TABLAS ESTADÍSTICAS.

TABLAS
ESTADÍSTICAS.
ESTADÍSTICA II
28.
Tabla 8
Test de Kolmogorov-Smirnov sobre Bondad de Ajuste
Nivel de significación
n
α
1
2
3
4
5
6
7
8
0.20
0.90000
0.68337
0.56481
0.49265
0.44698
0.41037
0.38148
0.35831
0.10
0.95000
0.77639
0.63604
0.56522
0.50945
0.46799
0.43607
0.40962
0.05
0.97500
0.84189
0.70760
0.62394
0.56328
0.51926
0.48342
0.45427
0.02
0.99000
0.90000
0.7 8456
0.68887
0.62718
0.5774 1
0.53844
0.50654
0.01
0.99500
0.92929
0.82900
0.73424
0.66853
0.61661
0.57581
0.54179
0.005
0.99750
0.95000
0.86428
0.77639
0.70543
0.65287
0.60975
0.57429
0.002
0.99900
0.96838
0.90000
0.82217
0.75000
0.69571
0.65071
0.61368
0.001
0.99950
0.97764
0.92065
0.85047
0.78137
0.72479
0.67930
0.64098
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
0.33910
0.32260
0.30829
0.29577
0.28470
0.27481
0.26589
0.25778
0.25039
0.24360
0.23735
0.23156
0.22517
0.221I5
0.21646
0.21205
0.20790
0.20399
0.20030
0.19680
0.19348
0.19032
0.18732
0.18445
0.18171
0.17909
0.17659
0.17418
0.17188
0.16966
0.16753
0.38746
0.36866
0.35242
0.33815
0.32549
0.31417
0.30397
0.29472
0.28627
0.27851
0.27136
0.26473
0.25858
0.25283
0.24746
0.24242
0.23768
0.23320
0.22898
0.22497
0.22117
0.21756
0.21412
0.21085
0.20771
0.21472
0.20185
0.19910
0.19646
0.19392
0.19148
0.43001
0.40925
0.39122
0.37543
0.36143
0.34890
0.33750
0.32733
0.31796
0.30936
0..30143
0.29408
0.28724
0.28087
0.2749tl
0.26931
0.26404
0.25908
0.25438
0.24993
0.24571
0.24170
0.23788
0.23424
0.23076
0.22743
0.22425
0.22119
0.21826
0.21544
0.21273
0.47960
0.45562
0.43670
0.41918
0.40362
0.38970
0.37713
0.36571
0.35528
0.34569
0.33685
0.32866
0.32104
0.31394
0.30728
0.30104
0.29518
0.28962
0.28438
0.27942
0.27471
0.27023
0.26596
0.26189
0.25801
0.25429
0.25073
0.24732
0.24404
0.24089
0.23785
0.51332
0.48893
0.46770
0.44905
0.43247
0.41762
0.40420
0.39201
0.38086
0.37062
0.36117
0.35241
0.34426
0.33666
0.32954
0.32286
0.31657
0.30963
0.30502
0.29971
0.29466
0.28986
0.28529
0.28094
0.27577
0.27271
0.26897
0.26532
0.26180
0.25843
0.25518
0.54443
0.51872
0.49539
0.47672
0.45921
0.44352
0.42934
0.41644
0.40464
0.39380
0.38379
0.37451
0.36588
0.35782
0.35027
0.34318
0.33651
0.33022
0.32425
0.31862
0.31327
0.30818
0.30333
0.29870
0.29428
0.29005
0.28600
0.28211
0.27838
0.27483
0.27135
0.58210
0.55500
0.53135
0.51047
0.49189
0.47520
0.45611
0.44637
0.43380
0.42224
0.41156
0.40165
0.39243
0.38382
0.37575
0.36787
0.36104
0.35431
0.34794
0.34190
0.33617
0.33072
0.32553
0.32058
0.31584
0.31131
0.30597
0.30281
0.29882
0.29498
0.29125
0.60846
0.58042
0-55588
0.53422
0.51490
0.49753
0.48182
0.46750
0.45540
0.44234
0.43119
0.42085
0.41122
0.40223
0.39380
0.38588
0.37743
0.37139
0.36473
0.35842
0.35242
0.34672
0.34129
0.33611
0.33115
0.32641
0.32187
0.31751
0.31333
0.30931
0.30544
29
TABLAS ESTADÍSTICAS.
n
40
41
42
43
44
45
46
47
48
49
50
n > 50
0.20
0.16547
0.16349
0.16158
0.15974
0.15795
0.15623
0.15457
0.15295
0.15139
0.14987
0.14840
0.10
0.18913
0.18687
0.18468
0.18257
0.18051
0.17856
0.17665
0.17481
0.17301
0.17128
0.16959
Nivel de significación α
0.05
0.02
0.01
0.21012
0.23494 0.25205
0.20760
0.23213 0.24904
0.20517
0.22941 0.24613
0.20283
0.22679 0.24332
0.20056
0.22426 0.24060
0.19837
0.22181 0.23798
0.19625
0.21944 0.23544
0.19420
0.21715 0.23298
0.19221
0.21493 0.23059
0.19028
0.21281 0.22832
0.18841
0.21068 0.22604
0.005
0.26803
0.26482
0.26173
0.25875
0.25587
0.25308
0.25038
0.24776
0.24523
0.24281
0.24039
0.002
0.28772
0.28429
0.28097
0.27778
0.27468
0.27169
0.26880
0.26600
0.26328
0.26069
0.25809
0.001
0.30171
0.29811
0.29465
0.29130
0.28806
0.28493
0.28190
0.27896
0.27611
0.27339
0.27067
1.07
1.22
n
1.36
n
1.73
n
1.85
n
1.95
n
n
1.52
n
1.63
n
ESTADÍSTICA II
30.
Tabla 9
Corrección de Lilliefors para Normalidad
Nivel de significación
0.10
n
0.20
0.15
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
n > 30
0.300
0.285
0.265
0.247
0.233
0.223
0.215
0.206
0.199
0.190
0.183
0.177
0.173
0.169
0.166
0.163
0.160
0.157
0.154
0.150
0.146
0.142
0.139
0.137
0.135
0.133
0.131
0.319
0.299
0.277
0.258
0.244
0.233
0.224
0.217
0.212
0.202
0.194
0.187
0.182
0.177
0.173
0.169
0.166
0.162
0.158
0.154
0.151
0.147
0.14S
0.143
0.140
0.138
0.136
0.736
0.352
0.315
0.294
0.276
0.261
0.249
0.239
0.230
0.223
0.214
0.207
0.201
0.195
0.189
0.184
0.179
0.174
0.170
0.167
0.164
0.161
0.158
0.155
0.153
0.150
0.147
0.144
0.768
n
0.805
n
α
0.05
0.01
0.381
0.337
0.319
0.300
0.285
0.271
0.258
0.249
0.242
0.234
0.227
0.220
0.213
0.206
0.200
0.195
0.190
0.186
0.182
0.179
0.176
0.173
0.171
0.168
0.166
0.163
0.161
0.417
0.405
0.364
0.348
0.331
0.311
0.294
0.284
0.275
0.268
0.261
0.257
0.250
0.245
0.239
0.235
0.231
0.226
0.220
0.213
0.207
0.200
0.197
0.194
0.192
0.190
0.187
0.886
n
1.031
n
n
31
TABLAS ESTADÍSTICAS.
Tabla 10
Prueba de homogeneidad de varianzas de Cochran
α = 0.05
n
k
2
3
4
5
6
7
8
9
10
2
0.998
0.966
0.906
0.841
0.780
0.727
0.679
0.638
0.602
3
0.975
0.870
0.767
0.683
0.616
0.561
0.515
0.477
0.445
4
0.939
0.797
0.684
0.598
0.532
0.480
0.437
0.402
0.373
5
0.905
0.745
0.628
0.544
0.480
0.430
0.391
0.358
0.331
6
0.877
0.707
0.589
0.506
0.444
0.397
0.350
0.328
0.302
7
0.853
0.677
0.559
0.478
0.418
0.372
0.336
0.306
0.282
8
0.833
0.653
0.536
0.456
0.398
0.353
0.318
0.290
0.266
9
0.815
0.633
0.517
0.438
0.381
0.338
0.304
0.276
0.254
10
0.801
0.616
0.501
0.424
0.368
0.352
0.292
0.265
0.243
11
0.788
0.602
0.488
0.411
0.336
0.315
0.282
0.256
0.735
17
0.734
0.546
0.436
0.364
0.313
0.275
0.246
0.222
0.203
37
0.660
0.474
0.372
0.306
0.261
0.227
0.202
0.182
0.165
145
0.581
0.403
0.309
0.251
0.211
0.183
0.161
0.144
0.130
1000
0.500
0.333
0.250
0.200
0.166
0.142
0.125
0.111
0.100
10
0.867
0.691
0.570
0.485
0.422
0.375
0.337
0.306
0.251
11
0.853
0.674
0.553
0.469
0.408
0.361
0.324
0.295
0.270
17
0.794
0.605
0.488
0.409
0.352
0.310
0.277
0.251
0.281
37
0.706
0.515
0.405
0.335
0.285
0.249
0.221
0.199
0.181
145
0.606
0.423
0.325
0.264
0.222
0.192
0.170
0.152
0.137
1000
0.500
0.333
0.250
0.200
0.166
0.142
0.125
0.111
0.100
α = 0.01
n
k
2
3
4
5
6
7
8
9
10
2
0.999
0.993
0.967
0.927
0.882
0.837
0.794
0.754
0.717
3
0.995
0.942
0.864
0.788
0.721
0.664
0.615
0.572
0.535
4
0.979
0.883
0.781
0.693
0.625
0.568
0.520
0.481
0.446
5
0.958
0.831
0.711
0.632
0.563
0.508
0.462
0.425
0.393
6
0.937
0.793
0.676
0.587
0.519
0.465
0.422
0.387
0.357
7
0.917
0.760
0.641
0.553
0.486
0.434
0.393
0.359
0.330
8
0.898
0.733
0.612
0.525
0.460
0.410
0.370
0.337
0.310
9
0.882
0.710
0.589
0.503
0.440
0.391
0.352
0.320
0.294
ESTADÍSTICA II
32.
Tabla 11
Test de Rachas
nn+=2
n+=3
n+=4
n+=5
n+=6
n+=7
n+=8
n+=9
2
3
4
5
6
7
8
9
10
α=0.05
0-4
0-5
0-5
0-5
0-5
0-5
2-3
2-5
2-5
α=0.01
0-4
0-5
0-5
0-5
0-5
0-5
0-5
0-5
0-5
α=0.05
0-5
0-6
0-6
2-7
2-7
2-7
2-7
2-7
3-7
α=0.01
0-5
0-6
0-7
0-7
0-7
0-7
0-7
2-7
2-7
α=0.05
0-5
0-6
2-7
2-8
3-8
3-8
3-9
3-9
3-9
α=0.01
0-5
0-7
0-8
0-9
2-9
2-9
2-9
2-9
2-9
α=0.05
0-5
2-7
2-8
3-8
3-9
3-9
3-10
4-10
4-10
α=0.01
0-5
0-7
0-9
2-9
2-10
2-10
2-11
3-10
3-11
α=0.05
05
2-7
3-8
3-9
3-10
4-10
4-11
4-11
5-11
α=0.01
05
0-7
2-9
2-10
2-11
3-11
3-12
3-12
3-13
α=0.05
0-5
2-7
3-8
3-9
4-10
4-11
4-12
5-12
5-12
α=0.01
0-5
0-7
2-9
2-10
3-11
3-12
3-12
4-13
4-14
α=0.05
2-5
2-7
3-9
3-10
4-11
4-12
5-12
5-13
6-13
α=0.01
0-5
0-7
2-9
2-11
3-12
3-12
4-13
4-14
4-14
α=0.05
2-5
2-7
3-9
4-10
4-11
5-12
5-13
6-13
6-14
α=0.01
0-5
2-7
2-9
3-10
3-12
4-13
4-14
4-15
5-15
n+=10 α=0.05
2-5
3-7
3-9
4-10
5-11
5-12
6-13
6-14
6-15
α=0.01
0-5
2-7
2-9
3-11
3-13
4-14
4-14
5-15
5-16
n+=11 α=0.05
2-5
3-7
3-9
4-11
5-12
5-13
6-14
6-14
7-15
α=0.01
0-5
2-7
2-9
3-11
4-13
4-14
4-15
5-16
5-17
n+=12 α=0.05
2-5
3-7
4-9
4-11
5-12
6-13
6-14
7-15
7-16
α=0.01
0-5
2-7
3-9
3-11
4-13
4-14
5-15
5-16
6-17
n+=13 α=0.05
2-5
3-7
4-9
4-11
5-12
6-13
6-14
7-15
8-16
α=0.01
0-5
2-7
3-9
3-11
4-13
5-15
5-16
6-17
6-18
n+=14 α=0.05
2-5
3-7
4-9
5-11
5-12
6-13
7-15
7-16
8-16
α=0.01
0-5
2-7
3-9
3-11
4-13
5-15
5-16
6-17
6-18
n+=15 α=0.05
2-5
3-7
4-9
5-11
6-13
6-14
7-15
8-16
8-17
α=0.01
0-5
2-7
3-9
4-11
4-13
5-15
5-16
6-17
7-18
33
TABLAS ESTADÍSTICAS.
n2
3
4
5
6
7
8
9
10
n+=16 α=0.05
2-5
3-7
4-9
5-11
6-13
6-14
7-15
8-16
8-17
α=0.01
0-5
2-7
3-9
4-11
4-13
5-15
6-16
6-17
7-19
n+=17 α=0.05
2-5
3-7
4-9
5-11
6-13
7-14
7-15
8-16
9-17
α=0.01
0-5
2-7
3-9
4-11
5-13
5-15
6-17
7-17
7-19
n+=18 α=0.05
2-5
3-7
4-9
5-11
6-13
7-14
8-15
8-17
9-18
α=0.01
0-5
2-7
3-9
4-11
5-13
5-15
6-17
7-18
7-19
n+=19 α=0.05
2-5
3-7
4-9
5-11
6-13
7-14
8-15
9-17
9-18
α=0.01
2-5
2-7
3-9
4-11
5-13
6-15
6-17
7-18
8-19
n+=20 α=0.05
2-5
3-7
4-9
5-11
6-13
7-14
8-16
9-17
9-18
α=0.01
2-5
2-7
3-9
4-11
5-13
6-15
6-17
7-18
8-19
n11
12
13
14
15
16
17
18
19
20
n+=2 α=0.05
2-5
2-5
2-5
2-5
2-5
2-5
2-5
2-5
2-5
2-5
α=0.01
0-5
0-5
0-5
0-5
0-5
0-5
0-5
0-5
2-5
2-5
n+=3 α=0.05
3-7
3-7
3-7
3-7
3-7
3-7
3-7
3-7
3-7
3-7
α=0.01
2-7
2-7
2-7
2-7
2-7
2-7
2-7
2-7
2-7
2-7
n+=4 α=0.05
3-9
4-9
4-9
4-9
4-9
4-9
4-9
4-9
4-9
4-9
α=0.01
2-9
3-9
3-9
3-9
3-9
3-9
3-9
3-9
3-9
3-9
n+=5 α=0.05 4-11
4-11
4-11
5-11
5-11
5-11
5-11
5-11
5-11
5-11
α=0.01 3-11
3-11
3-11
3-11
4 11
4-11
4-11
4-11
4-11
4-11
n+=6 α=0.05 5-12
5-12
5-12
5-12
6-13
6-13
6-13
6-13
6-13
6-13
α=0.01 4-13
4-13
4-13
4-13
4-13
4-13
5-13
5-13
5-13
5-13
n+=7 α=0.05 5-13
6-13
6-13
6-13
6-14
6-14
7-14
7-14
7-14
7-14
α=0.01 4-14
4-14
5-15
5-15
5-15
5-15
5-15
5-15
6-15
6-15
n+=8 α=0.05 6-14
6-14
6-14
7-15
7-15
7-15
7-15
8-15
8-15
8-16
α=0.01 4-15
5-15
5-16
5-16
5-16
6-16
6-17
6-17
6-17
6-17
n+=9 α=0.05 6-14
7-15
7-15
7-16
8-16
8-16
8-16
8-17
9-17
9-17
α=0.01 5-16
5-16
6-17
6-17
6-17
6-17
7-17
7-18
7-18
7-18
n+=10 α=0.05 7-15
7-16
8-16
8-16
8-17
8-17
9-17
9-18
9-18
9-18
α=0.01 5-17
6-17
6-18
6-18
7-18
7-19
7-19
7-19
8-19
8-19
ESTADÍSTICA II
34.
n-
11
12
13
14
15
16
17
18
19
20
n+=11 α=0.05 8-17
α=0.01 7-18
9-17
9-18
9-18
10-19
10-19
10-20
10-20
11-20
7-16
7-19
7-20
8-20
8-21
8-21
8-21
9-22
9-22
6-17
n+=12 α=0.05 9-17
8-16
8-17
8-17
9-18
9-18
9-18
10-19
10-19
10-19
α=0.01 7-19
6-18
6-18
7-19
7-19
7-20
8-20
8-20
8-21
8-21
n+=13 α=0.05 9-18
8-17
9-18
9-19
10-19
10-20
10-20
11-20
11-21
11-21
α=0.01 7-20
6-18
7-20
8-20
8-21
8-21
9-22
9-22
9-23
10-23
n+=14 α=0.05 9-18
8-17
9-19
10-19
10-20
11-20
11-21
11-21
12-22
12-22
α=0.01 8-20
7-19
8-20
8-21
8-22
9-22
9-23
9-23
10-23
10-24
n+=15 α=0.05 10-19
9-18
10-19
10-20
11-20
11-21
11-21
12-22
12-22
12-23
α=0.01 8-21
7-19
8-21
8-22
9-22
9-23
10-23
10-24
10-24
11-25
n+=16 α=0.05 10-19
9-18
10-20
11-20
11-21
11-22
12-22
12-22
12-23
12-23
α=0.01 8-21
7-20
8-21
9-22
9-23
10-23
10-24
10-24
10-25
10-25
n+=17 α=0.05 10-20
9-18
10-20
11-21
11-21
12-22
12-23
13-23
13-24
13-24
α=0.01 8-21
8-20
9-22
9-23
10-23
10-24
10-25
11-25
11-26
11-26
n+=18 α=0.05 10-20
10-19
11-20
11-21
12-22
12-22
13-23
13-24
14-25
14-25
α=0.01 9-22
8-20
9-22
9-23
10-24
10-24
11-25
11-26
12-26
12-27
n+=19 α=0.05 11-20
10-19
11-21
10-19
12-22
12-23
13-24
14-25
14-25
14-26
α=0.01 9-22
8-21
9-23
10-23
10-24
10-25
11-26
12-26
12-27
12-28
n+=20 α=0.05 7-16
10-19
11-21
12-22
12-23
12-23
13-24
14-25
14-26
15-26
α=0.01 6-17
8-21
10-23
10-24
11-25
10-25
11-26
12-27
12-28
13-28
35
TABLAS ESTADÍSTICAS.
Tabla 12
Prueba de Kolmogorov-Smirnov para dos muestras del mismo
tamaño
n
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
0.80
2
3
3
3
4
4
4
4
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
7
8
8
8
8
8
8
8
8
9
9
9
9
9
0.90
2
3
3
4
4
4
5
5
5
5
6
6
6
6
7
7
7
7
7
8
8
8
8
8
8
9
9
9
9
9
9
10
10
10
10
10
10
10
1 -α
0.95
0.98
0..99
3
4
4
5
5
5
6
6
6
6
7
7
7
7
8
8
8
8
8
9
9
9
9
9
10
10
10
10
10
10
11
11
11
11
11
12
12
4
5
5
5
6
6
7
7
7
7
8
8
8
9
9
9
9
10
10
10
10
10
11
11
11
11
11
12
12
12
12
12
Í2
13
13
13
4
5
5
6
6
7
7
7
8
8
8
9
9
9
9
10
10
10
10
11
11
11
11
11
12
12
12
12
12
13
13
13
13
14
14
14
ESTADÍSTICA II
36.
1 -α
n
n > 40
0.80
0.90
1.52
0.95
1.73
n
0.98
1.92
n
0..99
2 .15
n
2 .30
n
n
37
TABLAS ESTADÍSTICAS.
Tabla 13
Prueba de Kolmogorov-Smirnov para dos muestras de distinto
tamaño
1 -α
n1 n2
1 9
10
2 3
4
5
6
7
8
9
10
3 4
5
6
7
8
9
10
12
4 5
6
7
8
9
10
12
16
5 6
7
8
9
10
15
20
6 7
8
9
0.80
17/18
9/10
5/6
3/4
4/5
5/6
5/7
3/4
7/9
7/10
3/4
2/3
2/3
2/3
5/8
2/3
3/5
7/12
3/5
7/12
17/28
5/8
5/9
11/20
7/12
9/16
1/5
4/7
11/20
5/9
1/2
8/15
1/2
23/42
1/2
1/2
0.90
4/5
5/6
6/7
7/8
8/9
4/5
3/4
4/5
2/3
5/7
3/4
2/3
7/10
2/3
1/4
2/3
5/7
5/8
2/3
13/20
2/3
5/8
2/3
23/25
5/8
3/5
3/5
3/5
11/20
4/7
7/12
5/9
0.95
0.98
0.99
7/8
8/9
9/10
4/5
5/6
6/7
3/4
7/9
4/5
3/4
4/5
3/4
1/4
3/4
3/4
7/10
2/3
Í1/16
2/3
5/7
27/40
31/45
7/10
2/3
3/5
29/42
2/3
2/3
6/7
7/8
8/9
9/10
5/6
4/5
5/6
6/7
7/8
7/9
4/5
1/4
1/4
5/6
29/15
4/5
7/9
7/10
11/15
7/10
5/7
3/4
13/18
8/9
9/10
11/12
5/6
6/7
7/8
8/9
4/5
5/6
13/16
5/6
6/7
4/5
4/5
4/5
11/15
3/4
5/6
3/4
7/9
ESTADÍSTICA II
38.
1 -α
n1 n2
6 7
8
9
10
12
18
24
7 8
9
10
14
28
8 8
10
12
16
32
0.80
23/42
1/2
1/2
1/2
1/2
4/9
11/24
27/56
31/63
13/70
3/7
3/7
4/9
19/40
11/24
7/16
13/32
0.90
4/7
7/12
5/9
17/30
7/12
5/9
1/2
33/56
5/9
39/70
1/2
13/28
13/24
21/40
1/2
1/2
7/16
0.95
29/42
2/3
2/3
19/10
7/12
11/18
7/12
5/8
40/63
43/70
4/7
15/28
5/8
21/40
7/12
9/16
1/2
0.98
5/7
3/4
13/18
7/10
2/3
2/3
5/8
41/56
5/7
7/10
9/14
17/28
2/3
27/40
5/8
5/8
9/16
0.99
5/6
3/4
7/9
11/45
3/4
13/18
2/3
3/4
47/63
5/7
5/7
9/14
3/4
7/10
2/3
5/8
19/32
9 10
7/15
1/2
12
4/9
1/2
26/45
2/3
31/45
5/9
11/18
15
19/45
2/3
22/45
8/15
3/5
29/45
18
7/18
4/9
1/2
5/9
11/18
36
13/36
5/12
17/36
19/36
5/9
2/5
7/15
1/2
17/30
19/30
20
2/5
9/20
1/2
11/20
3/5
40
7/20
2/5
9/20
1/2
12 15
10 15
23/60
9/20
1/2
11/20
7/12
16
3/8
7/16
23/48
13/24
7/12
18
13/36
5/12
17/36
19/36
5/9
20
11/30
5/12
7/15
31/60
17/30
15 20
7/20
2/5
13/30
29/60
31/60
16 20
27/80
31/80
17/40
19/40
41/80
1.07
n1 + n2
n + n2
n + n2
n + n2
n + n2
1.22 1
1.36 1
1.48 1
1.63 1
n1 ·n2
n1 ·n 2
n1 ·n 2
n1 ·n 2
n1 ·n2