statistics quiz

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Do one of the following as appropriate. A) find the critical valve z a/2. B)find the critical valve t a/2, c) state neithier the normal nor that distribution applies. Confidence level 99%; n=28 ;σ is known; population appears to be very skewed

t distribution: Critical t values

Area in One Tail

0.005

0.01

0.025

0.05

0.10

Degrees of Freedom

Area in Two Tails

0.01

0.02

0.05

0.10

0.20

1

63.657

31.821

12.706

6.314

3.078

2

9.925

6.965

4.303

2.920

1.886

3

5.841

4.541

3.182

2.353

1.638

4

4.604

3.747

2.776

2.132

1.533

5

4.032

3.365

2.571

2.015

1.476

6

3.707

3.143

2.447

1.943

1.440

7

3.499

2.998

2.365

1.895

1.415

8

3.355

2.896

2.306

1.860

1.397

9

3.250

2.821

2.262

1.833

1.383

10

3.169

2.764

2.228

1.812

1.372

11

3.106

2.718

2.201

1.796

1.363

12

3.055

2.681

2.179

1.782

1.356

13

3.012

2.650

2.160

1.771

1.350

14

2.977

2.624

2.145

1.761

1.345

15

2.947

2.602

2.131

1.753

1.341

16

2.921

2.583

2.120

1.746

1.337

17

2.898

2.567

2.110

1.740

1.333

18

2.878

2.552

2.101

1.734

1.330

19

2.861

2.539

2.093

1.729

1.328

20

2.845

2.528

2.086

1.725

1.325

21

2.831

2.518

2.080

1.721

1.323

22

2.819

2.508

2.074

1.717

1.321

23

2.807

2.500

2.069

1.714

1.319

24

2.797

2.492

2.064

1.711

1.318

25

2.787

2.485

2.060

1.708

1.316

26

2.779

2.479

2.056

1.706

1.315

27

2.771

2.473

2.052

1.703

1.314

28

2.763

2.467

2.048

1.701

1.313

29

2.756

2.462

2.045

1.699

1.311

30

2.750

2.457

2.042

1.697

1.310

31

2.744

2.453

2.040

1.696

1.309

32

2.738

2.449

2.037

1.694

1.309

33

2.733

2.445

2.035

1.692

1.308

34

2.728

2.441

2.032

1.691

1.307

35

2.724

2.438

2.030

1.690

1.306

36

2.719

2.434

2.028

1.688

1.306

37

2.715

2.431

2.026

1.687

1.305

38

2.712

2.429

2.024

1.686

1.304

39

2.708

2.426

2.023

1.685

1.304

40

2.704

2.423

2.021

1.684

1.303

45

2.690

2.412

2.014

1.679

1.301

50

2.678

2.403

2.009

1.676

1.299

60

2.660

2.390

2.000

1.671

1.296

70

2.648

2.381

1.994

1.667

1.294

80

2.639

2.374

1.990

1.664

1.292

90

2.632

2.368

1.987

1.662

1.291

100

2.626

2.364

1.984

1.660

1.290

200

2.601

2.345

1.972

1.653

1.286

300

2.592

2.339

1.968

1.650

1.284

400

2.588

2.336

1.966

1.649

1.284

500

2.586

2.334

1.965

1.648

1.283

1000

2.581

2.330

1.962

1.646

1.282

2000

2.578

2.328

1.961

1.646

1.282

Large

2.576

2.326

1.960

1.645

1.282

Degrees of Freedom

Area in One Tail

0.005

0.01

0.03

0.05

0.10

Area in Two Tails

0.01

0.02

0.05

0.10

0.20

Negative z Scores

Standard Normal (z) Distribution: Cumulative Area from the Left

z

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

negative 3.50 and lower

.0001

-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

Note: For values of z below -3.49, use 0.0001 for the area.

*Use these common values that result from interpolation:

z score

Area

-1.645

0.0500

-2.575

0.0050

Positive z Scores

Standard Normal (z) Distribution: Cumulative Area from the Left

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

3.50 and up

.9999

Note: For values of z above 3.49, use 0.9999 for the area.

*Use these common values that result from interpolation:

z score

Area

1.645

0.9500

2.575

0.9950

Common Critical Values

Confidence Level

Critical Value

0.90

1.645

0.95

1.96

0.99

2.575

2. A data set includes 107 body temp. of healthy adult humans for ẋ= 98.7 ◦F and s= 0.72◦F. a)What is the best point estimate of the mean body temp of all healthy humans? The best point estimate is________◦F

b) using the sample statistics construct a 99% confidence interval estimate of the mean body temp. of all healthy humans. Do the confidence interval limits contain 98.6F? What does the sample suggest about the use of 98.6F as the mean body temp. What is the confidence interval estimate of the population mean µ? _______◦F<µ<_______◦F

C) Do the confidence interval limits contain 98.6F? Yes or No

D)What does that suggest about the use of 98.6F as the mean bidy temp.

t Distribution: Critical t Values

Area in One Tail

0.005

0.01

0.025

0.05

0.10

Area in Two Tails

Degrees of Freedom

0.01

0.02

0.05

0.10

0.20

1

63.657

31.821

12.706

6.314

3.078

2

9.925

6.965

4.303

2.920

1.886

3

5.841

4.541

3.182

2.353

1.638

4

4.604

3.747

2.776

2.132

1.533

5

4.032

3.365

2.571

2.015

1.476

6

3.707

3.143

2.447

1.943

1.440

7

3.499

2.998

2.365

1.895

1.415

8

3.355

2.896

2.306

1.860

1.397

9

3.250

2.821

2.262

1.833

1.383

10

3.169

2.764

2.228

1.812

1.372

11

3.106

2.718

2.201

1.796

1.363

12

3.055

2.681

2.179

1.782

1.356

13

3.012

2.650

2.160

1.771

1.350

14

2.977

2.624

2.145

1.761

1.345

15

2.947

2.602

2.131

1.753

1.341

16

2.921

2.583

2.120

1.746

1.337

17

2.898

2.567

2.110

1.740

1.333

18

2.878

2.552

2.101

1.734

1.330

19

2.861

2.539

2.093

1.729

1.328

20

2.845

2.528

2.086

1.725

1.325

21

2.831

2.518

2.080

1.721

1.323

22

2.819

2.508

2.074

1.717

1.321

23

2.807

2.500

2.069

1.714

1.319

24

2.797

2.492

2.064

1.711

1.318

25

2.787

2.485

2.060

1.708

1.316

26

2.779

2.479

2.056

1.706

1.315

27

2.771

2.473

2.052

1.703

1.314

28

2.763

2.467

2.048

1.701

1.313

29

2.756

2.462

2.045

1.699

1.311

30

2.750

2.457

2.042

1.697

1.310

31

2.744

2.453

2.040

1.696

1.309

32

2.738

2.449

2.037

1.694

1.309

33

2.733

2.445

2.035

1.692

1.308

34

2.728

2.441

2.032

1.691

1.307

35

2.724

2.438

2.030

1.690

1.306

36

2.719

2.434

2.028

1.688

1.306

37

2.715

2.431

2.026

1.687

1.305

38

2.712

2.429

2.024

1.686

1.304

39

2.708

2.426

2.023

1.685

1.304

40

2.704

2.423

2.021

1.684

1.303

45

2.690

2.412

2.014

1.679

1.301

50

2.678

2.403

2.009

1.676

1.299

60

2.660

2.390

2.000

1.671

1.296

70

2.648

2.381

1.994

1.667

1.294

80

2.639

2.374

1.990

1.664

1.292

90

2.632

2.368

1.987

1.662

1.291

100

2.626

2.364

1.984

1.660

1.290

200

2.601

2.345

1.972

1.653

1.286

300

2.592

2.339

1.968

1.650

1.284

400

2.588

2.336

1.966

1.649

1.284

500

2.586

2.334

1.965

1.648

1.283

1000

2.581

2.330

1.962

1.646

1.282

2000

2.578

2.328

1.961

1.646

1.282

Large

2.576

2.326

1.960

1.645

1.282

Negative z Scores

Standard Normal (z) Distribution: Cumulative Area from the Left

z

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

negative 3.50 and lower

.0001

-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

Note: For values of z below -3.49, use 0.0001 for the area.

*Use these common values that result from interpolation:

z score

Area

-1.645

0.0500

-2.575

0.0050

Positive z Scores

Standard Normal (z) Distribution: Cumulative Area from the Left

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

3.50 and up

.9999

Note: For values of z above 3.49, use 0.9999 for the area.

*Use these common values that result from interpolation:

z score

Area

1.645

0.9500

2.575

0.9950

Common Critical Values

Confidence Level

Critical Value

0.90

1.645

0.95

1.96

0.99

2.575

3. In a sample of seven cars, each car was tested for nitrogen-oxide emission (in grams per mile) and the following results were obtained; 0.18, 0.16, 0.06, 0.07, 0.08, 0.08, 0.14. assuming that this sample is representative of the cars in use, construct a 98% confidence interval estimate of the mean amount of nitrogen-oxide emissions for all cars. If the EPA requires that nitrogen-oxide emission be less than o.165g/mi, can we safely conclude that this requirement is being met?

a.) what is the confidence interval estimate of the mean amount of nitrogen-oxide emission for all cars?______g/mi <µ<g/mi.

b) can we safely conclude that the requirements that nitrogen-oxide emission be less then 0.165g/mi is being met?

t distribution: Critical t values

Area in One Tail

0.005

0.01

0.025

0.05

0.10

Degrees of Freedom

Area in Two Tails

0.01

0.02

0.05

0.10

0.20

1

63.657

31.821

12.706

6.314

3.078

2

9.925

6.965

4.303

2.920

1.886

3

5.841

4.541

3.182

2.353

1.638

4

4.604

3.747

2.776

2.132

1.533

5

4.032

3.365

2.571

2.015

1.476

6

3.707

3.143

2.447

1.943

1.440

7

3.499

2.998

2.365

1.895

1.415

8

3.355

2.896

2.306

1.860

1.397

9

3.250

2.821

2.262

1.833

1.383

10

3.169

2.764

2.228

1.812

1.372

11

3.106

2.718

2.201

1.796

1.363

12

3.055

2.681

2.179

1.782

1.356

13

3.012

2.650

2.160

1.771

1.350

14

2.977

2.624

2.145

1.761

1.345

15

2.947

2.602

2.131

1.753

1.341

16

2.921

2.583

2.120

1.746

1.337

17

2.898

2.567

2.110

1.740

1.333

18

2.878

2.552

2.101

1.734

1.330

19

2.861

2.539

2.093

1.729

1.328

20

2.845

2.528

2.086

1.725

1.325

21

2.831

2.518

2.080

1.721

1.323

22

2.819

2.508

2.074

1.717

1.321

23

2.807

2.500

2.069

1.714

1.319

24

2.797

2.492

2.064

1.711

1.318

25

2.787

2.485

2.060

1.708

1.316

26

2.779

2.479

2.056

1.706

1.315

27

2.771

2.473

2.052

1.703

1.314

28

2.763

2.467

2.048

1.701

1.313

29

2.756

2.462

2.045

1.699

1.311

30

2.750

2.457

2.042

1.697

1.310

31

2.744

2.453

2.040

1.696

1.309

32

2.738

2.449

2.037

1.694

1.309

33

2.733

2.445

2.035

1.692

1.308

34

2.728

2.441

2.032

1.691

1.307

35

2.724

2.438

2.030

1.690

1.306

36

2.719

2.434

2.028

1.688

1.306

37

2.715

2.431

2.026

1.687

1.305

38

2.712

2.429

2.024

1.686

1.304

39

2.708

2.426

2.023

1.685

1.304

40

2.704

2.423

2.021

1.684

1.303

45

2.690

2.412

2.014

1.679

1.301

50

2.678

2.403

2.009

1.676

1.299

60

2.660

2.390

2.000

1.671

1.296

70

2.648

2.381

1.994

1.667

1.294

80

2.639

2.374

1.990

1.664

1.292

90

2.632

2.368

1.987

1.662

1.291

100

2.626

2.364

1.984

1.660

1.290

200

2.601

2.345

1.972

1.653

1.286

300

2.592

2.339

1.968

1.650

1.284

400

2.588

2.336

1.966

1.649

1.284

500

2.586

2.334

1.965

1.648

1.283

1000

2.581

2.330

1.962

1.646

1.282

2000

2.578

2.328

1.961

1.646

1.282

Large

2.576

2.326

1.960

1.645

1.282

Degrees of Freedom

Area in One Tail

0.005

0.01

0.03

0.05

0.10

Area in Two Tails

0.01

0.02

0.05

0.10

0.20

Negative z Scores

Standard Normal (z) Distribution: Cumulative Area from the Left

z

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

negative 3.50 and lower

.0001

-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

Note: For values of z below -3.49, use 0.0001 for the area.

*Use these common values that result from interpolation:

z score

Area

-1.645

0.0500

-2.575

0.0050

Positive z Scores

Standard Normal (z) Distribution: Cumulative Area from the Left

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

3.50 and up

.9999

Note: For values of z above 3.49, use 0.9999 for the area.

*Use these common values that result from interpolation:

z score

Area

1.645

0.9500

2.575

0.9950

Common Critical Values

Confidence Level

Critical Value

0.90

1.645

0.95

1.96

0.99

2.575

5. use the given data set to complete parts (a) Through(c) below.(use a= 0.05)

x

y

10

9.13

8

8.14

13

8.75

9

8.77

11

9.27

14

8.09

6

6.12

4

3.09

12

9.13

7

7.26

5

4.73

a)find the linear correlation coefficient,r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variable. The linear correlation coefficient is r=___________

b)construct a scatterplot

c)determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.

d)Indentify the feature of the data that would be missed if part b was completed without constructing the scatter plot.

6.For a sample of 8 bears, researchers measured the distance around the bears chest and weighted the b ears. Minitab was used to find that the value of the linear correlation coefficient is r=0.953. using a=0.05, determine if there is a linear correlation between chest size and weight. What proportion of the variation between weight can be explained by the linear relationship between weight and chest size.

a.)Is there a linear correlation between chest size and weight?

b)What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?

Critical Values for the Correlation Coefficient

n

alpha = .05

alpha = .01

4

0.95

0.99

5

0.878

0.959

6

0.811

0.917

7

0.754

0.875

8

0.707

0.834

9

0.666

0.798

10

0.632

0.765

11

0.602

0.735

12

0.576

0.708

13

0.553

0.684

14

0.532

0.661

15

0.514

0.641

16

0.497

0.623

17

0.482

0.606

18

0.468

0.59

19

0.456

0.575

20

0.444

0.561

25

0.396

0.505

30

0.361

0.463

35

0.335

0.43

40

0.312

0.402

45

0.294

0.378

50

0.279

0.361

60

0.254

0.33

70

0.236

0.305

80

0.22

0.286

90

0.207

0.269

100

0.196

0.256

Note: To test H subscript 0: rho equals 0 against H subscript 1: rho not equal to 0, reject H subscript 0 if the absolute value of r is greater than the critical value in the table.