tabel complete (z, t, binomial)

7/28/2019 Tabel Complete (z, t, Binomial)

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Table 5 Areas of a Standard Normal Distribution

The table entries represent the area under the standardnormal curve from 0 to the specified value of z.

z

0.00.10.20.30.40.5

.00

.0000

.0398

.0793

.1179

.1554

.1915

.01

.0040

.0438

.0832

.1217

.1591

.1950

.02

.0080

.0478

.0871

.1255

.1628

.1985

.03

.0120

.0517

.0910

.1293

.1664

.2019

.04

.0160

.0557

.0948

.1331

.1700

.2054

.05

.0199

.0596

.0987

.1368

.1736

.2088

.06

.0239

.0636

.1026

.1406

.1772

.2123

.07

.0279

.0675

.1064

.1443

.1808

.2157

.08

.0319

.0714

.1103

.1480

.1844

.2190

.09

.0359

.0753

.1141

.1517

.1879

.2224

0.60.70.80.91.0

.2257

.2580

.2881

.3159

.3413

.2291

.2611

.2910

.3186

.3438

.2324

.2642

.2939

.3212

.3461

.2357

.2673

.2967

.3238

.3485

.2389

.2704

.2995

.3264

.3508

.2422

.2734

.3023

.3289

.3531

.2454

.2764

.3051

.3315

.3554

.2486

.2794

.3078

.3340

.3577

.2517

.2823

.3106

.3365

.3599

.2549

.2852

.3133

.3389

.3621

1.11.21.31.41.5

.3643

.3849

.4032

.4192

.4332

.3665

.3869

.4049

.4207

.4345

.3686

.3888

.4066

.4222

.4357

.3708

.3907

.4082

.4236

.4370

.3729

.3925

.4099

.4251

.4382

.3749

.3944

.4115

.4265

.4394

.3770

.3962

.4131

.4279

.4406

.3790

.3980

.4147

.4292

.4418

.3810

.3997

.4162

.4306

.4429

.3830

.4015

.4177

.4319

.4441

1.61.71.81.92.0

.4452

.4554

.4641

.4713

.4772

.4463

.4564

.4649

.4719

.4778

.4474

.4573

.4656

.4726

.4783

.4484

.4582

.4664

.4732

.4788

.4495

.4591

.4671

.4738

.4793

.4505

.4599

.4678

.4744

.4798

.4515

.4608

.4686

.4750

.4803

.4525

.4616

.4693

.4756

.4808

.4535

.4625

.4699

.4761

.4812

.4545

.4633

.4706

.4767

.4817

2.12.22.3

2.42.5

:4821.4861.4893

.4918

.4938

.4826

.4864

.4896

.4920

.4940

:4830.4868.4898

.4922

.4941

.4834

.4871

.4901

.4925

.4943

.4838

.4875

.4904

.4927

.4945

.4842

.4878

.4906

.4929

.4946

.4846

.4881

.4909

.4931

.4948

.4850

.4884

.4911

.4932

.4949

.4854

.4887

.4913

.4934

.4951

.4857

.4890

.4916

.4936

.4952

2.62.72.82.93.0

.4953

.4965

.4974

.4981

.4987

.4955

.4966

.4975

.4982

.4987

.4956

.4967

.4976

.4982

.4987

.4957

.4968

.4977

.4983

.4988

.4959

.4969

.4977

.4984

.4988

.4960

.4970

.4978

.4984

.4989

.4961

.4971

.4979

.4985

.4989

.4962

.4972

.4979

.4985

.4989

.4963

.4973

.4980

.4986

.4990

.4964

.4974

.4981

.4986

.4990

3.13.23.33.43.5

3.6

.4990

.4993

.4995

.4997

.4998

.4998

.4991

.4993

.4995

.4997

.4998

.4998

.4991

.4994

.4995

.4997

.4998

.4998

.4991

.4994

.4996

.4997

.4998

.4999

.4992

.4994

.4996

.4997

.4998

.4999

.4992

.4994

.4996

.4997

.4998

.4999

.4992

.4994

.4996

.4997

.4998

.4999

.4992

.4995

.4996

.4997

.4998

.4999

.4993

.4995

.4996

.4997

.4998

.4999

.4993

.4995

.4997

.4998

.4998

.4999

For values of z greater than or equal to 3.70, use 0.4999 to approximate the shaded area under the standard normal curve.


6/10

Table 6 Students t Distribution

Students t values generated by Minitab Version 9.2c 0.750 0.800 0.850 0.900 0.950 0.980 0.9

a 0.125 0.100 0.075 0.050 0.025 0.010 0.0

a 0.250 0.200 0.150 0.100 0.050 0.020 0.0

d.f.

1 2.414 3.078 4.165 6.314 12.706 31.821 63.6

2 1.604 1.886 2.282 2.920 4.303 6.965 9.9

cis a confidence level: 3 1.423 1.638 1.924 2.353 3.182 4.541 5.8

4 1.344 1.533 1.778 2.132 2.776 3.747 4.6

5 1.301 1.476 1.699 2.015 2.571 3.365 4.0

6 1.273 1.440 1.650 1.943 2.447 3.143 3.7

7 1.254 1.415 1.617 1.895 2.365 2.998 3.4

8 1.240 1.397 1.592 1.860 2.306 2.896 3.3

9 1.230 1.383 1.574 1.833 2.262 2.821 3.2

10 1.221 1.372 1.559 1.812 2.228 2.764 3.1

11 1.214 1.363 1.548 1.796 2.201 2.718 3.1

12 1.209 1.356 1.538 1.782 2.179 2.681 3.0ais the level of significance for a one-tailed test: 13 1.204 1.350 1.530 1.771 2.160 2.650 3.0

14 1.200 1.345 1.523 1.761 2.145 2.624 2.9

15 1.197 1.341 1.517 1.753 2.131 2.602 2.9

16 1.194 1.337 1.512 1.746 2.120 2.583 2.9

17 1.191 1.333 1.508 1.740 2.110 2.567 2.8

18 1.189 1.330 1.504 1.734 2.101 2.552 2.8

19 1.187 1.328 1.500 1.729 2.093 2.539 2.8

20 1.185 1.325 1.497 1.725 2.086 2.528 2.8

21 1.183 1.323 1.494 1.721 2.080 2.518 2.8

22 1.182 1.321 1.492 1.717 2.074 2.508 2.8

23 1.180 1.319 1.489 1.714 2.069 2.500 2.8

24 1.179 1.318 1.487 1.711 2.064 2.492 2.7

25 1.178 1.316 1.485 1.708 2.060 2.485 2.7

26 1.177 1.315 1.483 1.706 2.056 2.479 2.7

27 1.176 1.314 1.482 1.703 2.052 2.473 2.7

28 1.175 1.313 1.480 1.701 2.048 2.467 2.7

29 1.174 1.311 1.479 1.699 2.045 2.462 2.7

a is the level of significance for a two-tailed test 30 1.173 1.310 1.477 1.697 2.042 2.457 2.7

35 1.170 1.306 1.472 1.690 2.030 2.438 2.7

40 1.167 1.303 1.468 1.684 2.021 2.423 2.7

45 1.165 1.301 1.465 1.679 2.014 2.412 2.6

50 1.164 1.299 1.462 1.676 2.009 2.403 2.6

55 1.163 1.297 1.460 1.673 2.004 2.396 2.6

60 1.162 1.296 1.458 1.671 2.000 2.390 2.6

90 1.158 1.291 1.452 1.662 1.987 2.369 2.6

120 1.156 1.289 1.449 1.658 1.980 2.358 2.6

cc 1.15 1.28 1.44 1.645 1.96 2.33 2.


7/10

Areas of a Standard Normal Distribution

The table entries represent the area under the standard normal curve from 0 to thespecified value of z.

z

0.0

0.1

0.2

0.3

0.4

0.5

.00

.0000

.0398

.0793

.1179

.1554

.1915

.01

.0040

.0438

.0832

.1217

.1591

.1950

.02

.0080

.0478

.0871

.1255

.1628

.1985

.03

.0120

.0517

.0910

.1293

.1664

.2019

.04

.0160

.0557

.0948

.1331

.1700

.2054

.05

.0199

.0596

.0987

.1368

.1736

.2088

.06

.0239

.0636

.1026

.1406

.1772

.2123

.07

.0279

.0675

.1064

.1443

.1808

.2157

.08

.0319

.0714

.1103

.1480

.1844

.2190

.09

.0359

.0753

.1141

.1517

.1879

.2224

0.6

0.7

0.8

0.9

1.0

.2257

.2580

.2881

.3159

.3413

.2291

.2611

.2910

.3186

.3438

.2324

.2642

.2939

.3212

.3461

.2357

.2673

.2967

.3238

.3485

.2389

.2704

.2995

.3264

.3508

.2422

.2734

.3023

.3289

.3531

.2454

.2764

.3051

.3315

.3554

.2486

.2794

.3078

.3340

.3577

.2517

.2823

.3106

.3365

.3599

.2549

.2852

.3133

.3389

.3621

1.1

1.2

1.3

1.4

1.5

.3643

.3849

.4032

.4192

.4332

.3665

.3869

.4049

.4207

.4345

.3686

.3888

.4066

.4222

.4357

.3708

.3907

.4082

.4236

.4370

.3729

.3925

.4099

.4251

.4382

.3749

.3944

.4115

.4265

.4394

.3770

.3962

.4131

.4279

.4406

.3790

.3980

.4147

.4292

.4418

.3810

.3997

.4162

.4306

.4429

.3830

.4015

.4177

.4319

.4441

1.6

1.7

1.8

1.9

2.0

.4452

.4554

.4641

.4713

.4772

.4463

.4564

.4649

.4719

.4778

.4474

.4573

.4656

.4726

.4783

.4484

.4582

.4664

.4732

.4788

.4495

.4591

.4671

.4738

.4793

.4505

.4599

.4678

.4744

.4798

.4515

.4608

.4686

.4750

.4803

.4525

.4616

.4693

.4756

.4808

.4535

.4625

.4699

.4761

.4812

.4545

.4633

.4706

.4767

.4817

2.1

2.2

2.3

2.4

2.5

:4821

.4861

.4893

.4918

.4938

.4826

.4864

.4896

.4920

.4940

:4830

.4868

.4898

.4922

.4941

.4834

.4871

.4901

.4925

.4943

.4838

.4875

.4904

.4927

.4945

.4842

.4878

.4906

.4929

.4946

.4846

.4881

.4909

.4931

.4948

.4850

.4884

.4911

.4932

.4949

.4854

.4887

.4913

.4934

.4951

.4857

.4890

.4916

.4936

.4952

2.6

2.7

2.8

2.9

3.0

.4953

.4965

.4974

.4981

.4987

.4955

.4966

.4975

.4982

.4987

.4956

.4967

.4976

.4982

.4987

.4957

.4968

.4977

.4983

.4988

.4959

.4969

.4977

.4984

.4988

.4960

.4970

.4978

.4984

.4989

.4961

.4971

.4979

.4985

.4989

.4962

.4972

.4979

.4985

.4989

.4963

.4973

.4980

.4986

.4990

.4964

.4974

.4981

.4986

.4990

3.1

3.2

3.3

3.4

3.5

3.6

.4990

.4993

.4995

.4997

.4998

.4998

.4991

.4993

.4995

.4997

.4998

.4998

.4991

.4994

.4995

.4997

.4998

.4998

.4991

.4994

.4996

.4997

.4998

.4999

.4992

.4994

.4996

.4997

.4998

.4999

.4992

.4994

.4996

.4997

.4998

.4999

.4992

.4994

.4996

.4997

.4998

.4999

.4992

.4995

.4996

.4997

.4998

.4999

.4993

.4995

.4996

.4997

.4998

.4999

.4993

.4995

.4997

.4998

.4998

.4999For values of z greater than or equal to 3.70, use 0.4999 to approximate the shaded area under the standard normal curve.


8/10

Some Levels of Confidence and Their Corresponding

Critical Values

Commonly Used Critical Values z0from the Standard

Normal Distribution

Level of Confidence c Critical Value zc Type of Test Level of Significance

0.75 1.15 0.05 0.01

0.80 1.28

0.85 1.44 Left-tailed - 1.645 -2.330.90 1.645 Right-tailed 1.645 2.330.95 1.96 Two-tailed 1.96 2.580.99 2.58

Table 8 Critical Values of Pearson Product-Moment Correlation Coefficient, r

a =0.01 a = 0.05

n one tail two tails one tail two tails

3 1.00 1.00 .99 1.00For a right-tailed test, use a positive rvalue: 4 .98 .99 .90 .95

5 .93 .96 .81 .886 .88 .92 .73 .81

7 .83 .87 .67 .758 .79 .83 .62 .719 .75 .80 .58 .67

10 .72 .76 .54 .6311 .69 .73 .52 .6012 .66 .71 .50 .58

For a left-tailed test, use a negative rvalue: 13 .63 .68 .48 .5314 .61 .66 .46 .5315 .59 .64 .44 .5116 .57 .62 .42 .5017 .56 .61 .41 .4818 .54 .59 .40 .4719 .53 .58 .39 .4620 .52 .56 .38 .4421 .50 .55 .37 .4322 .49 .54 .36 .42

For a two-tailed test, use a positive rvalue 23 .48 .53 .35 .41and negative r value: 24 .47 .52 .34 .40

25 .46 .51 .34 .4026 .45 .50 .33 .3927 .45 .49 .32 .3828 .44 .48 .32 .3729 .43 .47 .31 .3730 .42 .46 .31 .36


9/10

Frequently Used Formulas

n = sample size N= population size f= frequency

Chapter 1

Class Width =classesofnumber

lowhigh (increase to next

integer)

Class Midpoint =2

lowerlimitupperlimit +

Lower boundary = lower boundary of previous class +class width

Chapter 2

Sample mean X=n

x

Population mean =N

x

Range = largest data value - smallest data value

Sample standard deviations s =1n

2)x(x

Computation formula s =1n

xSS

where

( )

=

n

2x2

xxSS

Population standard deviation( )

N

x =

2

Sample variance2s

Population variance2

o

Sample Coefficient of Variation 100=x

sCV

Sample mean for grouped datan

xfx

=

Sample standard deviation for grouped data

( )

1

2

=

n

fxxs

Chapter 3

Regression and Correlation

In all these formulas

( )

=

n

2x2

xxSS

( )

=

n

22

yySSy

( )( )

=

n

yxxyxySS

Least squares line bxay += wherexSS

xySSb = and

xbya =

Pearson product-moment correlation coefficient

ySSxSS

xySSr =

Coefficient of determination2

r=

Chapter 4

Probability of the complement of event A

( ) ( )APAnotP = 1Multiplication rule for independent events

( ) ( ) ( )BPAPBandAP =General multiplication rules

( ) ( ) ( )AgivenBPAPBandAP ,=

( ) ( ) ( )BgivenAPBPBandAP ,=Addition rule for mutually exclusive events

( ) ( ) ( )BPAPBorAP +=General addition rule

( ) ( ) ( ) ( )BandAPBPAPBorAP +=

Permutation rule( )!rn

n!rn,P

=

Combination rule( )!rnr!

n!rn,C

=

Chapter 5

Mean of a discrete probability distribution ( )= xxP

Standard deviation of a discrete probability distribution

( ) ( ) = xP2x

For Binomial Distributions

r = number of successes;p = probability of success; p1q =

Binomial probability distributionrn

qr

pr)!(nr!

n!P(r)

=

Mean np=

Standard deviation npq=

Chapter 6

Raw score x +=

Standard score

xz

=


10/10

Chapter 7

Mean ofxdistribution x=

Standard deviation ofx distributionn

x=

Standard score forx n

x

z

=

Chapter 8

Confidence Interval

for ( )30nwhen

n

zx

n

zx cc +

tabel complete (z, t, binomial)

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