A random variable X follows a normal distribution with mean 10 and variance 16. Consider random samples of different sizes from that population to answer the following questions.

Consider a sample of size n = 10.

1. .For n = 10, the sample mean = ?

DATA

10.96379154

19.77583113

9.973224476

16.59050784

1.499207681

3.909823388

5.168745954

4.829868228

5.390362528

9.636747816

2.Consider a sample of size n = 100.

.For n = 100, the sample mean = ?

DATA:

8.436132955

14.20325705

2.992052285

10.08032657

5.126590875

10.03289642

10.42844476

13.59500518

6.905971784

11.54967438

19.592477

14.57768692

10.89463356

11.38146333

11.05509116

13.77795004

15.04973286

10.80261998

2.681987351

5.719426806

17.15459464

14.70913619

2.442462826

7.403838279

15.35778781

8.43018486

5.677417246

4.824220266

12.84727321

2.098273651

8.722987584

12.20727543

11.48489562

6.955671122

6.995984475

13.73988769

7.098457243

13.43340616

16.98815711

11.19004653

11.13164333

7.029149199

10.76581273

9.312581167

6.430133251

9.172696334

8.521989255

13.15714715

13.94471499

16.75790943

8.881726242

8.948396751

16.09212293

11.51115273

-3.18869181

10.4709409

8.895400495

-2.426753528

9.632445906

10.40721716

8.961693564

11.17023319

16.03231456

10.50084054

1.826553014

3.26240868

18.7985245

11.30021817

7.737281774

6.091446519

11.70189196

6.111619112

15.83022484

10.35772246

9.67943495

10.84293788

9.496385499

14.33026798

5.937123458

10.25000645

11.65644451

-28.14697266

13.23631411

8.421590135

8.240646164

11.24035978

16.08823029

6.316591933

5.580692485

20.50924766

8.804514689

8.33655238

10.3939931

17.64503056

8.416624294

8.796192813

13.02474291

11.77622496

10.19575964

10.64057531

3.Consider a sample of size n = 999.

.For n = 999, the sample mean = ?

DATA :

8.571997821

7.900604285

11.83449629

8.769590093

1.784134181

11.12177077

10.28680915

10.21782398

8.477669578

13.04391961

7.004097168

13.23334461

10.89400601

10.33039214

12.98618943

4.189183781

15.1266943

8.688485903

6.345950422

8.399071046

13.31030606

17.08889274

8.458897608

11.96465862

6.421465767

10.95843916

14.21816367

10.47956746

12.72018497

11.91098025

10.6281789

9.844976628

13.33319804

14.20751348

9.985157046

7.054092091

6.883639142

11.5345131

13.99781129

8.029470589

12.75887032

8.924618012

9.734050107

1.826553014

6.525721144

7.029954102

18.94906407

2.736738932

11.52595021

14.44701982

10.49682967

9.378637767

11.17821855

4.621121004

10.34605364

9.48929144

15.45232979

10.19238996

8.26925432

11.2435703

6.671995177

12.09096925

7.133772922

13.52768438

6.934784576

0.811193129

13.60555532

11.80700681

8.983198566

9.577094059

11.90343599

23.26086931

-1.484662537

14.24493919

3.650544639

11.3759427

9.665924406

9.476640369

2.677076079

7.91954906

4.50867108

9.882938937

17.62236596

4.307054294

11.92264906

13.59775186

14.80911694

13.69230293

9.71717898

16.78741344

7.55978024

8.289727046

11.9453455

13.01619366

7.410259311

10.19238996

7.040831659

7.055692802

10.02432898

8.381817932

15.51181074

7.090890247

12.22832568

14.40189069

10.10787517

6.022306732

7.048062141

5.245889295

6.733458829

3.483270373

10.76986453

5.450471033

12.05841388

2.039302015

8.296098056

14.10979737

9.937726898

15.5300552

8.194011823

7.756649464

11.73881745

12.43837349

9.393808139

11.25095994

11.43713805

14.1248768

3.741639628

10.66538178

6.63028575

11.31797606

9.602623575

13.0341198

8.97339876

8.240646164

5.196549207

10.90687536

9.79320819

17.0727765

7.691893441

14.31491571

9.910182851

3.704968801

13.5416997

6.240649125

12.72828402

15.49761353

10.59257673

7.20374035

13.60279955

8.17094249

8.018411134

12.48237484

4.673562469

8.165162651

11.44693331

8.250077624

13.11179974

1.601798683

11.00890247

8.076318661

7.801983227

18.01010174

11.27669409

9.18082267

12.84451744

7.394388629

11.15778221

7.492723196

14.85737473

10.71445356

10.29079729

5.999160092

11.83959855

11.43909801

9.684041541

10.06104528

7.929353412

7.478930709

10.94679308

11.64145604

12.16110038

5.405787558

13.72333488

9.502242645

5.145180947

14.64068762

12.19623871

6.761562215

5.095595295

10.34328878

8.716220944

10.36786332

9.446995389

12.13882686

17.13196641

11.25963652

6.616306817

11.89179445

9.591555024

8.860712367

9.966184987

16.79257937

8.130761014

6.879491846

9.043448042

5.494599716

13.43650754

10.99154022

6.304413798

13.75839591

9.200190359

9.024862518

9.971696525

10.66320808

8.822099769

5.691105141

14.75038178

6.419182935

10.06135451

15.46007868

15.26760232

13.45468834

9.062015377

9.050060069

8.807711563

14.94817868

9.701840352

11.52035682

6.436054062

9.253500391

9.332758307

14.3176442

14.1201929

12.54799943

2.783959897

5.791422407

10.98270448

1.091608535

11.13100668

8.220064299

19.50261892

1.173754097

3.549299688

11.9474146

13.47650712

3.251003616

2.941793607

15.33758794

8.290063559

12.09447535

15.89743649

0.358046489

12.46680884

8.969287844

7.363665898

10.0607406

11.09538178

7.704171619

6.285623638

11.61386197

9.814963303

9.684041541

14.16202965

19.28564987

7.508721208

6.61061338

4.556183083

17.03223122

9.540150384

15.97006874

6.765809556

18.42053851

5.615453372

15.01596332

10.35864559

11.28570719

10.34605364

5.341877366

8.643520485

7.513914423

6.378337528

10.27883289

15.28074452

17.02220859

9.282749741

2.580123944

-0.558287613

13.73704097

9.034630491

7.590302883

5.701482476

12.33091669

5.347898221

16.37221092

10.56073077

9.932219907

14.2513966

7.578920556

15.52131496

10.83355644

9.605392986

11.94638233

9.516426215

7.327822712

13.20711479

6.565702531

16.32689989

7.239574441

14.26325641

10.07971721

9.799947545

5.56092007

15.67950337

9.329347702

8.931598384

5.791422407

5.359312379

10.84575731

7.590302883

12.79273991

13.95767529

15.52131496

9.553392627

13.58172656

9.280571501

5.767393557

15.74395017

9.912633939

10.02493834

10.52552423

21.46603609

13.98572411

8.792668521

7.06971721

12.365814

7.113163772

15.21848051

7.850218278

8.802595655

9.737419785

7.104823706

4.175086613

1.704316926

13.85805834

13.81395694

13.9263432

8.816665538

14.10203029

6.900605765

4.576201061

6.808055585

4.98068064

12.78883817

15.63870344

7.196318873

13.72286195

-2.352829799

10.17829734

14.40469194

10.11552856

14.56827365

7.739078026

13.92683432

9.689257493

7.456125129

11.8630999

16.14039891

9.355709406

6.910919435

7.083705239

19.50778485

5.827974999

9.084961928

14.00942554

5.979433152

4.757781678

17.16521754

13.57807949

14.99788257

7.317863745

9.031479092

12.48756805

10.02034994

4.216286723

13.19825631

11.56452643

11.5760952

10.37277914

12.35125299

11.72067303

13.5821904

9.878045855

9.160190782

8.758676156

17.4946729

5.075413608

9.30606009

7.864701982

10.42782631

12.88723186

7.371269274

12.11345196

16.18956619

0.898868418

9.030219442

21.25852577

11.00763828

3.703913788

6.053793438

4.848858478

18.08653567

9.516426215

11.50195774

14.43003046

8.505591066

7.656741471

8.358211997

5.539901647

14.60073352

11.53714609

12.74723789

8.47043

12.63519269

12.82956535

8.598382263

8.878547558

17.17131115

7.992417775

9.961901267

10.08308234

10.15686055

10.38353846

8.023940861

3.441379047

9.256615411

12.23047209

10.22701443

14.65511221

10.81480266

7.475943019

3.256078596

4.356330717

12.32403181

9.492683855

6.554188328

19.11750249

10.12930286

12.56376097

11.07601409

2.973498593

5.359312379

12.86860086

10.42506144

9.878959898

5.96419002

4.249174051

12.36399501

10.37554855

9.168007889

10.1865692

8.432167558

14.99788257

8.627954483

9.791061782

9.664696588

7.746253939

11.92161679

13.41530722

8.458242771

17.9718302

14.46980266

11.68616225

1.50801159

13.37058736

7.067316144

5.866783138

10.80074642

12.81935172

7.329732651

14.71526619

10.56165845

12.18521564

11.48391337

8.844132278

13.55167685

5.845328158

4.426652847

10.86203272

7.765594344

12.03783202

17.10366294

4.894797055

5.960624801

6.506494426

5.556381691

12.29439138

10.86892214

4.150239218

17.96513632

12.67868927

12.73176738

16.41281076

12.82092515

11.13100668

7.398927007

17.18662704

11.66278369

8.653565854

11.1443899

19.89530236

8.760285962

10.36048732

16.33119271

5.439939084

12.3135317

15.98971383

10.72751391

10.64956112

4.498448359

14.13321686

11.3587487

8.896037141

7.40534804

8.137927832

8.723951649

7.810164132

8.879820851

13.17933882

8.045691427

12.38991561

10.98396868

15.46553565

14.67020072

10.91692527

4.505533323

14.50597327

12.48274318

15.82404027

6.409578671

13.67640496

8.854655132

11.66011432

7.021886884

16.3301195

7.934246494

16.3907828

11.58800503

12.37310815

5.073458194

5.260131982

7.422696651

13.85221938

5.129801391

13.55258635

22.12232746

8.461207724

12.53452072

7.248114596

7.146805981

11.32928562

4.138615875

6.919577825

14.52739187

10.7458766

5.961134118

14.6090463

6.691421984

11.09188477

6.440601535

12.15225555

0.78529072

5.573361957

7.641834852

14.89728336

11.76575668

12.66606548

16.58101271

9.637666406

13.27038833

18.68843927

19.81264748

8.472403604

7.090890247

15.25524229

14.32972229

13.38412974

15.30129

7.520594661

7.390982571

7.397790139

8.035686986

10.96536951

4.061436155

6.490787453

5.946336639

15.31457772

7.860822987

15.59523869

0.592332324

8.970870365

5.800462784

17.31477485

8.760922608

13.96967152

16.20073479

17.13047484

4.98068064

23.50883394

18.38717824

11.46949787

10.0745149

14.15677277

4.229310687

17.08743755

6.079595803

14.09065251

13.31590854

14.23153324

12.56714429

3.70178557

7.069317033

11.97675035

13.04269633

9.359115463

7.813720256

15.64285074

13.94521521

-1.291122064

7.788804649

21.15025952

15.72259523

6.95812221

15.64366928

2.916982592

10.59133981

8.720086296

8.006983333

8.128714651

9.617384674

5.972839315

7.629811332

4.842546585

6.641618054

8.560579115

9.861202014

13.41398845

12.55325176

13.9736824

11.20252935

5.465050233

7.682853063

11.12973339

7.155482561

3.737474142

8.22850441

8.056373443

10.10787517

8.525590854

8.327875801

14.13895577

9.094070517

10.42259671

15.16097316

9.693859536

10.98964847

15.20774847

14.21070581

4.465961208

11.06396328

10.57742

6.690557964

4.463578332

9.938036126

4.909267116

7.987906681

9.569708962

11.44432306

14.81922143

6.307697074

9.745086825

13.44270575

9.320962161

8.461207724

12.39467226

5.599791873

2.986340658

6.585574991

13.27595444

7.598733898

4.785812305

5.003454387

8.439766387

6.78740096

5.704747562

9.277461029

15.896527

3.335841282

6.645537976

10.97797511

6.857040969

8.19502591

9.265019142

8.18044671

3.334622559

4.208446878

10.80886821

7.835357135

20.4616629

7.09128133

8.732319

7.09288204

12.66835741

11.20989171

7.102036104

13.30298462

4.948229869

3.885321601

9.62660695

5.655953171

14.1352996

15.45775038

8.954413059

11.25610313

7.940185494

10.27177521

10.40014129

10.2107754

13.42015483

15.70053089

6.983806341

5.884491

15.88115654

7.336226443

13.9387487

8.439766387

12.41557245

7.157847247

5.269990904

11.62847755

12.48274318

7.172399162

10.96442363

6.457390807

3.829605955

4.89824404

11.61818207

9.971082616

8.511825652

9.419178494

8.066696207

9.451629265

14.32313755

10.42382908

6.192791514

9.019187271

9.253186616

9.751526047

11.41138116

12.42328497

12.06470759

11.60358013

15.86407623

15.49211109

7.736204023

9.468609531

14.20751348

8.250414137

6.677179297

19.57086741

16.87821739

15.83198926

8.269586285

15.53563041

2.048142303

14.22137418

6.976885086

4.256049831

9.802403181

8.63443918

20.61940566

17.85912562

12.54237875

16.16537363

11.12877387

3.542551238

18.7916851

19.26767825

8.28

9.528754415

9.924261829

5.449888957

11.24196504

9.602623575

15.57334715

8.056719051

7.357199391

7.328968675

12.0507332

14.3170985

17.22226105

5.239686541

19.83141945

11.67814051

8.63314315

13.40694896

7.846330189

10.78733137

9.528135959

5.798871169

5.674124875

8.41596491

9.483425199

11.49670086

2.531702446

17.53578206

7.83358362

5.33765731

4.032714312

16.93253241

10.50207291

5.671923898

8.091420821

8.257485458

20.70467988

8.26623025

9.578940333

13.44403816

12.22011295

7.810164132

12.5969166

3.539167917

15.26614713

6.346878106

13.07260962

9.539536475

8.020139174

12.30124442

6.65769792

7.111576704

8.643520485

12.1092319

12.42144779

9.088731784

3.050914782

12.31859758

11.54439476

9.244155333

10.06900336

6.697879396

7.872109816

15.51497578

10.04911271

9.950578058

9.798419594

9.811589078

11.48391337

3.345645635

9.682195266

14.7011963

9.352298801

9.722085704

10.25000645

10.61145329

8.225466697

10.29263902

10.23896973

15.74824298

10.48018592

12.8452996

11.98990165

7.085305949

20.32749424

15.2494579

19.6198346

10.63561401

0.418436937

12.58031832

6.731748979

12.30991645

7.348440957

10.3881496

6.799215296

10.00290584

10.34820005

12.83625013

10.07848939

7.298295966

13.33623575

6.112601366

10.25552254

3.724941305

5.249618223

18.19076377

12.50839548

10.63933385

16.21093932

7.798067852

4.723639247

12.42181159

8.651296664

8.097591742

14.42269084

10.10726581

12.96037797

12.19268259

8.321527528

14.01144462

9.908040991

10.38384314

9.687106538

13.31117008

16.3907828

5.733505784

-0.353396647

8.783696356

14.7343201

9.595247573

4.441959643

14.00134013

4.704594428

2.078810465

14.35897164

14.95541826

8.458897608

7.695504135

6.872847987

13.00238753

14.19369826

8.731036612

0.663782228

10.47987669

17.32783519

3.328492565

18.8615343

10.38046437

10.33345714

13.9691713

13.7360951

8.064977262

10.36048732

6.918340912

8.565799615

5.617126842

8.957891876

13.62903847

10.2634988

7.391360012

12.03644049

8.940156729

3.067467585

19.6198346

10.73280262

12.61431978

8.641574166

17.25372956

11.36426024

5.480720827

17.81117706

9.338033376

10.88491106

9.732822289

9.502242645

4.90170012

9.447923074

15.0728886

9.699384716

8.083185346

10.30092451

13.51191375

6.202886905

4.346380845

4.801528374

6.298320184

17.03508704

12.68213626

13.87171895

5.753987605

7.695140337

14.35509719

2.383272911

11.57973318

8.776324901

17.411345

11.94879249

6.985425241

10.86610271

14.93439074

8.718799361

10.51533789

6.108190317

8.133489498

4.098034222

3.659148458

7.299833012

5.594744178

13.53943506

4.70606781

14.871481

8.748398866

How can you relate your answers above to the law of large numbers?

A.

The sample mean is equal to the population mean regardless what the sample size is.

B.

As the sample size increases, the positive distance between the sample mean and the population mean increases.

C.

As the sample size increases, the sample mean approaches the population mean.

D.

The sample size has no effect on the sample mean.