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ПРИЛОЖЕНИЯ. Критические точки распределения Стьюдента. Критические точки распределения Фишера - Снедекора. (k1 - число степеней свободы большей дисперсии;. k2 - число степеней свободы меньшей дисперсии). Таблица значений  tg  = t(g, n)



ПРИЛОЖЕНИЯ

Приложение 1

Таблица значений функции f(х) =

х
0, 0 0, 3989
0, 1
0, 2
0, 3
0, 4
0, 5
0, 6
0, 7
0, 8
0, 9
1, 0
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
1, 7
1, 8
1, 9
2, 0
2, 1
2, 2
2, 3
2, 4
2, 5
2, 6
2, 7
2, 8
2, 9
3, 0
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6
3, 7
3, 8
3, 9

Приложение 2

Таблица значений функции Ф(х) =

x Ф(х) x Ф(х) x Ф(х) x Ф(х)
0, 00 0, 0000 0, 32 0, 1255 0, 64 0, 2389 0, 96 0, 3315
0, 01 0, 0040 0, 33 0, 1293 0, 65 0, 2422 0, 97 0, 3340
0, 02 0, 0080 0, 34 0, 1331 0, 66 0, 2454 0, 98 0, 3365
0, 03 0, 0120 0, 35 0, 1368 0, 67 0, 2486 0, 99 0, 3389
0, 04 0, 0160 0, 36 0, 1406 0, 68 0, 2516 1, 00 0, 3413
0, 05 0, 0199 0, 37 0, 1443 0, 69 0, 2549 1, 01 0, 3438
0, 06 0, 0239 0, 38 0, 1480 0, 70 0, 2580 1, 02 0, 3461
0, 07 0, 0279 0, 39 0, 1517 0, 71 0, 2611 1, 03 0, 3485
0, 08 0, 0319 0, 40 0, 1554 0, 72 0, 2642 1, 04 0, 3508
0, 09 0, 0359 0, 41 0, 1591 0, 73 0, 2673 1, 05 0, 3531
0, 10 0, 0398 0, 42 0, 1628 0, 74 0, 2703 1, 06 0, 3554
0, 11 0, 0438 0, 43 0, 1664 0, 75 0, 2734 1, 07 0, 3577
0, 12 0, 0478 0, 44 0, 1700 0, 76 0, 2764 1, 08 0, 3599
0, 13 0, 0517 0, 45 0, 1736 0, 77 0, 2794 1, 09 0, 3621
0, 14 0, 0557 0, 46 0, 1772 0, 78 0, 2823 1, 10 0, 3643
0, 15 0, 0596 0, 47 0, 1808 0, 79 0, 2852 1, 11 0, 3665
0, 16 0, 0636 0, 48 0, 1844 0, 80 0, 2881 1, 12 0, 3686
0, 17 0, 0675 0, 49 0, 1879 0, 81 0, 2910 1, 13 0, 3708
0, 18 0, 0714 0, 50 0, 1915 0, 82 0, 2939 1, 14 0, 3729
0, 19 0, 0753 0, 51 0, 1950 0, 83 0, 2967 1, 15 0, 3749
0, 20 0, 0793 0, 52 0, 1985 0, 84 0, 2995 1, 16 0, 3770
0, 21 0, 0832 0, 53 0, 2019 0, 85 0, 3023 1, 17 0, 3790
0, 22 0, 0871 0, 54 0, 2054 0, 86 0, 3051 1, 18 0, 3810
0, 23 0, 0910 0, 55 0, 2088 0, 87 0, 3078 1, 19 0, 3830
0, 24 0, 0948 0, 56 0, 2123 0, 88 0, 3106 1, 20 0, 3849
0, 25 0, 0987 0, 57 0, 2157 0, 89 0, 3133 1, 21 0, 3869
0, 26 0, 1026 0, 58 0, 2190 0, 90 0, 3159 1, 22 0, 3883
0, 27 0, 1064 0, 59 0, 2224 0, 91 0, 3186 1, 23 0, 3907
0, 28 0, 1103 0, 60 0, 2257 0, 92 0, 3212 1, 24 0, 3925
0, 29 0, 1141 0, 61 0, 2291 0, 93 0, 3228 1, 25 0, 3944
0, 30 0, 1179 0, 62 0, 2324 0, 94 0, 3264 1, 26 0, 3962
0, 31 0, 1217 0, 63 0, 2357 0, 95 0, 3289 1, 27 0, 3980

Окончание прил. 2

 

x Ф(х) x Ф(х) x Ф(х) x Ф(х)
1, 28 0, 3997 1, 62 0, 4474 1, 95 0, 4744 2, 56 0, 4948
1, 29 0, 4015 1, 63 0, 4484 1, 96 0, 4750 2, 58 0, 4951
1, 30 0, 4032 1, 64 0, 4495 1, 97 0, 4756 2, 60 0, 4953
1, 31 0, 4049 1, 65 0, 4505 1, 98 0, 4761 2, 62 0, 4956
1, 32 0, 4066 1, 66 0, 4515 1, 99 0, 4767 2, 64 0, 4959
1, 33 0, 4082 1, 67 0, 4525 2, 00 0, 4772 2, 66 0, 4961
1, 34 0, 4099 1, 68 0, 4535 2, 02 0, 4783 2, 68 0, 4963
1, 35 0, 4115 1, 69 0, 4545 2, 04 0, 4793 2, 70 0, 4965
1, 36 0, 4131 1, 70 0, 4554 2, 06 0, 4803 2, 72 0, 4967
1, 37 0, 4147 1, 71 0, 4564 2, 08 0, 4812 2, 74 0, 4969
1, 38 0, 4162 1, 72 0, 4573 2, 10 0, 4821 2, 76 0, 4971
1, 39 0, 4177 1, 73 0, 4582 2, 12 0, 4830 2, 78 0, 4973
1, 40 0, 4192 1, 74 0, 4591 2, 14 0, 4838 2, 80 0, 4974
1, 41 0, 4207 1, 75 0, 4599 2, 16 0, 4846 2, 82 0, 4976
1, 43 0, 4236 1, 76 0, 4608 2, 18 0, 4854 2, 84 0, 4977
1, 44 0, 4251 1, 77 0, 4616 2, 20 0, 4861 2, 86 0, 4979
1, 45 0, 4265 1, 78 0, 4625 2, 22 0, 4868 2, 88 0, 4980
1, 46 0, 4279 1, 79 0, 4633 2, 24 0, 4875 2, 92 0, 4982
1, 47 0, 4292 1, 80 0, 4641 2, 26 0, 4881 2, 94 0, 4984
1, 48 0, 4306 1, 81 0, 4649 2, 28 0, 4887 2, 96 0, 4985
1, 49 0, 4319 1, 82 0, 4656 2, 30 0, 4893 2, 98 0, 4986
1, 50 0, 4332 1, 83 0, 4664 2, 32 0, 4898 3, 00 0, 49865
1, 51 0, 4345 1, 84 0, 4671 2, 34 0, 4904 3, 20 0, 49931
1, 52 0, 4357 1, 85 0, 4678 2, 36 0, 4909 3, 40 0, 49966
1, 53 0, 4370 1, 86 0, 4686 2, 38 0, 4913 3, 60 0, 499841
1, 54 0, 4382 1, 87 0, 4693 2, 40 0, 4918 3, 80 0, 499928
1, 55 0, 4394 1, 88 0, 4699 2, 42 0, 4922 4, 00 0, 499968
1, 56 0, 4406 1, 89 0, 4706 2, 44 0, 4927 4, 50 0, 499997
1, 57 0, 4418 1, 90 0, 4713 2, 46 0, 4931 5, 00 0, 499997
1, 58 0, 4429 1, 91 0, 4719 2, 48 0, 4934    
1, 59 0, 4441 1, 92 0, 4726 2, 50 0, 4938    
1, 60 0, 4452 1, 93 0, 4732 2, 52 0, 4941    
1, 61 0, 4463 1, 94 0, 4738 2, 54 0, 4945    

 


Приложение 3

Таблица значений функции Пуассона

m

a

0, 1 0, 2 0, 3 0, 4 0, 5 0, 6 0, 7 0, 8 0, 9
0, 9048 0, 8187 0, 7408 0, 6703 0, 6065 0, 5488 0, 4966 0, 4493 0, 4066
0, 0905 0, 1638 0, 2222 0, 2681 0, 3033 0, 3293 0, 3476 0, 3595 0, 3696
0, 0045 0, 0164 0, 0333 0, 0536 0, 0758 0, 0988 0, 1217 0, 1438 0, 1647
0, 0002 0, 0011 0, 0033 0, 0072 0, 0126 0, 0198 0, 0284 0, 0383 0, 0494
- - 0, 0002 0, 0007 0, 0016 0, 0030 0, 0050 0, 0077 0, 0111
- - - 0, 0001 0, 0002 0, 0004 0, 0007 0, 0012 0, 0020
- - - - - - 0, 0001 0, 0002 0, 0003

 

 

a

m 1, 0 2, 0 3, 0 4, 0 5, 0 6, 0 7, 0 8, 0 9, 0
0, 3679 0, 1353 0, 0498 0, 0183 0, 0067 0, 0025 0, 0009 0, 0003 0, 0001
0, 3679 0, 2707 0, 1494 0, 0733 0, 0337 0, 0149 0, 0064 0, 0027 0, 0011
0, 1839 0, 2707 0, 2240 0, 1465 0, 0842 0, 0446 0, 0223 0, 0107 0, 0050
0, 0613 0, 1804 0, 2240 0, 1954 0, 1404 0, 0892 0, 0521 0, 0286 0, 0150
0, 0153 0, 0902 0, 1680 0, 1954 0, 1755 0, 1339 0, 0912 0, 0572 0, 0337
0, 0081 0, 0361 0, 1008 0, 1563 0, 1755 0, 1606 0, 1277 0, 0916 0, 0607
0, 0005 0, 0120 0, 0504 0, 1042 0, 1462 0, 1606 0, 1490 0, 1221 0, 0911
0, 0001 0, 0034 0, 0216 0, 0595 0, 1044 0, 1377 0, 1490 0, 1396 0, 1171
- 0, 0009 0, 0081 0, 0298 0, 0655 0, 1033 0, 1304 0, 1396 0, 1318
- 0, 0002 0, 0027 0, 0132 0, 0363 0, 0688 0, 1014 0, 1241 0, 1318
- - 0, 0008 0, 0053 0, 0181 0, 0413 0, 0710 0, 0993 0, 1186
- - 0, 0002 0, 0019 0, 0082 0, 0025 0, 0452 0, 0722 0, 0970
- - 0, 0001 0, 0006 0, 0034 0, 0113 0, 0264 0, 0481 0, 0728
- - - 0, 0002 0, 0013 0, 0052 0, 0142 0, 0296 0, 0504
- - - 0, 0001 0, 0005 0, 0022 0, 0071 0, 0169 0, 0324
- - - - 0, 0002 0, 0009 0, 0033 0, 0090 0, 0194
- - - - - 0, 0003 0, 0014 0, 0045 0, 0109
- - - - - 0, 0001 0, 0006 0, 0021 0, 0058
- - - - - - 0, 0002 0, 0009 0, 0029
- - - - - - 0, 0001 0, 0004 0, 0014
- - - - - - - 0, 0002 0, 0006
- - - - - - - 0, 0001 0, 0003
- - - - - - - - 0, 0001

 


Приложение 4

Критические точки распределения c2

Число степеней свободы k

Уровень значимости a
0, 01 0, 025 0, 05 0, 95 0, 975 0, 99
6, 6 5, 0 3, 8 0, 0039 0, 00098 0, 00016
9, 2 7, 4 6, 0 0, 103 0, 051 0, 020
11, 3 9, 4 7, 8 0, 352 0, 216 0, 115
13, 3 11, 1 9, 5 0, 711 0, 484 0, 297
15, 1 12, 8 11, 1 1, 15 0, 831 0, 554
16, 8 14, 4 12, 6 1, 64 1, 24 0, 872
18, 5 16, 0 14, 1 2, 17 1, 69 1, 24
20, 1 17, 5 15, 5 2, 73 2, 18 1, 65
21, 7 19, 0 16, 9 3, 33 2, 70 2, 09
23, 2 20, 5 18, 3 3, 94 3, 25 2, 56
24, 7 21, 9 19, 7 4, 57 3, 82 3, 05
26, 2 23, 3 21, 0 5, 23 4, 40 3, 57
27, 7 24, 7 22, 4 5, 89 5, 01 4, 11
29, 1 26, 1 23, 7 6, 57 5, 63 4, 66
30, 6 27, 5 25, 0 7, 26 6, 26 5, 23
32, 0 28, 8 26, 3 7, 96 6, 91 5, 81
33, 4 30, 2 27, 6 8, 67 7, 56 6, 41
34, 8 31, 5 28, 9 9, 39 8, 23 7, 01
36, 2 32, 9 30, 1 10, 1 8, 91 7, 63
37, 6 34, 2 31, 4 10, 9 9, 59 8, 26
38, 9 35, 5 32, 7 11, 6 10, 3 8, 90
40, 3 36, 8 33, 9 12, 3 11, 0 9, 54
41, 6 38, 1 35, 2 13, 1 11, 7 10, 2
43, 0 39, 4 36, 4 13, 8 12, 4 10, 9
44, 3 40, 6 37, 7 14, 6 13, 1 11, 5
45, 6 41, 9 38, 9 15, 4 13, 8 12, 2
47, 0 43, 2 40, 1 16, 2 14, 6 12, 9
48, 3 44, 5 41, 3 16, 9 15, 3 13, 6
49, 6 45, 7 42, 6 17, 7 16, 0 14, 3
50, 9 47, 0 43, 8 18, 5 16, 8 15, 0

 

 


Приложение 5

Критические точки распределения Стьюдента

Число степеней свободы k

Уровень значимости a(двусторонняя критическая область)
0, 1 0, 05 0, 02 0, 01 0, 002 0, 001
6, 31 12, 7 31, 82 63, 7 318, 3 637, 0
2, 92 4, 30 6, 97 9, 92 22, 33 31, 6
2, 35 3, 18 4, 54 5, 84 10, 22 12, 9
2, 13 2, 78 3, 75 4, 60 7, 17 8, 61
2, 01 2, 57 3, 37 4, 03 5, 89 6, 86
1, 94 2, 45 3, 14 3, 71 5, 21 5, 96
1, 89 2, 36 3, 00 3, 50 4, 79 5, 40
1, 86 2, 31 2, 90 3, 36 4, 50 5, 04
1, 83 2, 26 2, 82 3, 25 4, 30 4, 78
1, 81 2, 23 2, 76 3, 17 4, 14 4, 59
1, 80 2, 20 2, 72 3, 11 4, 03 4, 44
1, 78 2, 18 2, 68 3, 05 3, 93 4, 32
1, 77 2, 16 2, 65 3, 01 3, 85 4, 22
1, 76 2, 14 2, 62 2, 98 3, 79 4, 14
1, 75 2, 13 2, 60 2, 95 3, 73 4, 07
1, 75 2, 12 2, 58 2, 92 3, 69 4, 01
1, 74 2, 11 2, 57 2, 90 3, 65 3, 96
1, 73 2, 10 2, 55 2, 88 3, 61 3, 92
1, 73 2, 09 2, 54 2, 86 3, 58 3, 88
1, 73 2, 09 2, 53 2, 85 3, 55 3, 85
1, 72 2, 08 2, 52 2, 83 3, 53 3, 82
1, 72 2, 07 2, 51 2, 82 3, 51 3, 79
1, 71 2, 07 2, 50 2, 81 3, 49 3, 77
1, 71 2, 06 2, 49 2, 80 3, 47 3, 74
1, 71 2, 06 2, 49 2, 79 3, 45 3, 72
1, 71 2, 06 2, 48 2, 78 3, 44 3, 71
1, 71 2, 05 2, 47 2, 77 3, 42 3, 69
1, 70 2, 05 2, 46 2, 76 3, 40 3, 66
1, 70 2, 05 2, 46 2, 76 3, 40 3, 66
1, 70 2, 04 2, 46 2, 75 3, 39 3, 65
1, 68 2, 02 2, 42 2, 70 3, 31 3, 55
1, 67 2, 00 2, 39 2, 66 3, 23 3, 46
1, 66 1, 98 2, 36 2, 62 3, 17 3, 37
¥ 1, 64 1, 96 2, 33 2, 58 3, 09 3, 37

Число степеней свободы k

 0, 05 0, 025 0, 01 0, 005 0, 001 0, 0005

Уровень значимости a(односторонняя критическая область)

 


Приложение 6

Критические точки распределения Фишера - Снедекора

(k1 - число степеней свободы большей дисперсии;

k2 - число степеней свободы меньшей дисперсии)

Уровень значимости a= 0, 01

k2

k1
11
98, 49 34, 12 21, 20 16, 26 13, 74 12, 25 11, 26 10, 56 10, 04 9, 65 9, 33 9, 07 8, 86 8, 68 8, 53 8, 40 99, 01 30, 81 18, 00 13, 27 10, 92 9, 55 8, 65 8, 02 7, 56 7, 20 6, 93 6, 70 6, 51 6, 36 6, 23 6, 11 90, 17 29, 46 16, 69 12, 06 9, 78 8, 45 7, 59 6, 99 6, 55 6, 22 5, 95 5, 74 5, 56 5, 42 5, 29 5, 18 99, 25 28, 71 15, 98 11, 39 9, 15 7, 85 7, 01 6, 42 5, 99 5, 67 5, 41 5, 20 5, 03 4, 89 4, 77 4, 67 99, 33 28, 24 15, 52 10, 97 8, 75 7, 46 6, 63 6, 06 5, 64 5, 32 5, 06 4, 86 4, 69 4, 56 4, 44 4, 34 99, 30 27, 91 15, 21 10, 67 8, 47 7, 19 6, 37 5, 80 5, 39 5, 07 4, 82 4, 62 4, 46 4, 32 4, 20 4, 10 99, 34 27, 67 14, 98 10, 45 8, 26 7, 00 6, 19 5, 62 5, 21 4, 88 4, 65 4, 44 4, 28 4, 14 4, 03 3, 93 99, 36 27, 49 14, 80 10, 27 8, 10 6, 84 6, 03 5, 47 5, 06 4, 74 4, 50 4, 30 4, 14 4, 00 3, 89 3, 79 99, 36 27, 34 14, 66 10, 15 7, 98 6, 71 5, 91 5, 35 4, 95 4, 63 4, 39 4, 19 4, 03 3, 89 3, 78 3, 68 99, 40 27, 23 14, 54 10, 05 7, 87 6, 62 5, 82 5, 26 4, 85 4, 54 4, 30 4, 10 3, 94 3, 80 3, 69 3, 59 99, 41 27, 13 14, 45 9, 96 7, 79 6, 54 5, 74 5, 18 4, 78 4, 46 4, 22 4, 02 3, 86 3, 73 3, 62 3, 52 99, 42 27, 05 14, 37 9, 89 7, 72 6, 47 5, 67 5, 11 4, 71 4, 40 4, 16 3, 96 3, 80 3, 67 3, 55 3, 46

 

Уровень значимости a= 0, 05

k1

k2

18, 51

10, 13

7, 71

6, 61

5, 99

5, 59

5, 32

5, 12

4, 96

4, 84

4, 75

4, 67

4, 60

4, 54

4, 49

4, 45

 19, 00 9, 55 6, 94 5, 79 5, 14 4, 74 4, 46 4, 26 4, 10 3, 98 3, 88 3, 80 3, 74 3, 68 3, 63 3, 59 19, 16 9, 28 6, 59 5, 41 4, 76 4, 35 4, 07 3, 86 3, 71 3, 59 3, 49 3, 41 3, 34 3, 29 3, 24 3, 20 19, 25 9, 12 6, 39 5, 19 4, 53 4, 12 3, 84 3, 63 3, 48 3, 36 3, 26 3, 18 3, 11 3, 06 3, 01 2, 96 19, 30 9, 01 6, 26 5, 05 4, 39 3, 97 3, 69 3, 48 3, 33 3, 20 3, 11 3, 02 2, 96 2, 90 2, 85 2, 81 19, 33 8, 94 6, 16 4, 95 4, 28 3, 87 3, 58 3, 37 3, 22 3, 09 3, 00 2, 92 2, 85 2, 79 2, 74 2, 70 19, 36 8, 88 6, 09 4, 88 4, 21 3, 79 3, 50 3, 29 3, 14 3, 01 2, 92 2, 84 2, 77 2, 70 2, 66 2, 62 19, 37 8, 84 6, 04 4, 82 4, 15 3, 73 3, 44 3, 23 3, 07 2, 95 2, 85 2, 77 2, 70 2, 64 2, 59 2, 55 19, 38 8, 81 6, 00 4, 78 4, 10 3, 68 3, 39 3, 18 3, 02 2, 90 2, 80 2, 72 2, 65 2, 59 2, 54 2, 50

19, 39

8, 78

5, 96

4, 74

4, 06

3, 63

3, 34

3, 13

2, 97

2, 86

2, 76

2, 67

2, 60

2, 55

2, 49

2, 45

19, 40

8, 76

5, 93

4, 70

4, 03

3, 60

3, 31

3, 10

2, 94

2, 82

2, 72

2, 63

2, 56

2, 51

2, 45

2, 41

19, 41

8, 74

5, 91

4, 68

4, 00

3, 57

3, 28

3, 07

2, 91

2, 79

2, 69

2, 60

2, 53

2, 48

2, 42

2, 38
                                         

Приложение 7

Таблица значений

х х х
0, 1 0, 2 0, 3 0, 4 0, 5 0, 6 0, 7 0, 8 0, 9 1, 0 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 1, 7 1, 8 1, 9 2, 0 0, 9048 0, 8187 0, 7408 0, 6703 0, 6065 0, 5488 0, 4966 0, 4493 0, 4066 0, 3679 0, 3329 0, 3012 0, 2725 0, 2466 0, 2231 0, 2019 0, 1827 0, 1653 0, 1496 0, 1353 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 2, 7 2, 8 2, 9 3, 0 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 3, 7 3, 8 3, 9 4, 0 0, 1224 0, 1108 0, 1002 0, 0907 0, 0821 0, 0743 0, 0672 0, 0608 0, 0550 0, 0498 0, 0450 0, 0408 0, 0369 0, 0334 0, 0302 0, 0273 0, 0247 0, 0224 0, 0202 0, 0183 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 4, 7 4, 8 4, 9 5, 0 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 5, 7 5, 8 5, 9 6, 0 0, 0166 0, 0150 0, 0135 0, 0123 0, 0111 0, 0100 0, 0091 0, 0082 0, 0074 0, 0067 0, 0061 0, 0055 0, 0050 0, 0045 0, 0041 0, 0037 0, 0033 0, 0030 0, 0027 0, 0025

 

Приложение 8

Таблица значений  tg  = t(g, n)

n

g

 

n

g

0, 95 0, 99 0, 999   0, 95 0, 99 0, 999
2, 78 2, 57 2, 45 2, 37 2, 31 2, 26 2, 23 2, 20 2, 18 2, 16 2, 15 2, 13 2, 12 2, 11 2, 10 4, 60 4, 03 3, 71 3, 50 3, 36 3, 25 3, 17 3, 11 3, 06 3, 01 2, 98 2, 95 2, 92 2, 90 2, 88 8, 61 6, 86 5, 96 5, 41 5, 04 4, 78 4, 59 4, 44 4, 32 4, 22 4, 14 4, 07 4, 02 3, 97 3, 92   ¥ 2, 093 2, 064 2, 045 2, 032 2, 023 2, 016 2, 009 2, 001 1, 996 1, 991 1, 987 1, 984 1, 980 1, 960 2, 861 2, 797 2, 756 2, 720 2, 708 2, 692 2, 679 2, 662 2, 649 2, 640 2, 633 2, 627 2, 617 2, 576 3, 883 3, 745 3, 659 3, 600 3, 558 3, 527 3, 502 3, 464 3, 439 3, 418 3, 403 3, 392 3, 374 3, 291

 

 



  

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