherecentsamplesupportstheexpectationsofthenumberofhomesoftheviewingaudienceofthefournetworks.

​

a.

Statethenullandalternativehypothesestobetested.

b.

Computetheteststatistic.

c.

Thenullhypothesisistobetestedatthe5%levelofsignificance.Determinethecriticalvalueforthistest.

d.

Whatdoyouconclude?

ANSWER:

a.

H0:p1=.186,p2=.125,p3=.289,p4=.4

Ha:ProportionsarenotasstatedinH0

b.

Teststatistic=4.39

c.

Criticalvalue=7.815

d.

DonotrejectH0;thereisnoevidencethattheproportionsaredifferentfromthosestatedinH0.

49.

Priortothestartoftheseason,itwasexpectedthataudienceproportionsforthefourmajornewsnetworkswouldbeCBS-30%,NBC-35%,ABC-25%,andBBC-10%.Arecentsampleofhomesyieldedthefollowingviewingaudiencedata.

NumberofHomes

CBS

860

NBC

980

ABC

680

BBC

510

​

Wewanttodeterminewhetherornottherecentsamplesupportstheexpectationsofthenumberofhomesoftheviewingaudienceofthefournetworks.

a.

Statethenullandalternativehypothesestobetested.

b.

Computetheteststatistic.

c.

Thenullhypothesisistobetestedata5%levelofsignificance.Determinethecriticalvalueforthistest.

d.

Whatdoyouconclude?

ANSWER:

a.

H0:p1=.30,p2=.35,p3=.25,p4=.10

Ha:ProportionsarenotasstatedinH0

b.

Teststatistic=158.097

c.

Criticalchi-square=7.815

d.

RejectH0andconcludethattheproportionsaredifferentfromthosestatedinH0.

50.

Theresultsofarecentstudyregardingsmokingandthreetypesofillnessareshowninthefollowingtable.

​

Illness

Non-Smokers

Smokers

Totals

Emphysema

50

150

200

Heartproblem

50

150

200

Cancer

100

500

600

Totals

200

800

1000

​

​

​

​

​

​

Weareinterestedindeterminingwhetherornotillnessisindependentofsmoking.

a.

Statethenullandalternativehypothesestobetested.

b.

Showthetableoftheexpectedfrequenciesanddeterminetheteststatistic.

c.

Thenullhypothesisistobetestedatthe.01level.Determinethecriticalvalueforthistest.

d.

Whatdoyouconclude?

​

ANSWER:

a.

H0:Illnessisindependentofsmoking

Ha:Illnessisnotindependentofsmoking

​

b.

Illness

Non-Smokers

Smokers

Totals

Emphysema

40

160

200

Heartproblem

40

160

200

Cancer

120

480

600

Totals

200

800

1000

​

Chi-square=10.42

​

c.Criticalchi-square=9.210

d.RejecttheH0;therefore,illnessisnotindependentofsmoking.

51.

Inthelastpresidentialelection,beforethecandidatesstartedtheirmajorcampaigns,thepercentagesofregisteredvoterswhofavoredthevariouscandidateswereasfollows.

​

Percentages

Republicans

34%

Democrats

43%

Independents

23%

​

​

​

​

​

Afterthemajorcampaignsbegan,arandomsampleof400votersshowedthat172favoredtheRepublicancandidate;164wereinfavoroftheDemocraticcandidate;and64favoredtheIndependentcandidate.Weareinterestedindeterminingwhethertheproportionofvoterswhofavoredthevariouscandidateshadchanged.

​

a.

Computetheteststatistic.

b.

Usingthep-valueapproach,testtoseeiftheproportionshavechanged.Let

α=.05.

c.

Usingthecriticalvalueapproach,testthehypotheses.

Use

α

=.05.

ANSWER:

a.

χ2=18.42

b.

p-value<.005,rejectH0;theproportionshavechanged.

c.

χ2=18.42>

5.991;rejectH0;theproportionshavechanged.

52.

Duringthefirstfewweeksofthenewtelevisionseason,theeveningnewsaudienceproportionswererecordedasABC-31%,CBS-34%,andNBC-35%.Asampleof600homestakenrecentlyyieldedthefollowingviewingaudiencedata.

NumberofHomes

ABC

150

CBS

200

NBC

250

​

Wewanttodeterminewhetherornottherehasbeenasignificantchangeintheproportionofviewingaudienceofthethreenetworks.

a.

Statethenullandalternativehypothesestobetested.

b.

Computetheexpectedfrequencies.

c.

Computetheteststatistic.

d.

Thenullhypothesisistobetestedatthe.05levelofsignificance.Determinethecriticalvalueforthistest.Whatdoyouconclude?

e.

Determinethep-valueandperformthetest.

ANSWER:

a.

H0:Therehasnotbeenachange

Ha:Therehasbeenachange

b.

ExpectedFrequencies

186

204

210

c.

Chi-square=14.67

d.

Criticalvalue=5.991.Rejectthenullhypothesis.Therehasbeenasignificantchange.

e.

p-value<.005(actualp-valueusingExcel=.0007),rejectH0.

53.

Theresultsofarecentstudyregardingsmokingandthreetypesofillnessareshowninthefollowingtable.

Illness

Non-Smokers

Smokers

Totals

Emphysema

20

60

80

Heartproblem

70

80

150

Cancer

30

40

70

Totals

120

180

300

​

​

​

​

​

​

Weareinterestedindeterminingwhetherornotillnessisindependentofsmoking.

a.

Statethenullandalternativehypothesestobetested.

b.

Showthetableoftheexpectedfrequencies.

c.

Computetheteststatistic.

d.

Thenullhypothesisistobetestedatthe1%level.Determinethecriticalvalueforthistest.Whatdoyouconclude?

e.

Determinethep-valueandperformthetest.

ANSWER:

a.

H0:Illnessisindependentofsmoking