Tablica rozkladu chi kwadrat2, Szkoła, Zarządzanie, Statystyka matematyczna

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Warto
ś
ci krytyczne rozkładu chi-kwadrat
X ~ χ
2
ν
- X zmienna losowa o rozkładzie chi-kwadrat z liczbą stopni swobody ν,
α - poziom istotności,
χ
2
α, ν
- wartość krytyczna - liczba taka, Ŝe P(X > χ
2
α, ν
) = α
ν
\ a
0,995
0,990
0,975
0,950
0,900
0,100
0,050
0,025
0,010
0,005
0,0
4
393
0,0002
0,0010
0,0039
0,0158
2,7055
3,8415
5,0239
6,6349
7,8794
1
0,0100
0,0201
0,0506
0,1026
0,2107
4,6052
5,9915
7,3778
9,2104
10,5965
2
3
0,0717
0,1148
0,2158
0,3518
0,5844
6,2514
7,8147
9,3484
11,3449
12,8381
4
0,2070
0,2971
0,4844
0,7107
1,0636
7,7794
9,4877
11,1433
13,2767
14,8602
0,4118
0,5543
0,8312
1,1455
1,6103
9,2363
11,0705
12,8325
15,0863
16,7496
5
6
0,6757
0,8721
1,2373
1,6354
2,2041
10,6446
12,5916
14,4494
16,8119
18,5475
7
0,9893
1,2390
1,6899
2,1673
2,8331
12,0170
14,0671
16,0128
18,4753
20,2777
8
1,3444
1,6465
2,1797
2,7326
3,4895
13,3616
15,5073
17,5345
20,0902
21,9549
9
1,7349
2,0879
2,7004
3,3251
4,1682
14,6837
16,9190
19,0228
21,6660
23,5893
10
2,1558
2,5582
3,2470
3,9403
4,8652
15,9872
18,3070
20,4832
23,2093
25,1881
11
2,6032
3,0535
3,8157
4,5748
5,5778
17,2750
19,6752
21,9200
24,7250
26,7569
12
3,0738
3,5706
4,4038
5,2260
6,3038
18,5493
21,0261
23,3367
26,2170
28,2997
3,5650
4,1069
5,0087
5,8919
7,0415
19,8119
22,3620
24,7356
27,6882
29,8193
13
4,0747
4,6604
5,6287
6,5706
7,7895
21,0641
23,6848
26,1189
29,1412
31,3194
14
15
4,6009
5,2294
6,2621
7,2609
8,5468
22,3071
24,9958
27,4884
30,5780
32,8015
16
5,1422
5,8122
6,9077
7,9616
9,3122
23,5418
26,2962
28,8453
31,9999
34,2671
5,6973
6,4077
7,5642
8,6718
10,0852
24,7690
27,5871
30,1910
33,4087
35,7184
17
18
6,2648
7,0149
8,2307
9,3904
10,8649
25,9894
28,8693
31,5264
34,8052
37,1564
19
6,8439
7,6327
8,9065
10,1170 11,6509
27,2036
30,1435
32,8523
36,1908
38,5821
20
7,4338
8,2604
9,5908
10,8508 12,4426
28,4120
31,4104
34,1696
37,5663
39,9969
21
8,0336
8,8972
10,2829 11,5913 13,2396
29,6151
32,6706
35,4789
38,9322
41,4009
22
8,6427
9,5425
10,9823 12,3380 14,0415
30,8133
33,9245
36,7807
40,2894
42,7957
23
9,2604
10,1957 11,6885 13,0905 14,8480
32,0069
35,1725
38,0756
41,6383
44,1814
24
9,8862
10,8563 12,4011 13,8484 15,6587
33,1962
36,4150
39,3641
42,9798
45,5584
10,5196 11,5240 13,1197 14,6114 16,4734
34,3816
37,6525
40,6465
44,3140
46,9280
25
11,1602 12,1982 13,8439 15,3792 17,2919
35,5632
38,8851
41,9231
45,6416
48,2898
26
27
11,8077 12,8785 14,5734 16,1514 18,1139
36,7412
40,1133
43,1945
46,9628
49,6450
28
12,4613 13,5647 15,3079 16,9279 18,9392
37,9159
41,3372
44,4608
48,2782
50,9936
13,1211 14,2564 16,0471 17,7084 19,7677
39,0875
42,5569
45,7223
49,5878
52,3355
29
30
13,7867 14,9535 16,7908 18,4927 20,5992
40,2560
43,7730
46,9792
50,8922
53,6719
31
14,4577 15,6555 17,5387 19,2806 21,4336
41,4217
44,9853
48,2319
52,1914
55,0025
32
15,1340 16,3622 18,2908 20,0719 22,2706
42,5847
46,1942
49,4804
53,4857
56,3280
33
15,8152 17,0735 19,0467 20,8665 23,1102
43,7452
47,3999
50,7251
54,7754
57,6483
34
16,5013 17,7891 19,8062 21,6643 23,9522
44,9032
48,6024
51,9660
56,0609
58,9637
35
17,1917 18,5089 20,5694 22,4650 24,7966
46,0588
49,8018
53,2033
57,3420
60,2746
36
17,8868 19,2326 21,3359 23,2686 25,6433
47,2122
50,9985
54,4373
58,6192
61,5811
18,5859 19,9603 22,1056 24,0749 26,4921
48,3634
52,1923
55,6680
59,8926
62,8832
37
19,2888 20,6914 22,8785 24,8839 27,3430
49,5126
53,3835
56,8955
61,1620
64,1812
38
39
19,9958 21,4261 23,6543 25,6954 28,1958
50,6598
54,5722
58,1201
62,4281
65,4753
40
20,7066 22,1642 24,4331 26,5093 29,0505
51,8050
55,7585
59,3417
63,6908
66,7660
24,3110 25,9012 28,3662 30,6123 33,3504
57,5053
61,6562
65,4101
69,9569
73,1660
45
50
27,9908 29,7067 32,3574 34,7642 37,6886
63,1671
67,5048
71,4202
76,1538
79,4898
55
31,7349 33,5705 36,3981 38,9581 42,0596
68,7962
73,3115
77,3804
82,2920
85,7491
60
35,5344 37,4848 40,4817 43,1880 46,4589
74,3970
79,0820
83,2977
88,3794
91,9518
65
39,3832 41,4436 44,6030 47,4496 50,8829
79,9730
84,8206
89,1772
94,4220
98,1049
70
43,2753 45,4417 48,7575 51,7393 55,3289
85,5270
90,5313
95,0231
100,4251 104,2148
75
47,2061 49,4751 52,9419 56,0541 59,7946
91,0615
96,2167
100,8393 106,3929 110,2854
80
51,1719 53,5400 57,1532 60,3915 64,2778
96,5782
101,8795 106,6285 112,3288 116,3209
55,1695 57,6339 61,3888 64,7494 68,7771 102,0789 107,5217 112,3933 118,2356 122,3244
85
59,1963 61,7540 65,6466 69,1260 73,2911 107,5650 113,1452 118,1359 124,1162 128,2987
90
95
63,2495 65,8983 69,9249 73,5198 77,8184 113,0377 118,7516 123,8580 129,9725 134,2466
100
67,3275 70,0650 74,2219 77,9294 82,3581 118,4980 124,3421 129,5613 135,8069 140,1697
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