講義分析成果ap statistics frq

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2017AP?STATISTICS -RESPONSEQUESTIONS

InferentialStatistics

Standardizedteststatistic: statisticparameter

standarddeviationofstatistic

Confidenceinterval:statistic?

criticalvalue?standarddeviationofstatistic

Single-Sample

Statistic

StandardDeviationofStatistic

SampleMean

s

n

SampleProportion

p(1p)

n

Two-Sample

Statistic

StandardDeviationofStatistic

Differenceofsamplemeans

s2s2

1 2

n1 n2

Specialcasewhens1s2

s11

n1 n2

Differenceofsampleproportions

p1(1p1)p2(1p2)

n1 n2

Specialcasewhenp1p2

p1p 11

n1 n2

Chi-squareteststatistic?

observedexpected2expected

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STATISTICSSECTIONII

PartAQuestions1-5

Spendabout65minutesonthispartoftheexam.

PercentofSectionIIscore—75

Directions:Showallyourwork.Indicateclearlythemethodsyouuse,becauseyouwillbescoredonthecorrectnessofyourmethodsaswellasontheaccuracyandcompletenessofyourresultsandexnations.

ResearchersstudyingapackofgraywolvesinNorthAmericacollecteddataonthelengthx,inmeters,fromnosetotipoftail,andtheweighty,inkilograms,ofthewolves.Ascatterplotofweightversuslengthrevealedarelationshipbetweenthetwovariablesdescribedaspositive,linear,andstrong.

Forthesituationdescribedabove,exinwhatismeantbyeachofthefollowingwords.

Positive:

Linear:

Strong:

Thed ollectedfromthewolveswereusedtocreatetheleast-squaresequation

y?=-16.46+35.02x.

Interpretthemeaningoftheslopeoftheleast-squaresregressionlineincontext.

Onewolfinthepackwithalengthof1.4metershadaresidualof-9.67kilograms.Whatwastheweightofthewolf?

Themanagerofalocalfast-foodrestaurantisconcernedaboutcustomerswhoaskforawatercupwhencinganorderbutfillthecupwithasoftdrinkfromthebeveragefountaininsteadoffillingthecupwithwater.Themanagerselectedarandomsampleof80customerswhoaskedforawatercupwhencinganorderandfoundthat23ofthosecustomersfilledthecupwithasoftdrinkfromthebeveragefountain.

Constructandinterpreta95percentconfidenceintervalfortheproportionofallcustomerswho,havingaskedforawatercupwhencinganorder,willfillthecupwithasoftdrinkfromthebeveragefountain.

Themanagerestimatesthateachcustomerwhoasksforawatercupbutfillsitwithasoftdrinkcoststherestaurant$0.25.SupposethatinthemonthofJune3,000customersaskforawatercupwhencinganorder.Usetheconfidenceintervalconstructedinpart(a)togiveanintervalestimateforthecosttotherestaurantforthemonthofJunefromthecustomerswhoaskforawatercupbutfillthecupwith

asoftdrink.

Agrocerystorepurchasesmelonsfromtwodistributors,JandK.DistributorJprovidesmelonsfromorganicfarms.ThedistributionofthediametersofthemelonsfromDistributorJisapproximaynormalwithmean133millimeters(mm)andstandarddeviation5mm.

ForamelonselectedatrandomfromDistributorJ,whatistheprobabilitythatthemelonwillhaveadiametergreaterthan137mm?

DistributorKprovidesmelonsfromnonorganicfarms.Theprobabilityis0.8413thatamelonselectedatrandomfromDistributorKwillhaveadiametergreaterthan137mm.Forallthemelonsatthegrocerystore,70percentofthemelonsareprovidedbyDistributorJand30percentareprovidedbyDistributorK.

Foramelonselectedatrandomfromthegrocerystore,whatistheprobabilitythatthemelonwillhaveadiametergreaterthan137mm?

Giventhatamelonselectedatrandomfromthegrocerystorehasadiametergreaterthan137mm,whatistheprobabilitythatthemelonwillbefromDistributorJ?

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Thechemicalsinclayusedtomakepotterycandifferdependingonthegeographicalregionwheretheclayoriginated.Sometimes,archaeologistsuseachemicalysisofclaytohelpidentifywhereapieceofpotteryoriginated.Suchanysismeasurestheamountofachemicalintheclayasapercentofthetotalweightofthepieceofpottery.Theboxplotsbelowsummarizeysesdoneforthreechemicals—X,Y,andZ—onpiecesofpotterythatoriginatedatoneofthreesites:I,II,orIII.

ForchemicalZ,describehowthepercentsfoundinthepiecesofpotteryaresimilarandhowtheydifferamongthethreesites.

Considerapieceofpotteryknowntohaveoriginatedatoneofthethreesites,buttheactualsiteisnotknown.

SupposeanysisoftheclayrevealsthatthesumofthepercentsofthethreechemicalsX,Y,andZis20.5%.Basedontheboxplots,whichsite—I,II,orIII—isthemostlikelysitewherethepieceofpotteryoriginated?Justifyyourchoice.

Supposeonlyonechemicalcouldbeyzedinthepieceofpottery.Whichchemical—X,Y,orZ—wouldbethemostusefulinidentifyingthesitewherethepieceofpotteryoriginated?Justifyyourchoice.

Thetableandthebarchartbelowsummarizeatdiagnosis,inyears,forarandomsampleof207menandwomencurrentlybeingtreatedforschizophrenia.

Age-Group(years)

20to29

30to39

40to49

50to59

Total

Women

46

40

21

12

119

Men

53

23

9

3

88

Total

99

63

30

15

207

Dothedataprovideconvincingstatisticalevidenceofanassociationbetweenage-groupandgenderinthediagnosisofschizophrenia?

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STATISTICSSECTIONII

PartBQuestion6

Spendabout25minutesonthispartoftheexam.

PercentofSectionIIscore—25

Directions:Showallyourwork.Indicateclearlythemethodsyouuse,becauseyouwillbescoredonthecorrectnessofyourmethodsaswellasontheaccuracyandcompletenessofyourresultsandexnations.

Consideranexperimentinwhichtwomenandtwowomenwillberandomlyassignedtoeitheratreatmentgrouporacontrolgroupinsuchawaythateachgrouphastwopeople.ThepeopleareidentifiedasMan1,Man2,Woman1,andWoman2.Thesixpossiblearrangementsareshownbelow.

ArrangementA

Treatment

Control

Man1

Man2

Woman1

Woman2

ArrangementB

Treatment

Control

Man1

Woman1

Man2

Woman2

ArrangementC

Treatment

Control

Man1

Woman2

Man2

Woman1

ArrangementD

Treatment

Control

Woman1

Woman2

Man1

Man2

ArrangementE

Treatment

Control

Man2

Woman2

Man1

Woman1

ArrangementF

Treatment

Control

Man2

Woman1

Man1

Woman2

Twopossiblemethodsofassignmentarebeingconsidered:thesequentialcoinflipmethod,asdescribedinpart(a),andthechipmethod,asdescribedinpart(b).Foreaethod,theorderoftheassignmentwillbeMan1,Man2,Woman1,Woman2.

Forthesequentialcoinflipmethod,afaircoinisflippeduntilonegrouphastwopeople.An eoftailsassignsthe tothetreatmentgroup,andan eofheadsassignsthe tothecontrolgroup.Assoonasonegrouphastwopeople,theremainingpeopleareautomaticallyassignedtotheothergroup.

Completethetablebelowbycalculatingtheprobabilityofeacharrangementoccurringifthesequentialcoinflipmethodisused.

Arrangement

A

B

C

D

E

F

Probability

Forthesequentialcoinflipmethod,whatistheprobabilitythatMan1andMan2areassignedtothesamegroup?

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Thesixarrangementsarerepeatedbelow.

ArrangementA

Treatment

Control

Man1

Man2

Woman1

Woman2

ArrangementB

Treatment

Control

Man1

Woman1

Man2

Woman2

ArrangementC

Treatment

Control

Man1

Woman2

Man2

Woman1

ArrangementD

Treatment

Control

Woman1

Woman2

Man1

Man2

ArrangementE

Treatment

Control

Man2

Woman2

Man1

Woman1

ArrangementF

Treatment

Control

Man2

Woman1

Man1

Woman2

Forthechipmethod,twochipsaremarked“treatment”andtwochipsaremarked“control.”Eachselectsonechipatrandomwithoutrecement.

Completethetablebelowbycalculatingtheprobabilityofeacharrangementoccurringifthechipmethodisused.

Arrangement

A

B

C

D

E

F

Probability

Forthechipmethod,whatistheprobabilitythatMan1andMan2areassignedtothesamegroup?

Sixteenparticipantsconsistingof10studentsand6teachersatanelementaryschoolwillbeusedforanexperimenttodeterminelunchpreferencefortheschoolpopulationofstudentsandteachers.Astheparticipan tertheschoolcafeteriaforlunch,theywillberandomlyassignedtoreceiveoneoftwolunchessothat8willreceiveasalad,and8willreceiveagrilledcheesesandwich.Thestudentswillenterthecafeteriafirst,andtheteacherswillenternext.Whiethod,thesequentialcoinflipmethodorthechipmethod,shouldbeusedtoassignthetreatments?Justifyyourchoice.

STOPENDOFEXAM

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z

Probability

Tableentryforzistheprobabilitylyingbelowz.

TableAStandardnormalprobabilities

z

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

–3.4

.0003

.0003

.0003

.0003

.0003

.0003

.0003

.0003

.0003

.0002

–3.3

.0005

.0005

.0005

.0004

.0004

.0004

.0004

.0004

.0004

.0003

–3.2

.0007

.0007

.0006

.0006

.0006

.0006

.0006

.0005

.0005

.0005

–3.1

.0010

.0009

.0009

.0009

.0008

.0008

.0008

.0008

.0007

.0007

–3.0

.0013

.0013

.0013

.0012

.0012

.0011

.0011

.0011

.0010

.0010

–2.9

.0019

.0018

.0018

.0017

.0016

.0016

.0015

.0015

.0014

.0014

–2.8

.0026

.0025

.0024

.0023

.0023

.0022

.0021

.0021

.0020

.0019

–2.7

.0035

.0034

.0033

.0032

.0031

.0030

.0029

.0028

.0027

.0026

–2.6

.0047

.0045

.0044

.0043

.0041

.0040

.0039

.0038

.0037

.0036

–2.5

.0062

.0060

.0059

.0057

.0055

.0054

.0052

.0051

.0049

.0048

–2.4

.0082

.0080

.0078

.0075

.0073

.0071

.0069

.0068

.0066

.0064

–2.3

.0107

.0104

.0102

.0099

.0096

.0094

.0091

.0089

.0087

.0084

–2.2

.0139

.0136

.0132

.0129

.0125

.0122

.0119

.0116

.0113

.0110

–2.1

.0179

.0174

.0170

.0166

.0162

.0158

.0154

.0150

.0146

.0143

–2.0

.0228

.0222

.0217

.0212

.0207

.0202

.0197

.0192

.0188

.0183

–1.9

.0287

.0281

.0274

.0268

.0262

.0256

.0250

.0244

.0239

.0233

–1.8

.0359

.0351

.0344

.0336

.0329

.0322

.0314

.0307

.0301

.0294

–1.7

.0446

.0436

.0427

.0418

.0409

.0401

.0392

.0384

.0375

.0367

–1.6

.0548

.0537

.0526

.0516

.0505

.0495

.0485

.0475

.0465

.0455

–1.5

.0668

.0655

.0643

.0630

.0618

.0606

.0594

.0582

.0571

.0559

–1.4

.0808

.0793

.0778

.0764

.0749

.0735

.0721

.0708

.0694

.0681

–1.3

.0968

.0951

.0934

.0918

.0901

.0885

.0869

.0853

.0838

.0823

–1.2

.1151

.1131

.1112

.1093

.1075

.1056

.1038

.1020

.1003

.0985

–1.1

.1357

.1335

.1314

.1292

.1271

.1251

.1230

.1210

.1190

.1170

–1.0

.1587

.1562

.1539

.1515

.1492

.1469

.1446

.1423

.1401

.1379

–0.9

.1841

.1814

.1788

.1762

.1736

.1711

.1685

.1660

.1635

.1611

–0.8

.2119

.2090

.2061

.2033

.2005

.1977

.1949

.1922

.1894

.1867

–0.7

.2420

.2389

.2358

.2327

.2296

.2266

.2236

.2206

.2177

.2148

–0.6

.2743

.2709

.2676

.2643

.2611

.2578

.2546

.2514

.2483

.2451

–0.5

.3085

.3050

.3015

.2981

.2946

.2912

.2877

.2843

.2810

.2776

–0.4

.3446

.3409

.3372

.3336

.3300

.3264

.3228

.3192

.3156

.3121

–0.3

.3821

.3783

.3745

.3707

.3669

.3632

.3594

.3557

.3520

.3483

–0.2

.4207

.4168

.4129

.4090

.4052

.4013

.3974

.3936

.3897

.3859

–0.1

.4602

.4562

.4522

.4483

.4443

.4404

.4364

.4325

.4286

.4247

–0.0

.5000

.4960

.4920

.4880

.4840

.4801

.4761

.4721

.4681

.4641

Probability

Tableentryforzistheprobabilitylyingbelowz.

z

TableA( )

z

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

0.0

.5000

.5040

.5080

.5120

.5160

.5199

.5239

.5279

.5319

.5359

0.1

.5398

.5438

.5478

.5517

.5557

.5596

.5636

.5675

.5714

.5753

0.2

.5793

.5832

.5871

.5910

.5948

.5987

.6026

.6064

.6103

.6141

0.3

.6179

.6217

.6255

.6293

.6331

.6368

.6406

.6443

.6480

.6517

0.4

.6554

.6591

.6628

.6664

.6700

.6736

.6772

.6808

.6844

.6879

0.5

.6915

.6950

.6985

.7019

.7054

.7088

.7123

.7157

.7190

.7224

0.6

.7257

.7291

.7324

.7357

.7389

.7422

.7454

.7486

.7517

.7549

0.7

.7580

.7611

.7642

.7673

.7704

.7734

.7764

.7794

.7823

.7852

0.8

.7881

.7910

.7939

.7967

.7995

.8023

.8051

.8078

.8106

.8133

0.9

.8159

.8186

.8212

.8238

.8264

.8289

.8315

.8340

.8365

.8389

1.0

.8413

.8438

.8461

.8485

.8508

8531

.8554

.8577

.8599

.8621

1.1

.8643

.8665

.8686

.8708

.8729

.8749

.8770

.8790

.8810

.8830

1.2

.8849

.8869

.8888

.8907

.8925

.8944

.8962

.8980

.8997

.9015

1.3

.9032

.9049

.9066

.9082

.9099

.9115

.9131

.9147

.9162

.9177

1.4

.9192

.9207

.9222

.9236

.9251

.9265

.9279

.9292

.9306

.9319

1.5

.9332

.9345

.9357

.9370

.9382

.9394

.9406

.9418

.9429

.9441

1.6

.9452

.9463

.9474

.9484

.9495

.9505

.9515

.9525

.9535

.9545

1.7

.9554

.9564

.9573

.9582

.9591

.9599

.9608

.9616

.9625

.9633

1.8

.9641

.9649

.9656

.9664

.9671

.9678

.9686

.9693

.9699

.9706

1.9

.9713

.9719

.9726

.9732

.9738

.9744

.9750

.9756

.9761

.9767

2.0

.9772

.9778

.9783

.9788

.9793

9798

.9803

.9808

.9812

.9817

2.1

.9821

.9826

.9830

.9834

.9838

.9842

.9846

.9850

.9854

.9857

2.2

.9861

.9864

.9868

.9871

.9875

.9878

.9881

.9884

.9887

.9890

2.3

.9893

.9896

.9898

.9901

.9904

.9906

.9909

.9911

.9913

.9916

2.4

.9918

.9920

.9922

.9925

.9927

.9929

.9931

.9932

.9934

.9936

2.5

.9938

.9940

.9941

.9943

.9945

.9946

.9948

.9949

.9951

.9952

2.6

.9953

.9955

.9956

.9957

.9959

.9960

.9961

.9962

.9963

.9964

2.7

.9965

.9966

.9967

.9968

.9969

.9970

.9971

.9972

.9973

.9974

2.8

.9974

.9975

.9976

.9977

.9977

.9978

.9979

.9979

.9980

.9981

2.9

.9981

.9982

.9982

.9983

.9984

.9984

.9985

.9985

.9986

.9986

3.0

.9987

.9987

.9987

.9988

.9988

9989

.9989

.9989

.9990

.9990

3.1

.9990

.9991

.9991

.9991

.9992

.9992

.9992

.9992

.9993

.9993

3.2

.9993

.9993

.9994

.9994

.9994

.9994

.9994

.9995

.9995

.9995

3.3

.9995

.9995

.9995

.9996

.9996

.9996

.9996

.9996

.9996

.9997

3.4

.9997

.9997

.9997

.9997

.9997

.9997

.9997

.9997

.9997

.9998

2017AP?STATISTICS

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Probabilityp

TableentryforpandCisthepointt*withprobabilityplyingaboveitandprobabilityClyingbetweent*andt*.

t*

TableBtdistributioncriticalvalues

df

Tailprobabilityp

.25

.20

.15

.10

.05

.025

.02

.01

.005

.0025

.001

.0005

1

1.000

1.376

1.963

3.078

6.314

12.71

15.89

31.82

63.66

127.3

318.3

636.6

2

.816

1.061

1.386

1.886

2.920

4.303

4.849

6.965

9.925

14.09

22.33

31.60

3

.765

.978

1.250

1.638

2.353

3.182

3.482

4.541

5.841

7.453

10.21

12.92

4

.741

.941

1.190

1.533

2.132

2.776

2.999

3.747

4.604

5.598

7.173

8.610

5

.727

.920

1.156

1.476

2.015

2.571

2.757

3.365

4.032

4.773

5.893

6.869

6

.718

.906

1.134

1.440

1.943

2.447

2.612

3.143

3.707

4.317

5.208

5.959

7

.711

.896

1.119

1.415

1.895

2.365

2.517

2.998

3.499

4.029

4.785

5.408

8

.706

.889

1.108

1.397

1.860

2.306

2.449

2.896

3.355

3.833

4.501

5.041

9

.703

.883

1.100

1.383

1.833

2.262

2.398

2.821

3.250

3.690

4.297

4.781

10

.700

.879

1.093

1.372

1.812

2.228

2.359

2.764

3.169

3.581

4.144

4.587

11

.697

.876

1.088

1.363

1.796

2.201

2.328

2.718

3.106

3.497

4.025

4.437

12

.695

.873

1.083

1.356

1.782

2.179

2.303

2.681

3.055

3.428

3.930

4.318

13

.694

.870

1.079

1.350

1.771

2.160

2.282

2.650

3.012

3.372

3.852

4.221

14

.692

.868

1.076

1.345

1.761

2.145

2.264

2.624

2.977

3.326

3.787

4.140

15

.691

.866

1.074

1.341

1.753

2.131

2.249

2.602

2.947

3.286

3.733

4.073

16

.690

.865

1.071

1.337

1.746

2.120

2.235

2.583

2.921

3.252

3.686

4.015

17

.689

.863

1.069

1.333

1.740

2.110

2.224

2.567

2.898

3.222

3.646

3.965

18

.688

.862

1.067

1.330

1.734

2.101

2.214

2.552

2.878

3.197

3.611

3.922

19

.688

.861

1.066

1.328

1.729

2.093

2.205

2.539

2.861

3.174

3.579

3.883

20

.687

.860

1.064

1.325

1.725

2.086

2.197

2.528

2.845

3.153

3.552

3.850

21

.686

.859

1.063

1.323

1.721

2.080

2.189

2.518

2.831

3.135

3.527

3.819

22

.686

.858

1.061

1.321

1.717

2.074

2.183

2.508

2.819

3.119

3.505

3.792

23

.685

.858

1.060

1.319

1.714

2.069

2.177

2.500

2.807

3.104

3.485

3.768

24

.685

.857

1.059

1.318

1.711

2.064

2.172

2.492

2.797

3.091

3.467

3.745

25

.684

.856

1.058

1.316

1.708

2.060

2.167

2.485

2.787

3.078

3.450

3.725

26

.684

.856

1.058

1.315

1.706

2.056

2.162

2.479

2.779

3.067

3.435

3.707

27

.684

.855

1.057

1.314

1.703

2.052

2.158

2.473

2.771

3.057

3.421

3.690

28

.683

.855

1.056

1.313

1.701

2.048

2.154

2.467

2.763

3.047

3.408

3.674

29

.683

.854

1.055

1.311

1.699

2.045

2.150

2.462

2.756

3.038

3.396

3.659

30

.683

.854

1.055

1.310

1.697

2.042

2.147

2.457

2.750

3.030

3.385

3.646

40

.681

.851

1.050

1.303

1.684

2.021

2.123

2.423

2.704

2.971

3.307

3.551

50

.679

.849

1.047

1.299

1.676

2.009

2.109

2.403

2.678

2.937

3.261

3.496

60

.679

.848

1.045

1.296

1.671

2.000

2.099

2.390

2.660

2.915

3.232

3.460

80

.678

.846

1.043

1.292

1.664

1.990

2.088

2.374

2.639

2.887

3.195

3.416

100

.677

.845

1.042

1.290

1.660

1.984

2.081

2.364

2.626

2.871

3.174

3.390

1000

.675

.842

1.037

1.282

1.646

1.962

2.056

2.330

2.581

2.813

3.098

3.300

.674

.841

1.036

1.282

1.645

1.960

2.054

2.326

2.576

2.807

3.091

3.291

50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9%

ConfidencelevelC

2017AP?STATISTICS

-RESPONSEQUESTIONS

-

PAGE

16

-

Probabilityp

Tableentryforpisthepoint

(2)withprobabilityplying

aboveit.

(2)

TableC c2criticalvalues

df

Tailprobabilityp

.25

.20

.15

.10

.05

.025

.02

.01

.005

.0025

.001

.0005

1

1.32

1.64

2.07

2.71

3.84

5.02

5.41

6.63

7.88

9.14

10.83

12.12

2

2.77

3.22

3.79

4.61

5.99

7.38

7.82

9.21

10.60

11.98

13.82

15.20

3

4.11

4.64

5.32

6.25

7.81

9.35

9.84

11.34

12.84

14.32

16.27

17.73

4

5.39

5.99

6.74

7.78

9.49

11.14

11.67

13.28

14.86

16.42

18.47

20.00

5

6.63

7.29

8.12

9.24

11.07

12.83

13.39

15.09

16.75

18.39

20.51

22.11

6

7.84

8.56

9.45

10.64

12.59

14.45

15.03

16.81

18.55

20.25

22.46

24.10

7

9.04

9.80

10.75

12.02

14.07

16.01

16.62

18.48

20.28

22.04

24.32

26.02

8

10.22

11.03

12.03

13.36

15.51

17.53

18.17

20.09

21.95

23.77

26.12

27.87

9

11.39

12.24

13.29

14.68

16.92

19.02

19.6