I. táblázat folytatása.

Függelék

I. táblázat.

Az N(0,1) normális eloszlás F(u) eloszlásfüggvénye

u ^{0 1 2 3 4 5 6 7 8 9}

0.0 0.5000 0

0.5039 9

0.5079 8

0.5119 7

0.5159 5

0.5199 4

0.5239 2

0.5279 0

0.5318 8

0.5358 6 0.1 0.5398

3

0.5438 0

0.5477 6

0.5517 2

0.5556 7

0.5596 2

0.5635 6

0.5674 9

0.5714 2

0.5753 5 0.2 0.5792

6 0.5831

7 0.5870

6 0.5909

5 0.5948

3 0.5987

1 0.6025

7 0.6064

2 0.6102

6 0.6140 9 0.3 0.6179

1

0.6217 2

0.6255 2

0.6293 0

0.6330 7

0.6368 3

0.6405 8

0.6443 1

0.6480 3

0.6517 3 0.4 0.6554

2 0.6591

0 0.6627

6 0.6664

0 0.6700

3 0.6736

4 0.6772

4 0.6808

2 0.6843

9 0.6879 3 0.5 0.6914

6 0.6949

7 0.6984

7 0.7019

4 0.7054

0 0.7088

4 0.7122

6 0.7156

6 0.7190

4 0.7224 0 0.6 0.7257

5

0.7290 7

0.7323 7

0.7356 5

0.7389 1

0.7421 5

0.7453 7

0.7485 7

0.7517 5

0.7549 0 0.7 0.7580

4 0.7611

5 0.7642

4 0.7673

0 0.7703

5 0.7733

7 0.7763

7 0.7793

5 0.7823

0 0.7852 4 0.8 0.78810.79100.79380.79670.79950.80230.80510.80780.81050.8132

0 u

F(u)

1-F(u) f(u)

1.0 0.8413

4 0.8437

5 0.8461

4 0.8484

9 0.8508

3 0.8531

4 0.8554

3 0.8576

9 0.8599

3 0.8621 4 1.1 0.8643

3 0.8665

0 0.8686

4 0.8707

6 0.8728

6 0.8749

3 0.8769

8 0.8790

0 0.8810

0 0.8829 8 1.2 0.8849

3

0.8868 6

0.8887 7

0.8906 5

0.8925 1

0.8943 5

0.8961 7

0.8979 6

0.8997 3

0.9014 7 1.3 0.9032

0 0.9049

0 0.9065

8 0.9082

4 0.9098

8 0.9114

9 0.9130

8 0.9146

6 0.9162

1 0.9177 4 1.4 0.9192

4

0.9207 3

0.9222 0

0.9236 4

0.9250 7

0.9264 7

0.9278 5

0.9292 2

0.9305 6

0.9318 9 1.5 0.9331

9 0.9344

8 0.9357

4 0.9369

9 0.9382

2 0.9394

3 0.9406

2 0.9417

9 0.9429

5 0.9440 8 1.6 0.9452

0 0.9463

0 0.9473

8 0.9484

5 0.9495

0 0.9505

3 0.9515

4 0.9525

4 0.9535

2 0.9544 9 1.7 0.9554

3

0.9563 7

0.9572 8

0.9581 8

0.9590 7

0.9599 4

0.9608 0

0.9616 4

0.9624 6

0.9632 7 1.8 0.9640

7 0.9648

5 0.9656

2 0.9663

8 0.9671

2 0.9678

4 0.9685

6 0.9692

6 0.9699

5 0.9706 2 1.9 0.9712

8

0.9719 3

0.9725 7

0.9732 0

0.9738 1

0.9744 1

0.9750 0

0.9755 8

0.9761 5

0.9767 0 2.0 0.9772

5 0.9777

8 0.9783

1 0.9788

2 0.9793

2 0.9798

2 0.9803

0 0.9807

7 0.9812

4 0.9816 9 2.1 0.9821

4 0.9825

7 0.9830

0 0.9834

1 0.9838

2 0.9842

2 0.9846

1 0.9850

0 0.9853

7 0.9857 4 2.2 0.9861

0

0.9864 5

0.9867 9

0.9871 3

0.9874 5

0.9877 8

0.9880 9

0.9884 0

0.9887 0

0.9889 9 2.3 0.9892

8 0.9895

6 0.9898

3 0.9901

0 0.9903

6 0.9906

1 0.9908

6 0.9911

1 0.9913

4 0.9915 8 2.4 0.9918

0 0.9920

2 0.9922

4 0.9924

5 0.9926

6 0.9928

6 0.9930

5 0.9932

4 0.9934

3 0.9936 1 2.5 0.9937

9 0.9939

6 0.9941

3 0.9943

0 0.9944

6 0.9946

1 0.9947

7 0.9949

2 0.9950

6 0.9952 0 2.6 0.9953

4

0.9954 7

0.9956 0

0.9957 3

0.9958 5

0.9959 8

0.9960 9

0.9962 1

0.9963 2

0.9964 3 2.7 0.9965

3 0.9966

4 0.9967

4 0.9968

3 0.9969

3 0.9970

2 0.9971

1 0.9972

0 0.9972

8 0.9973 6 2.8 0.9974

4

0.9975 2

0.9976 0

0.9976 7

0.9977 4

0.9978 1

0.9978 8

0.9979 5

0.9980 1

0.9980 7 2.9 0.9981

3 0.9981

9 0.9982

5 0.9983

1 0.9983

6 0.9984

1 0.9984

6 0.9985

1 0.9985

6 0.9986 1 3.0 0.9986

5

0.9986 9

0.9987 4

0.9987 8

0.9988 2

0.9988 6

0.9988 9

0.9989 3

0.9989 6

0.9990 0

I. táblázat folytatása.

Az N(0,1) normális eloszlás 

^{1F u} 



^109

értékei, ha u  310 .

u ^{0 1 2 3 4 5 6 7 8 9}

3.1 96767 1

93550 4

90432 3

87409 9

84480 6

81641 9

78891 2

76226 0

73644 0

711429 3.2 68720

2 66373

8 64101

6 61901

4 59771

1 57708

6 55712

2 53779

8 51909

5 500996 3.3 48348

3 46653

8 45014

4 43428

6 41894

8 40411

3 38976

7 37589

5 36248

2 349515 3.4 33698

1 32486

5 31315

6 30184

0 29090

6 28034

1 27013

5 26027

6 25075

3 241555 3.5 23267

3 22409

7 21581

6 20782

2 20010

5 19265

6 18546

7 17853

0 17183

6 165377 3.6 15914

6

15313 5

14733 7

14174 6

13635 3

13115 4

12614 1

12130 8

11664 9

112158 3.7 10783

0 10365

9 99641 95768 92038 88445 84983 81650 78440 75349 3.8 72372 69507 66749 64094 61539 59081 56715 54438 52248 50142 3.9 48116 46167 44293 42491 40758 39092 37491 35952 34473 33052 4.0 31686 30374 29113 27902 26739 25622 24549 23519 22530 21580 4.1 20669 19794 18954 18148 17375 16633 15922 15239 14584 13956 4.2 13354 12777 12223 11692 11183 10696 10228 9780 9351 8940 4.3 8546 8169 7807 7461 7130 6812 6508 6217 5939 5672 4.4 5417 5173 4939 4716 4502 4297 4102 3914 3736 3564 4.5 3401 3244 3095 2952 2815 2685 2560 2441 2327 2218 4.6 2115 2015 1921 1830 1744 1661 1583 1508 1436 1368 4.7 1302 1240 1181 1124 1070 1018 969.2 922.3 877.6 835.0 4.8 794.4 755.6 718.7 683.6 650.1 618.1 587.7 558.8 531.2 504.9 4.9 479.9 456.0 433.4 411.8 391.2 371.6 353.0 335.3 318.4 302.4 5.0 287.1 272.6 258.8 245.6 233.1 221.3 210.0 199.2 189.0 179.3 5.1 170.1 161.4 153.0 145.1 137.6 130.5 123.7 117.3 111.2 105.3 5.2 99.83 94.60 89.64 84.92 80.45 76.20 72.17 68.35 64.72 61.28 5.3 58.02 54.93 51.99 49.21 46.57 44.07 41.70 39.46 37.33 35.31 5.4 33.40 31.58 29.87 28.24 26.70 25.24 23.86 22.56 21.32 20.15 5.5 19.04 17.99 16.99 16.05 15.16 14.32 13.52 12.77 12.06 11.38 5.6 10.75 10.14 9.574 9.035 8.526 8.045 7.590 7.160 6.754 6.370 5.7 6.008 5.665 5.342 5.036 4.748 4.476 4.218 3.976 3.746 3.530

II. táblázat.

A

^2

-eloszlás kritikus értékei

a

n 0.999 0.990 0.975 0.950 0.900 0.100 0.050 0.025 0.010 0.001 1 0.000

0 0.000

2 0.001

0 0.003

9 0.015

8 2.706 3.841 5.024 6.635 10.827 2 0.002

0 0.020

1 0.050

6 0.102

6 0.210

7 4.605 5.991 7.378 9.210 13.815 3 0.024

3 0.114

8 0.215

8 0.351

8 0.584

4 6.251 7.815 9.348 11.34

516.266 4 0.090

8 0.297

1 0.484

4 0.710

7 1.064 7.779 9.488 11.14

3 13.27

718.466 5 0.210

2 0.554

3 0.831

2 1.145 1.610 9.236 11.07

0 12.83

2 15.08

620.515 6 0.381

0 0.872

1 1.237 1.635 2.204 10.64

5 12.59

2 14.44

9 16.81

222.457 7 0.598

5 1.239 1.690 2.167 2.833 12.01

7 14.06

7 16.01

3 18.47

524.321 8 0.857

1 1.647 2.180 2.733 3.490 13.36

2 15.50

7 17.53

5 20.09

026.124 9 1.152 2.088 2.700 3.325 4.168 14.68 16.91 19.02 21.6627.877

f⁽²)

^ a

^_a

11 1.834 3.053 3.816 4.575 5.578 17.27 5

19.67 5

21.92 0

24.72 5

31.264 12 2.214 3.571 4.404 5.226 6.304 18.54

9

21.02 6

23.33 7

26.21 7

32.909 13 2.617 4.107 5.009 5.892 7.041 19.81

2

22.36 2

24.73 6

27.68 8

34.527 14 3.041 4.660 5.629 6.571 7.790 21.06

4

23.68 5

26.11 9

29.14 1

36.124 15 3.483 5.229 6.262 7.261 8.547 22.30

7

24.99 6

27.48 8

30.57 8

37.698 16 3.942 5.812 6.908 7.962 9.312 23.54

2

26.29 6

28.84 5

32.00 0

39.252 17 4.416 6.408 7.564 8.672 10.08

5

24.76 9

27.58 7

30.19 1

33.40 9

40.791 18 4.905 7.015 8.231 9.390 10.86

5

25.98 9

28.86 9

31.52 6

34.80 5

42.312 19 5.407 7.633 8.907 10.11

7

11.65 1

27.20 4

30.14 4

32.85 2

36.19 1

43.819 20 5.921 8.260 9.591 10.85

1

12.44 3

28.41 2

31.41 0

34.17 0

37.56 6

45.314 21 6.447 8.897 10.28

3

11.59 1

13.24 0

29.61 5

32.67 1

35.47 9

38.93 2

46.796 22 6.983 9.542 10.98

2 12.33

8 14.04

1 30.81

3 33.92

4 36.78

1 40.28

948.268 23 7.529 10.19

6

11.68 9

13.09 1

14.84 8

32.00 7

35.17 2

38.07 6

41.63 8

49.728 24 8.085 10.85

6 12.40

1 13.84

8 15.65

9 33.19

6 36.41

5 39.36

4 42.98

051.179 25 8.649 11.52

4 13.12

0 14.61

1 16.47

3 34.38

2 37.65

2 40.64

6 44.31

452.619 26 9.222 12.19

8 13.84

4 15.37

9 17.29

2 35.56

3 38.88

5 41.92

3 45.64

254.051 27 9.803 12.87

8 14.57

3 16.15

1 18.11

4 36.74

1 40.11

3 43.19

5 46.96

355.475 28 10.39

1 13.56

5 15.30

8 16.92

8 18.93

9 37.91

6 41.33

7 44.46

1 48.27

856.892 29 10.98

6 14.25

6 16.04

7 17.70

8 19.76

8 39.08

7 42.55

7 45.72

2 49.58

858.301 30 11.58

8 14.95

3 16.79

1 18.49

3 20.59

9 40.25

6 43.77

3 46.97

9 50.89

259.702 40 17.91

7 22.16

4 24.43

3 26.50

9 29.05

1 51.80

5 55.75

8 59.34

2 63.69

173.403 50 24.67

4 29.70

7 32.35

7 34.76

4 37.68

9 63.16

7 67.50

5 71.42

0 76.15

486.660 60 31.73

8 37.48

5 40.48

2 43.18

8 46.45

9 74.39

7 79.08

2 83.29

8 88.37

999.608 70 39.03 45.44 48.75 51.73 55.32 85.52 90.53 95.02 100.4 112.31

6 2 8 9 9 7 1 3 25 7 80 46.52

0 53.54

0 57.15

3 60.39

1 64.27

8 96.57

8 101.8

79 106.6

29 112.3

29124.83 9

III. táblázat.

A Student-féle t-eloszlás

t_{a 2}

kritikus értékei

a

n

0.200 0.100 0.050 0.025 0.010 0.005 0.001 1 3.078 6.314 12.70

6 25.45

2 63.65

6 127.3

21 636.5 78 2 1.886 2.920 4.303 6.205 9.925 14.08

9 31.60 0 3 1.638 2.353 3.182 4.177 5.841 7.453 12.92 4 4 1.533 2.132 2.776 3.495 4.604 5.598 8.610 5 1.476 2.015 2.571 3.163 4.032 4.773 6.869 6 1.440 1.943 2.447 2.969 3.707 4.317 5.959 7 1.415 1.895 2.365 2.841 3.499 4.029 5.408 8 1.397 1.860 2.306 2.752 3.355 3.833 5.041 9 1.383 1.833 2.262 2.685 3.250 3.690 4.781 10 1.372 1.812 2.228 2.634 3.169 3.581 4.587 11 1.363 1.796 2.201 2.593 3.106 3.497 4.437 12 1.356 1.782 2.179 2.560 3.055 3.428 4.318

a/2

0 f(t)

a/2

ta/2 -ta/2

16 1.337 1.746 2.120 2.473 2.921 3.252 4.015

17 1.333 1.740 2.110 2.458 2.898 3.222 3.965

18 1.330 1.734 2.101 2.445 2.878 3.197 3.922

19 1.328 1.729 2.093 2.433 2.861 3.174 3.883

20 1.325 1.725 2.086 2.423 2.845 3.153 3.850

21 1.323 1.721 2.080 2.414 2.831 3.135 3.819

22 1.321 1.717 2.074 2.405 2.819 3.119 3.792

23 1.319 1.714 2.069 2.398 2.807 3.104 3.768

24 1.318 1.711 2.064 2.391 2.797 3.091 3.745

25 1.316 1.708 2.060 2.385 2.787 3.078 3.725

26 1.315 1.706 2.056 2.379 2.779 3.067 3.707

27 1.314 1.703 2.052 2.373 2.771 3.057 3.689

28 1.313 1.701 2.048 2.368 2.763 3.047 3.674

29 1.311 1.699 2.045 2.364 2.756 3.038 3.660

30 1.310 1.697 2.042 2.360 2.750 3.030 3.646

40 1.303 1.684 2.021 2.329 2.704 2.971 3.551

60 1.296 1.671 2.000 2.299 2.660 2.915 3.460

12 0 1.289 1.658 1.980 2.270 2.617 2.860 3.373