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tabla chi2, Apuntes de Estadística

Universidad de León (ULE)Estadística

Asignatura: estadistica, Profesor: marola marola, Carrera: Psicología, Universidad: UPSA

Tipo: Apuntes

2013/2014

Subido el 03/01/2014

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ESTADÍSTICA INFERENCIAL______________________________________TABLA DE DISTRIBUCIONES CHI-CUADRADO
Mª del Mar González-Tablas Sastre VII
Tabla 3 Distribución Chi Cuadrado χ2
δ/p
0,9990
0,9975
0,9950
0,9900
0,9750
0,9500
0,9000
0,8500
0,8000
0,7500
0,7000
0,6500
0,6000
0,5500
0,5000
1
10,8274
9,1404
7,8794
6,6349
5,0239
3,8415
2,7055
2,0722
1,6424
1,3233
1,0742
0,8735
0,7083
0,5707
0,4549
2
13,8150
11,9827
10,5965
9,2104
7,3778
5,9915
4,6052
3,7942
3,2189
2,7726
2,4079
2,0996
1,8326
1,5970
1,3863
3
16,2660
14,3202
12,8381
11,3449
9,3484
7,8147
6,2514
5,3170
4,6416
4,1083
3,6649
3,2831
2,9462
2,6430
2,3660
4
18,4662
16,4238
14,8602
13,2767
11,1433
9,4877
7,7794
6,7449
5,9886
5,3853
4,8784
4,4377
4,0446
3,6871
3,3567
5
20,5147
18,3854
16,7496
15,0863
12,8325
11,0705
9,2363
8,1152
7,2893
6,6257
6,0644
5,5731
5,1319
4,7278
4,3515
6
22,4575
20,2491
18,5475
16,8119
14,4494
12,5916
10,6446
9,4461
8,5581
7,8408
7,2311
6,6948
6,2108
5,7652
5,3481
7
24,3213
22,0402
20,2777
18,4753
16,0128
14,0671
12,0170
10,7479
9,8032
9,0371
8,3834
7,8061
7,2832
6,8000
6,3458
8
26,1239
23,7742
21,9549
20,0902
17,5345
15,5073
13,3616
12,0271
11,0301
10,2189
9,5245
8,9094
8,3505
7,8325
7,3441
9
27,8767
25,4625
23,5893
21,6660
19,0228
16,9190
14,6837
13,2880
12,2421
11,3887
10,6564
10,0060
9,4136
8,8632
8,3428
10
29,5879
27,1119
25,1881
23,2093
20,4832
18,3070
15,9872
14,5339
13,4420
12,5489
11,7807
11,0971
10,4732
9,8922
9,3418
11
31,2635
28,7291
26,7569
24,7250
21,9200
19,6752
17,2750
15,7671
14,6314
13,7007
12,8987
12,1836
11,5298
10,9199
10,3410
12
32,9092
30,3182
28,2997
26,2170
23,3367
21,0261
18,5493
16,9893
15,8120
14,8454
14,0111
13,2661
12,5838
11,9463
11,3403
13
34,5274
31,8830
29,8193
27,6882
24,7356
22,3620
19,8119
18,2020
16,9848
15,9839
15,1187
14,3451
13,6356
12,9717
12,3398
14
36,1239
33,4262
31,3194
29,1412
26,1189
23,6848
21,0641
19,4062
18,1508
17,1169
16,2221
15,4209
14,6853
13,9961
13,3393
15
37,6978
34,9494
32,8015
30,5780
27,4884
24,9958
22,3071
20,6030
19,3107
18,2451
17,3217
16,4940
15,7332
15,0197
14,3389
0,4500
0,4000
0,3500
0,3000
0,2500
0,2000
0,1500
0,1000
0,0500
0,0250
0,0100
0,0050
0,0025
0,0001
0,3573
0,2750
0,2059
0,1485
0,1015
0,0642
0,0358
0,0158
0,0039
0,0010
0,0002
0,0000
0,0000
0,0000
1,1957
1,0217
0,8616
0,7133
0,5754
0,4463
0,3250
0,2107
0,1026
0,0506
0,0201
0,0100
0,0050
0,0020
2,1095
1,8692
1,6416
1,4237
1,2125
1,0052
0,7978
0,5844
0,3518
0,2158
0,1148
0,0717
0,0449
0,0243
3,0469
2,7528
2,4701
2,1947
1,9226
1,6488
1,3665
1,0636
0,7107
0,4844
0,2971
0,2070
0,1449
0,0908
3,9959
3,6555
3,3251
2,9999
2,6746
2,3425
1,9938
1,6103
1,1455
0,8312
0,5543
0,4118
0,3075
0,2102
4,9519
4,5702
4,1973
3,8276
3,4546
3,0701
2,6613
2,2041
1,6354
1,2373
0,8721
0,6757
0,5266
0,3810
5,9125
5,4932
5,0816
4,6713
4,2549
3,8223
3,3583
2,8331
2,1673
1,6899
1,2390
0,9893
0,7945
0,5985
6,8766
6,4226
5,9753
5,5274
5,0706
4,5936
4,0782
3,4895
2,7326
2,1797
1,6465
1,3444
1,1042
0,8571
7,8434
7,3570
6,8763
6,3933
5,8988
5,3801
4,8165
4,1682
3,3251
2,7004
2,0879
1,7349
1,4501
1,1519
8,8124
8,2955
7,7832
7,2672
6,7372
6,1791
5,5701
4,8652
3,9403
3,2470
2,5582
2,1558
1,8274
1,4787
9,7831
9,2373
8,6952
8,1479
7,5841
6,9887
6,3364
5,5778
4,5748
3,8157
3,0535
2,6032
2,2321
1,8338
10,7553
10,1820
9,6115
9,0343
8,4384
7,8073
7,1138
6,3038
5,2260
4,4038
3,5706
3,0738
2,6612
2,2141
11,7288
11,1291
10,5315
9,9257
9,2991
8,6339
7,9008
7,0415
5,8919
5,0087
4,1069
3,5650
3,1118
2,6172
12,7034
12,0785
11,4548
10,8215
10,1653
9,4673
8,6963
7,7895
6,5706
5,6287
4,6604
4,0747
3,5820
3,0407
13,6790
13,0298
12,3809
11,7212
11,0365
10,3070
9,4993
8,5468
7,2609
6,2621
5,2294
4,6009
4,0697
3,4825
δ/π
0,9990
0,9975
0,9950
0,9900
0,9750
0,9500
0,9000
0,8500
0,8000
0,7500
0,7000
0,6500
0,6000
0,5500
0,5000
16
39,2518
36,4555
34,2671
31,9999
28,8453
26,2962
23,5418
21,7931
20,4651
19,3689
18,4179
17,5646
16,7795
16,0425
15,3385
17
40,7911
37,9462
35,7184
33,4087
30,1910
27,5871
24,7690
22,9770
21,6146
20,4887
19,5110
18,6330
17,8244
17,0646
16,3382
18
42,3119
39,4220
37,1564
34,8052
31,5264
28,8693
25,9894
24,1555
22,7595
21,6049
20,6014
19,6993
18,8679
18,0860
17,3379
19
43,8194
40,8847
38,5821
36,1908
32,8523
30,1435
27,2036
25,3289
23,9004
22,7178
21,6891
20,7638
19,9102
19,1069
18,3376
20
45,3142
42,3358
39,9969
37,5663
34,1696
31,4104
28,4120
26,4976
25,0375
23,8277
22,7745
21,8265
20,9514
20,1272
19,3374
21
46,7963
43,7749
41,4009
38,9322
35,4789
32,6706
29,6151
27,6620
26,1711
24,9348
23,8578
22,8876
21,9915
21,1470
20,3372
22
48,2676
45,2041
42,7957
40,2894
36,7807
33,9245
30,8133
28,8224
27,3015
26,0393
24,9390
23,9473
23,0307
22,1663
21,3370
23
49,7276
46,6231
44,1814
41,6383
38,0756
35,1725
32,0069
29,9792
28,4288
27,1413
26,0184
25,0055
24,0689
23,1852
22,3369
24
51,1790
48,0336
45,5584
42,9798
39,3641
36,4150
33,1962
31,1325
29,5533
28,2412
27,0960
26,0625
25,1064
24,2037
23,3367
25
52,6187
49,4351
46,9280
44,3140
40,6465
37,6525
34,3816
32,2825
30,6752
29,3388
28,1719
27,1183
26,1430
25,2218
24,3366
26
54,0511
50,8291
48,2898
45,6416
41,9231
38,8851
35,5632
33,4295
31,7946
30,4346
29,2463
28,1730
27,1789
26,2395
25,3365
27
55,4751
52,2152
49,6450
46,9628
43,1945
40,1133
36,7412
34,5736
32,9117
31,5284
30,3193
29,2266
28,2141
27,2569
26,3363
28
56,8918
53,5939
50,9936
48,2782
44,4608
41,3372
37,9159
35,7150
34,0266
32,6205
31,3909
30,2791
29,2486
28,2740
27,3362
29
58,3006
54,9662
52,3355
49,5878
45,7223
42,5569
39,0875
36,8538
35,1394
33,7109
32,4612
31,3308
30,2825
29,2908
28,3361
30
59,7022
56,3325
53,6719
50,8922
46,9792
43,7730
40,2560
37,9902
36,2502
34,7997
33,5302
32,3815
31,3159
30,3073
29,3360
0,4500
0,4000
0,3500
0,3000
0,2500
0,2000
0,1500
0,1000
0,0500
0,0250
0,0100
0,0050
0,0025
0,0001
14,6555
13,9827
13,3096
12,6243
11,9122
11,1521
10,3090
9,3122
7,9616
6,9077
5,8122
5,1422
4,5734
3,9417
15,6328
14,9373
14,2406
13,5307
12,7919
12,0023
11,1249
10,0852
8,6718
7,5642
6,4077
5,6973
5,0916
4,4162
16,6108
15,8932
15,1738
14,4399
13,6753
12,8570
11,9462
10,8649
9,3904
8,2307
7,0149
6,2648
5,6234
4,9048
17,5894
16,8504
16,1089
15,3517
14,5620
13,7158
12,7727
11,6509
10,1170
8,9065
7,6327
6,8439
6,1673
5,4067
18,5687
17,8088
17,0458
16,2659
15,4518
14,5784
13,6039
12,4426
10,8508
9,5908
8,2604
7,4338
6,7228
5,9210
19,5485
18,7683
17,9843
17,1823
16,3444
15,4446
14,4393
13,2396
11,5913
10,2829
8,8972
8,0336
7,2889
6,4467
20,5288
19,7288
18,9243
18,1007
17,2396
16,3140
15,2787
14,0415
12,3380
10,9823
9,5425
8,6427
7,8648
6,9829
21,5095
20,6902
19,8657
19,0211
18,1373
17,1865
16,1219
14,8480
13,0905
11,6885
10,1957
9,2604
8,4503
7,5291
22,4908
21,6525
20,8084
19,9432
19,0373
18,0618
16,9686
15,6587
13,8484
12,4011
10,8563
9,8862
9,0441
8,0847
23,4724
22,6156
21,7524
20,8670
19,9393
18,9397
17,8184
16,4734
14,6114
13,1197
11,5240
10,5196
9,6462
8,6494
24,4544
23,5794
22,6975
21,7924
20,8434
19,8202
18,6714
17,2919
15,3792
13,8439
12,1982
11,1602
10,2561
9,2222
25,4367
24,5440
23,6437
22,7192
21,7494
20,7030
19,5272
18,1139
16,1514
14,5734
12,8785
11,8077
10,8733
9,8029
26,4195
25,5092
24,5909
23,6475
22,6572
21,5880
20,3857
18,9392
16,9279
15,3079
13,5647
12,4613
11,4973
10,3907
27,4025
26,4751
25,5391
24,5770
23,5666
22,4751
21,2468
19,7677
17,7084
16,0471
14,2564
13,1211
12,1278
10,9861
28,3858
27,4416
26,4881
25,5078
24,4776
23,3641
22,1103
20,5992
18,4927
16,7908
14,9535
13,7867
12,7646
11,5876
p = Probabilidad de encontrar un valor mayor o igual que el chi cuadrado tabulado
δ = Grados de Libertad
3
p
2
p9
2
z
9
2
1
δ
+
δ
−δ≈χδ 122z 2
pp −δ−χ≈ δ

Vista previa parcial del texto

¡Descarga tabla chi2 y más Apuntes en PDF de Estadística solo en Docsity!

ESTADÍSTICA INFERENCIAL______________________________________TABLA DE DISTRIBUCIONES CHI-CUADRADO

p = Probabilidad de encontrar un valor mayor o igual que el chi cuadrado tabulado δ = Grados de Libertad

3 p 9 1 2       δ

2

 - Tabla 3 Distribución Chi Cuadrado χ Mª del Mar González-Tablas Sastre VII
  • 0, δ /p
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
    • 10,
      • 9,
      • 7,
      • 6,
      • 5,
      • 3,
      • 2,
      • 2,
      • 1,
      • 1,
      • 1,
      • 0,
      • 0,
      • 0,
      • 0, - 13, - 11, - 10, - 9, - 7, - 5, - 4, - 3, - 3, - 2, - 2, - 2, - 1, - 1, - 1, - 16, - 14, - 12, - 11, - 9, - 7, - 6, - 5, - 4, - 4, - 3, - 3, - 2, - 2, - 2, - 18, - 16, - 14, - 13, - 11, - 9, - 7, - 6, - 5, - 5, - 4, - 4, - 4, - 3, - 3, - 20, - 18, - 16, - 15, - 12, - 11, - 9, - 8, - 7, - 6, - 6, - 5, - 5, - 4, - 4, - 22, - 20, - 18, - 16, - 14, - 12, - 10, - 9, - 8, - 7, - 7, - 6, - 6, - 5, - 5, - 24, - 22, - 20, - 18, - 16, - 14, - 12, - 10, - 9, - 9, - 8, - 7, - 7, - 6, - 6, - 26, - 23, - 21, - 20, - 17, - 15, - 13, - 12, - 11, - 10, - 9, - 8, - 8, - 7, - 7, - 27, - 25, - 23, - 21, - 19, - 16, - 14, - 13, - 12, - 11, - 10, - 10, - 9, - 8, - 8, - 29, - 27, - 25, - 23, - 20, - 18, - 15, - 14, - 13, - 12, - 11, - 11, - 10, - 9, - 9, - 31, - 28, - 26, - 24, - 21, - 19, - 17, - 15, - 14, - 13, - 12, - 12, - 11, - 10, - 10, - 32, - 30, - 28, - 26, - 23, - 21, - 18, - 16, - 15, - 14, - 14, - 13, - 12, - 11, - 11, - 34, - 31, - 29, - 27, - 24, - 22, - 19, - 18, - 16, - 15, - 15, - 14, - 13, - 12, - 12, - 36, - 33, - 31, - 29, - 26, - 23, - 21, - 19, - 18, - 17, - 16, - 15, - 14, - 13, - 13, - 37, - 34, - 32, - 30, - 27, - 24, - 22, - 20, - 19, - 18, - 17, - 16, - 15, - 15, - 14,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 1, - 1, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 2, - 1, - 1, - 1, - 1, - 1, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 0, - 3, - 2, - 2, - 2, - 1, - 1, - 1, - 1, - 0, - 0, - 0, - 0, - 0, - 0, - 3, - 3, - 3, - 2, - 2, - 2, - 1, - 1, - 1, - 0, - 0, - 0, - 0, - 0, - 4, - 4, - 4, - 3, - 3, - 3, - 2, - 2, - 1, - 1, - 0, - 0, - 0, - 0, - 5, - 5, - 5, - 4, - 4, - 3, - 3, - 2, - 2, - 1, - 1, - 0, - 0, - 0, - 6, - 6, - 5, - 5, - 5, - 4, - 4, - 3, - 2, - 2, - 1, - 1, - 1, - 0, - 7, - 7, - 6, - 6, - 5, - 5, - 4, - 4, - 3, - 2, - 2, - 1, - 1, - 1, - 8, - 8, - 7, - 7, - 6, - 6, - 5, - 4, - 3, - 3, - 2, - 2, - 1, - 1, - 9, - 9, - 8, - 8, - 7, - 6, - 6, - 5, - 4, - 3, - 3, - 2, - 2, - 1, - 10, - 10, - 9, - 9, - 8, - 7, - 7, - 6, - 5, - 4, - 3, - 3, - 2, - 2, - 11, - 11, - 10, - 9, - 9, - 8, - 7, - 7, - 5, - 5, - 4, - 3, - 3, - 2, - 12, - 12, - 11, - 10, - 10, - 9, - 8, - 7, - 6, - 5, - 4, - 4, - 3, - 3, - 13, - 13, - 12, - 11, - 11, - 10, - 9, - 8, - 7, - 6, - 5, - 4, - 4, - 3,
  • 0, δ/π
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
    • 39,
    • 36,
    • 34,
    • 31,
    • 28,
    • 26,
    • 23,
    • 21,
    • 20,
    • 19,
    • 18,
    • 17,
    • 16,
    • 16,
    • 15, - 40, - 37, - 35, - 33, - 30, - 27, - 24, - 22, - 21, - 20, - 19, - 18, - 17, - 17, - 16, - 42, - 39, - 37, - 34, - 31, - 28, - 25, - 24, - 22, - 21, - 20, - 19, - 18, - 18, - 17, - 43, - 40, - 38, - 36, - 32, - 30, - 27, - 25, - 23, - 22, - 21, - 20, - 19, - 19, - 18, - 45, - 42, - 39, - 37, - 34, - 31, - 28, - 26, - 25, - 23, - 22, - 21, - 20, - 20, - 19, - 46, - 43, - 41, - 38, - 35, - 32, - 29, - 27, - 26, - 24, - 23, - 22, - 21, - 21, - 20, - 48, - 45, - 42, - 40, - 36, - 33, - 30, - 28, - 27, - 26, - 24, - 23, - 23, - 22, - 21, - 49, - 46, - 44, - 41, - 38, - 35, - 32, - 29, - 28, - 27, - 26, - 25, - 24, - 23, - 22, - 51, - 48, - 45, - 42, - 39, - 36, - 33, - 31, - 29, - 28, - 27, - 26, - 25, - 24, - 23, - 52, - 49, - 46, - 44, - 40, - 37, - 34, - 32, - 30, - 29, - 28, - 27, - 26, - 25, - 24, - 54, - 50, - 48, - 45, - 41, - 38, - 35, - 33, - 31, - 30, - 29, - 28, - 27, - 26, - 25, - 55, - 52, - 49, - 46, - 43, - 40, - 36, - 34, - 32, - 31, - 30, - 29, - 28, - 27, - 26, - 56, - 53, - 50, - 48, - 44, - 41, - 37, - 35, - 34, - 32, - 31, - 30, - 29, - 28, - 27, - 58, - 54, - 52, - 49, - 45, - 42, - 39, - 36, - 35, - 33, - 32, - 31, - 30, - 29, - 28, - 59, - 56, - 53, - 50, - 46, - 43, - 40, - 37, - 36, - 34, - 33, - 32, - 31, - 30, - 29,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
  • 0,
    • 14,
    • 13,
    • 13,
    • 12,
    • 11,
    • 11,
    • 10,
      • 9,
      • 7,
      • 6,
      • 5,
      • 5,
      • 4,
      • 3,
        • 15,
        • 14,
        • 14,
        • 13,
        • 12,
        • 12,
        • 11,
        • 10, - 8, - 7, - 6, - 5, - 5, - 4, - 16, - 15, - 15, - 14, - 13, - 12, - 11, - 10, - 9, - 8, - 7, - 6, - 5, - 4, - 17, - 16, - 16, - 15, - 14, - 13, - 12, - 11, - 10, - 8, - 7, - 6, - 6, - 5, - 18, - 17, - 17, - 16, - 15, - 14, - 13, - 12, - 10, - 9, - 8, - 7, - 6, - 5, - 19, - 18, - 17, - 17, - 16, - 15, - 14, - 13, - 11, - 10, - 8, - 8, - 7, - 6, - 20, - 19, - 18, - 18, - 17, - 16, - 15, - 14, - 12, - 10, - 9, - 8, - 7, - 6, - 21, - 20, - 19, - 19, - 18, - 17, - 16, - 14, - 13, - 11, - 10, - 9, - 8, - 7, - 22, - 21, - 20, - 19, - 19, - 18, - 16, - 15, - 13, - 12, - 10, - 9, - 9, - 8, - 23, - 22, - 21, - 20, - 19, - 18, - 17, - 16, - 14, - 13, - 11, - 10, - 9, - 8, - 24, - 23, - 22, - 21, - 20, - 19, - 18, - 17, - 15, - 13, - 12, - 11, - 10, - 9, - 25, - 24, - 23, - 22, - 21, - 20, - 19, - 18, - 16, - 14, - 12, - 11, - 10, - 9, - 26, - 25, - 24, - 23, - 22, - 21, - 20, - 18, - 16, - 15, - 13, - 12, - 11, - 10, - 27, - 26, - 25, - 24, - 23, - 22, - 21, - 19, - 17, - 16, - 14, - 13, - 12, - 10, - 28, - 27, - 26, - 25, - 24, - 23, - 22, - 20, - 18, - 16, - 14, - 13, - 12, - 11, - p - z - χ δ ≈δ − z δ