Tablas De Distribucion Normal Estandar nf50
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Tabla 1: Función de Distribución Normal Estándar 0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
-3.0
0.001350 0.001306 0.001264 0.001223 0.001183 0.001144 0.001107 0.001070 0.001035 0.001001
-2.9
0.001866 0.001807 0.001750 0.001695 0.001641 0.001589 0.001538 0.001489 0.001441 0.001395
-2.8
0.002555 0.002477 0.002401 0.002327 0.002256 0.002186 0.002118 0.002052 0.001988 0.001926
-2.7
0.003467 0.003364 0.003264 0.003167 0.003072 0.002980 0.002890 0.002803 0.002718 0.002635
-2.6
0.004661 0.004527 0.004396 0.004269 0.004145 0.004025 0.003907 0.003793 0.003681 0.003573
-2.5
0.006210 0.006037 0.005868 0.005703 0.005543 0.005386 0.005234 0.005085 0.004940 0.004799
-2.4
0.008198 0.007976 0.007760 0.007549 0.007344 0.007143 0.006947 0.006756 0.006569 0.006387
-2.3
0.010724 0.010444 0.010170 0.009903 0.009642 0.009387 0.009137 0.008894 0.008656 0.008424
-2.2
0.013903 0.013553 0.013209 0.012874 0.012545 0.012224 0.011911 0.011604 0.011304 0.011011
-2.1
0.017864 0.017429 0.017003 0.016586 0.016177 0.015778 0.015386 0.015003 0.014629 0.014262
-2.0
0.022750 0.022216 0.021692 0.021178 0.020675 0.020182 0.019699 0.019226 0.018763 0.018309
-1.9
0.028717 0.028067 0.027429 0.026803 0.026190 0.025588 0.024998 0.024419 0.023852 0.023295
-1.8
0.035930 0.035148 0.034380 0.033625 0.032884 0.032157 0.031443 0.030742 0.030054 0.029379
-1.7
0.044565 0.043633 0.042716 0.041815 0.040930 0.040059 0.039204 0.038364 0.037538 0.036727
-1.6
0.054799 0.053699 0.052616 0.051551 0.050503 0.049471 0.048457 0.047460 0.046479 0.045514
-1.5
0.066807 0.065522 0.064255 0.063008 0.061780 0.060571 0.059380 0.058208 0.057053 0.055917
-1.4
0.080757 0.079270 0.077804 0.076359 0.074934 0.073529 0.072145 0.070781 0.069437 0.068112
-1.3
0.096800 0.095098 0.093418 0.091759 0.090123 0.088508 0.086915 0.085343 0.083793 0.082264
-1.2
0.115070 0.113139 0.111232 0.109349 0.107488 0.105650 0.103835 0.102042 0.100273 0.098525
-1.1
0.135666 0.133500 0.131357 0.129238 0.127143 0.125072 0.123024 0.121000 0.119000 0.117023
-1.0
0.158655 0.156248 0.153864 0.151505 0.149170 0.146859 0.144572 0.142310 0.140071 0.137857
-0.9
0.184060 0.181411 0.178786 0.176186 0.173609 0.171056 0.168528 0.166023 0.163543 0.161087
-0.8
0.211855 0.208970 0.206108 0.203269 0.200454 0.197663 0.194895 0.192150 0.189430 0.186733
-0.7
0.241964 0.238852 0.235762 0.232695 0.229650 0.226627 0.223627 0.220650 0.217695 0.214764
-0.6
0.274253 0.270931 0.267629 0.264347 0.261086 0.257846 0.254627 0.251429 0.248252 0.245097
-0.5
0.308538 0.305026 0.301532 0.298056 0.294599 0.291160 0.287740 0.284339 0.280957 0.277595
-0.4
0.344578 0.340903 0.337243 0.333598 0.329969 0.326355 0.322758 0.319178 0.315614 0.312067
-0.3
0.382089 0.378280 0.374484 0.370700 0.366928 0.363169 0.359424 0.355691 0.351973 0.348268
-0.2
0.420740 0.416834 0.412936 0.409046 0.405165 0.401294 0.397432 0.393580 0.389739 0.385908
-0.1
0.460172 0.456205 0.452242 0.448283 0.444330 0.440382 0.436441 0.432505 0.428576 0.424655
-0.0
0.500000 0.496011 0.492022 0.488034 0.484047 0.480061 0.476078 0.472097 0.468119 0.464144
0.0
0.500000 0.503989 0.507978 0.511966 0.515953 0.519939 0.523922 0.527903 0.531881 0.535856
0.1
0.539828 0.543795 0.547758 0.551717 0.555670 0.559618 0.563559 0.567495 0.571424 0.575345
0.2
0.579260 0.583166 0.587064 0.590954 0.594835 0.598706 0.602568 0.606420 0.610261 0.614092
0.3
0.617911 0.621720 0.625516 0.629300 0.633072 0.636831 0.640576 0.644309 0.648027 0.651732
0.4
0.655422 0.659097 0.662757 0.666402 0.670031 0.673645 0.677242 0.680822 0.684386 0.687933
0.5
0.691462 0.694974 0.698468 0.701944 0.705401 0.708840 0.712260 0.715661 0.719043 0.722405
0.6
0.725747 0.729069 0.732371 0.735653 0.738914 0.742154 0.745373 0.748571 0.751748 0.754903
0.7
0.758036 0.761148 0.764238 0.767305 0.770350 0.773373 0.776373 0.779350 0.782305 0.785236
0.8
0.788145 0.791030 0.793892 0.796731 0.799546 0.802337 0.805105 0.807850 0.810570 0.813267
0.9
0.815940 0.818589 0.821214 0.823814 0.826391 0.828944 0.831472 0.833977 0.836457 0.838913
1.0
0.841345 0.843752 0.846136 0.848495 0.850830 0.853141 0.855428 0.857690 0.859929 0.862143
1.1
0.864334 0.866500 0.868643 0.870762 0.872857 0.874928 0.876976 0.879000 0.881000 0.882977
1.2
0.884930 0.886861 0.888768 0.890651 0.892512 0.894350 0.896165 0.897958 0.899727 0.901475
1.3
0.903200 0.904902 0.906582 0.908241 0.909877 0.911492 0.913085 0.914657 0.916207 0.917736
1.4
0.919243 0.920730 0.922196 0.923641 0.925066 0.926471 0.927855 0.929219 0.930563 0.931888
1.5
0.933193 0.934478 0.935745 0.936992 0.938220 0.939429 0.940620 0.941792 0.942947 0.944083
1.6
0.945201 0.946301 0.947384 0.948449 0.949497 0.950529 0.951543 0.952540 0.953521 0.954486
1.7
0.955435 0.956367 0.957284 0.958185 0.959070 0.959941 0.960796 0.961636 0.962462 0.963273
1.8
0.964070 0.964852 0.965620 0.966375 0.967116 0.967843 0.968557 0.969258 0.969946 0.970621
i
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
1.9
0.971283 0.971933 0.972571 0.973197 0.973810 0.974412 0.975002 0.975581 0.976148 0.976705
2.0
0.977250 0.977784 0.978308 0.978822 0.979325 0.979818 0.980301 0.980774 0.981237 0.981691
2.1
0.982136 0.982571 0.982997 0.983414 0.983823 0.984222 0.984614 0.984997 0.985371 0.985738
2.2
0.986097 0.986447 0.986791 0.987126 0.987455 0.987776 0.988089 0.988396 0.988696 0.988989
2.3
0.989276 0.989556 0.989830 0.990097 0.990358 0.990613 0.990863 0.991106 0.991344 0.991576
2.4
0.991802 0.992024 0.992240 0.992451 0.992656 0.992857 0.993053 0.993244 0.993431 0.993613
2.5
0.993790 0.993963 0.994132 0.994297 0.994457 0.994614 0.994766 0.994915 0.995060 0.995201
2.6
0.995339 0.995473 0.995604 0.995731 0.995855 0.995975 0.996093 0.996207 0.996319 0.996427
2.7
0.996533 0.996636 0.996736 0.996833 0.996928 0.997020 0.997110 0.997197 0.997282 0.997365
2.8
0.997445 0.997523 0.997599 0.997673 0.997744 0.997814 0.997882 0.997948 0.998012 0.998074
2.9
0.998134 0.998193 0.998250 0.998305 0.998359 0.998411 0.998462 0.998511 0.998559 0.998605
3.0
0.998650 0.998694 0.998736 0.998777 0.998817 0.998856 0.998893 0.998930 0.998965 0.998999
Ejemplos: Si X ∼ N(0,1), entonces Pr(X ≤ −1.96) = 0.024998 y Pr(X ≤ 2.00) = 0.977250. Fuente: Tabla construida utilizando la función @cnorm de EViews® 3.1.
ii
Tabla 2: Valores Críticos de la Distribución t de Student. FUNCION DE DISTRIBUCION 0.005
0.010
0.025
0.050
1
-63.657
-31.821
-12.706
-6.314
2
-9.925
-6.965
-4.303
-2.920
3
-5.841
-4.541
-3.182
-2.353
4
-4.604
-3.747
-2.776
5
-4.032
-3.365
6
-3.707
7
-3.499
8 9
0.100
0.900
0.950
0.975
0.990
0.995
-3.078
3.078
6.314
12.706
31.821
63.657
-1.886
1.886
2.920
4.303
6.965
9.925
-1.638
1.638
2.353
3.182
4.541
5.841
-2.132
-1.533
1.533
2.132
2.776
3.747
4.604
-2.571
-2.015
-1.476
1.476
2.015
2.571
3.365
4.032
-3.143
-2.447
-1.943
-1.440
1.440
1.943
2.447
3.143
3.707
-2.998
-2.365
-1.895
-1.415
1.415
1.895
2.365
2.998
3.499
-3.355
-2.896
-2.306
-1.860
-1.397
1.397
1.860
2.306
2.896
3.355
-3.250
-2.821
-2.262
-1.833
-1.383
1.383
1.833
2.262
2.821
3.250
10
-3.169
-2.764
-2.228
-1.812
-1.372
1.372
1.812
2.228
2.764
3.169
G
11
-3.106
-2.718
-2.201
-1.796
-1.363
1.363
1.796
2.201
2.718
3.106
R
12
-3.055
-2.681
-2.179
-1.782
-1.356
1.356
1.782
2.179
2.681
3.055
A
13
-3.012
-2.650
-2.160
-1.771
-1.350
1.350
1.771
2.160
2.650
3.012
D
14
-2.977
-2.624
-2.145
-1.761
-1.345
1.345
1.761
2.145
2.624
2.977
O
15
-2.947
-2.602
-2.131
-1.753
-1.341
1.341
1.753
2.131
2.602
2.947
S 16
-2.921
-2.583
-2.120
-1.746
-1.337
1.337
1.746
2.120
2.583
2.921
D
17
-2.898
-2.567
-2.110
-1.740
-1.333
1.333
1.740
2.110
2.567
2.898
E
18
-2.878
-2.552
-2.101
-1.734
-1.330
1.330
1.734
2.101
2.552
2.878
19
-2.861
-2.539
-2.093
-1.729
-1.328
1.328
1.729
2.093
2.539
2.861
L
20
-2.845
-2.528
-2.086
-1.725
-1.325
1.325
1.725
2.086
2.528
2.845
B
21
-2.831
-2.518
-2.080
-1.721
-1.323
1.323
1.721
2.080
2.518
2.831
E
22
-2.819
-2.508
-2.074
-1.717
-1.321
1.321
1.717
2.074
2.508
2.819
R
23
-2.807
-2.500
-2.069
-1.714
-1.319
1.319
1.714
2.069
2.500
2.807
T
24
-2.797
-2.492
-2.064
-1.711
-1.318
1.318
1.711
2.064
2.492
2.797
A
25
-2.787
-2.485
-2.060
-1.708
-1.316
1.316
1.708
2.060
2.485
2.787
26
-2.779
-2.479
-2.056
-1.706
-1.315
1.315
1.706
2.056
2.479
2.779
27
-2.771
-2.473
-2.052
-1.703
-1.314
1.314
1.703
2.052
2.473
2.771
28
-2.763
-2.467
-2.048
-1.701
-1.313
1.313
1.701
2.048
2.467
2.763
29
-2.756
-2.462
-2.045
-1.699
-1.311
1.311
1.699
2.045
2.462
2.756
30
-2.750
-2.457
-2.042
-1.697
-1.310
1.310
1.697
2.042
2.457
2.750
40
-2.704
-2.423
-2.021
-1.684
-1.303
1.303
1.684
2.021
2.423
2.704
I
D
60
-2.660
-2.390
-2.000
-1.671
-1.296
1.296
1.671
2.000
2.390
2.660
90
-2.632
-2.368
-1.987
-1.662
-1.291
1.291
1.662
1.987
2.368
2.632
120
-2.617
-2.358
-1.980
-1.658
-1.289
1.289
1.658
1.980
2.358
2.617
INF
-2.576
-2.327
-1.960
-1.645
-1.282
1.282
1.645
1.960
2.327
2.576
Ejemplos: Si X ∼ t(20), entonces Pr(X ≤ −2.528) = 0.01 y Pr(X ≤ 1.725) = 0.95; si X ∼ t(n) con n suficientemente grande, entonces Pr(X ≤ −1.960) ≈ 0.025 y Pr(X ≤ 2.327) ≈ 0.99. Fuente: Tabla construida utilizando la función @qtdist de EViews® 3.1.
iii
Tabla 3: Valores Críticos de la Distribución Chi-Cuadrado. FUNCION DE DISTRIBUCION 0.005
0.010
0.025
0.050
0.100
0.900
0.950
0.975
0.990
0.995
1
0.000039 0.000157 0.000982 0.003932 0.0158
2.71
3.84
5.02
6.63
7.88
2
0.0100
0.0201
0.0506
0.10
0.21
4.61
5.99
7.38
9.21
10.60
3
0.0717
0.11
0.22
0.35
0.58
6.25
7.81
9.35
11.34
12.84
4
0.21
0.30
0.48
0.71
1.06
7.78
9.49
11.14
13.28
14.86
5
0.41
0.55
0.83
1.15
1.61
9.24
11.07
12.83
15.09
16.75
6
0.68
0.87
1.24
1.64
2.20
10.64
12.59
14.45
16.81
18.55
7
0.99
1.24
1.69
2.17
2.83
12.02
14.07
16.01
18.48
20.28
8
1.34
1.65
2.18
2.73
3.49
13.36
15.51
17.53
20.09
21.95
R
9
1.73
2.09
2.70
3.33
4.17
14.68
16.92
19.02
21.67
23.59
A
10
2.16
2.56
3.25
3.94
4.87
15.99
18.31
20.48
23.21
25.19
O
11
2.60
3.05
3.82
4.57
5.58
17.28
19.68
21.92
24.72
26.76
S
12
3.07
3.57
4.40
5.23
6.30
18.55
21.03
23.34
26.22
28.30
13
3.57
4.11
5.01
5.89
7.04
19.81
22.36
24.74
27.69
29.82
D
14
4.07
4.66
5.63
6.57
7.79
21.06
23.68
26.12
29.14
31.32
E
15
4.60
5.23
6.26
7.26
8.55
22.31
25.00
27.49
30.58
32.80
G
D
16
5.14
5.81
6.91
7.96
9.31
23.54
26.30
28.85
32.00
34.27
L
17
5.70
6.41
7.56
8.67
10.09
24.77
27.59
30.19
33.41
35.72
I
18
6.26
7.01
8.23
9.39
10.86
25.99
28.87
31.53
34.81
37.16
B
19
6.84
7.63
8.91
10.12
11.65
27.20
30.14
32.85
36.19
38.58
E
20
7.43
8.26
9.59
10.85
12.44
28.41
31.41
34.17
37.57
40.00
T
21
8.03
8.90
10.28
11.59
13.24
29.62
32.67
35.48
38.93
41.40
A
22
8.64
9.54
10.98
12.34
14.04
30.81
33.92
36.78
40.29
42.80
D
23
9.26
10.20
11.69
13.09
14.85
32.01
35.17
38.08
41.64
44.18
24
9.89
10.86
12.40
13.85
15.66
33.20
36.42
39.36
42.98
45.56
25
10.52
11.52
13.12
14.61
16.47
34.38
37.65
40.65
44.31
46.93
26
11.16
12.20
13.84
15.38
17.29
35.56
38.89
41.92
45.64
48.29
27
11.81
12.88
14.57
16.15
18.11
36.74
40.11
43.19
46.96
49.64
28
12.46
13.56
15.31
16.93
18.94
37.92
41.34
44.46
48.28
50.99
29
13.12
14.26
16.05
17.71
19.77
39.09
42.56
45.72
49.59
52.34
30
13.79
14.95
16.79
18.49
20.60
40.26
43.77
46.98
50.89
53.67
R
2
Ejemplos: Si X ∼ χ (20), entonces Pr(X ≤ 9.59) = 0.025 y Pr(X ≤ 34.17) = 0.975. Fuente: Tabla construida utilizando la función @qchisq de EViews® 3.1.
iv
Tabla 4-1: Valores Críticos de la Distribución F - Función de Distribución = 0.90. GRADOS DE LIBERTAD DEL NUMERADOR 1
2
3
4
5
6
7
8
9
10
1
39.86
49.50
53.59
55.83
57.24
58.20
58.91
59.44
59.86
60.19
2
8.53
9.00
9.16
9.24
9.29
9.33
9.35
9.37
9.38
9.39
3
5.54
5.46
5.39
5.34
5.31
5.28
5.27
5.25
5.24
5.23
G
4
4.54
4.32
4.19
4.11
4.05
4.01
3.98
3.95
3.94
3.92
R
5
4.06
3.78
3.62
3.52
3.45
3.40
3.37
3.34
3.32
3.30
D
6
3.78
3.46
3.29
3.18
3.11
3.05
3.01
2.98
2.96
2.94
O
7
3.59
3.26
3.07
2.96
2.88
2.83
2.78
2.75
2.72
2.70
S
8
3.46
3.11
2.92
2.81
2.73
2.67
2.62
2.59
2.56
2.54
9
3.36
3.01
2.81
2.69
2.61
2.55
2.51
2.47
2.44
2.42
10
3.29
2.92
2.73
2.61
2.52
2.46
2.41
2.38
2.35
2.32
A
D E
11
3.23
2.86
2.66
2.54
2.45
2.39
2.34
2.30
2.27
2.25
L
12
3.18
2.81
2.61
2.48
2.39
2.33
2.28
2.24
2.21
2.19
I
13
3.14
2.76
2.56
2.43
2.35
2.28
2.23
2.20
2.16
2.14
B
14
3.10
2.73
2.52
2.39
2.31
2.24
2.19
2.15
2.12
2.10
E
15
3.07
2.70
2.49
2.36
2.27
2.21
2.16
2.12
2.09
2.06
T
16
3.05
2.67
2.46
2.33
2.24
2.18
2.13
2.09
2.06
2.03
A
17
3.03
2.64
2.44
2.31
2.22
2.15
2.10
2.06
2.03
2.00
D
18
3.01
2.62
2.42
2.29
2.20
2.13
2.08
2.04
2.00
1.98
19
2.99
2.61
2.40
2.27
2.18
2.11
2.06
2.02
1.98
1.96
20
2.97
2.59
2.38
2.25
2.16
2.09
2.04
2.00
1.96
1.94
21
2.96
2.57
2.36
2.23
2.14
2.08
2.02
1.98
1.95
1.92
R
D E L
22
2.95
2.56
2.35
2.22
2.13
2.06
2.01
1.97
1.93
1.90
D
23
2.94
2.55
2.34
2.21
2.11
2.05
1.99
1.95
1.92
1.89
E
24
2.93
2.54
2.33
2.19
2.10
2.04
1.98
1.94
1.91
1.88
N
25
2.92
2.53
2.32
2.18
2.09
2.02
1.97
1.93
1.89
1.87
M
26
2.91
2.52
2.31
2.17
2.08
2.01
1.96
1.92
1.88
1.86
I
27
2.90
2.51
2.30
2.17
2.07
2.00
1.95
1.91
1.87
1.85
N
28
2.89
2.50
2.29
2.16
2.06
2.00
1.94
1.90
1.87
1.84
A
29
2.89
2.50
2.28
2.15
2.06
1.99
1.93
1.89
1.86
1.83
D
30
2.88
2.49
2.28
2.14
2.05
1.98
1.93
1.88
1.85
1.82
40
2.84
2.44
2.23
2.09
2.00
1.93
1.87
1.83
1.79
1.76
60
2.79
2.39
2.18
2.04
1.95
1.87
1.82
1.77
1.74
1.71
90
2.76
2.36
2.15
2.01
1.91
1.84
1.78
1.74
1.70
1.67
120
2.75
2.35
2.13
1.99
1.90
1.82
1.77
1.72
1.68
1.65
INF
2.71
2.30
2.08
1.95
1.85
1.77
1.72
1.67
1.63
1.60
O
O R
Ejemplos: Si X ∼ F(2,20), Pr(X ≤ 2.59) = 0.90; si X ∼ F(3,n) con n suficientemente grande, Pr(X ≤ 2.08) ≈ 0.90. Fuente: Tabla construida utilizando la función @qfdist de EViews® 3.1.
v
Tabla 4-2: Valores Críticos de la Distribución F - Función de Distribución = 0.95. GRADOS DE LIBERTAD DEL NUMERADOR 1 1
2
3
4
5
6
7
8
9
10
161.45 199.50 215.71 224.58 230.16 233.99 236.77 238.88 240.54 241.88
2
18.51
19.00
19.16
19.25
19.30
19.33
19.35
19.37
19.38
19.40
3
10.13
9.55
9.28
9.12
9.01
8.94
8.89
8.85
8.81
8.79
G
4
7.71
6.94
6.59
6.39
6.26
6.16
6.09
6.04
6.00
5.96
R
5
6.61
5.79
5.41
5.19
5.05
4.95
4.88
4.82
4.77
4.74
D
6
5.99
5.14
4.76
4.53
4.39
4.28
4.21
4.15
4.10
4.06
O
7
5.59
4.74
4.35
4.12
3.97
3.87
3.79
3.73
3.68
3.64
S
8
5.32
4.46
4.07
3.84
3.69
3.58
3.50
3.44
3.39
3.35
9
5.12
4.26
3.86
3.63
3.48
3.37
3.29
3.23
3.18
3.14
10
4.96
4.10
3.71
3.48
3.33
3.22
3.14
3.07
3.02
2.98
A
D E
11
4.84
3.98
3.59
3.36
3.20
3.09
3.01
2.95
2.90
2.85
L
12
4.75
3.89
3.49
3.26
3.11
3.00
2.91
2.85
2.80
2.75
I
13
4.67
3.81
3.41
3.18
3.03
2.92
2.83
2.77
2.71
2.67
B
14
4.60
3.74
3.34
3.11
2.96
2.85
2.76
2.70
2.65
2.60
E
15
4.54
3.68
3.29
3.06
2.90
2.79
2.71
2.64
2.59
2.54
T
16
4.49
3.63
3.24
3.01
2.85
2.74
2.66
2.59
2.54
2.49
A
17
4.45
3.59
3.20
2.96
2.81
2.70
2.61
2.55
2.49
2.45
D
18
4.41
3.55
3.16
2.93
2.77
2.66
2.58
2.51
2.46
2.41
19
4.38
3.52
3.13
2.90
2.74
2.63
2.54
2.48
2.42
2.38
20
4.35
3.49
3.10
2.87
2.71
2.60
2.51
2.45
2.39
2.35
21
4.32
3.47
3.07
2.84
2.68
2.57
2.49
2.42
2.37
2.32
R
D E L
22
4.30
3.44
3.05
2.82
2.66
2.55
2.46
2.40
2.34
2.30
D
23
4.28
3.42
3.03
2.80
2.64
2.53
2.44
2.37
2.32
2.27
E
24
4.26
3.40
3.01
2.78
2.62
2.51
2.42
2.36
2.30
2.25
N
25
4.24
3.39
2.99
2.76
2.60
2.49
2.40
2.34
2.28
2.24
M
26
4.23
3.37
2.98
2.74
2.59
2.47
2.39
2.32
2.27
2.22
I
27
4.21
3.35
2.96
2.73
2.57
2.46
2.37
2.31
2.25
2.20
N
28
4.20
3.34
2.95
2.71
2.56
2.45
2.36
2.29
2.24
2.19
A
29
4.18
3.33
2.93
2.70
2.55
2.43
2.35
2.28
2.22
2.18
D
30
4.17
3.32
2.92
2.69
2.53
2.42
2.33
2.27
2.21
2.16
40
4.08
3.23
2.84
2.61
2.45
2.34
2.25
2.18
2.12
2.08
60
4.00
3.15
2.76
2.53
2.37
2.25
2.17
2.10
2.04
1.99
90
3.95
3.10
2.71
2.47
2.32
2.20
2.11
2.04
1.99
1.94
120
3.92
3.07
2.68
2.45
2.29
2.18
2.09
2.02
1.96
1.91
INF
3.84
3.00
2.61
2.37
2.21
2.10
2.01
1.94
1.88
1.83
O
O R
Ejemplos: Si X ∼ F(2,20), Pr(X ≤ 3.49) = 0.95; si X ∼ F(3,n) con n suficientemente grande, Pr(X ≤ 2.61) ≈ 0.95. Fuente: Tabla construida utilizando la función @qfdist de EViews® 3.1.
vi
Tabla 4-3: Valores Críticos de la Distribución F - Función de Distribución = 0.99. GRADOS DE LIBERTAD DEL NUMERADOR 1
2
3
4
5
6
7
8
9
10
1
4052
5000
5403
5625
5764
5859
5928
5981
6022
6056
2
98.50
99.00
99.17
99.25
99.30
99.33
99.36
99.37
99.39
99.40
3
34.12
30.82
29.46
28.71
28.24
27.91
27.67
27.49
27.35
27.23
G
4
21.20
18.00
16.69
15.98
15.52
15.21
14.98
14.80
14.66
14.55
R
5
16.26
13.27
12.06
11.39
10.97
10.67
10.46
10.29
10.16
10.05
D
6
13.75
10.92
9.78
9.15
8.75
8.47
8.26
8.10
7.98
7.87
O
7
12.25
9.55
8.45
7.85
7.46
7.19
6.99
6.84
6.72
6.62
S
8
11.26
8.65
7.59
7.01
6.63
6.37
6.18
6.03
5.91
5.81
9
10.56
8.02
6.99
6.42
6.06
5.80
5.61
5.47
5.35
5.26
10
10.04
7.56
6.55
5.99
5.64
5.39
5.20
5.06
4.94
4.85
A
D E
11
9.65
7.21
6.22
5.67
5.32
5.07
4.89
4.74
4.63
4.54
L
12
9.33
6.93
5.95
5.41
5.06
4.82
4.64
4.50
4.39
4.30
I
13
9.07
6.70
5.74
5.21
4.86
4.62
4.44
4.30
4.19
4.10
B
14
8.86
6.51
5.56
5.04
4.69
4.46
4.28
4.14
4.03
3.94
E
15
8.68
6.36
5.42
4.89
4.56
4.32
4.14
4.00
3.89
3.80
T
16
8.53
6.23
5.29
4.77
4.44
4.20
4.03
3.89
3.78
3.69
A
17
8.40
6.11
5.18
4.67
4.34
4.10
3.93
3.79
3.68
3.59
D
18
8.29
6.01
5.09
4.58
4.25
4.01
3.84
3.71
3.60
3.51
19
8.18
5.93
5.01
4.50
4.17
3.94
3.77
3.63
3.52
3.43
20
8.10
5.85
4.94
4.43
4.10
3.87
3.70
3.56
3.46
3.37
21
8.02
5.78
4.87
4.37
4.04
3.81
3.64
3.51
3.40
3.31
R
D E L
22
7.95
5.72
4.82
4.31
3.99
3.76
3.59
3.45
3.35
3.26
D
23
7.88
5.66
4.76
4.26
3.94
3.71
3.54
3.41
3.30
3.21
E
24
7.82
5.61
4.72
4.22
3.90
3.67
3.50
3.36
3.26
3.17
N
25
7.77
5.57
4.68
4.18
3.85
3.63
3.46
3.32
3.22
3.13
M
26
7.72
5.53
4.64
4.14
3.82
3.59
3.42
3.29
3.18
3.09
I
27
7.68
5.49
4.60
4.11
3.78
3.56
3.39
3.26
3.15
3.06
N
28
7.64
5.45
4.57
4.07
3.75
3.53
3.36
3.23
3.12
3.03
A
29
7.60
5.42
4.54
4.04
3.73
3.50
3.33
3.20
3.09
3.00
D
30
7.56
5.39
4.51
4.02
3.70
3.47
3.30
3.17
3.07
2.98
40
7.31
5.18
4.31
3.83
3.51
3.29
3.12
2.99
2.89
2.80
60
7.08
4.98
4.13
3.65
3.34
3.12
2.95
2.82
2.72
2.63
90
6.93
4.85
4.01
3.53
3.23
3.01
2.84
2.72
2.61
2.52
120
6.85
4.79
3.95
3.48
3.17
2.96
2.79
2.66
2.56
2.47
INF
6.64
4.61
3.78
3.32
3.02
2.80
2.64
2.51
2.41
2.32
O
O R
Ejemplos: Si X ∼ F(2,20), Pr(X ≤ 5.85) = 0.99; si X ∼ F(3,n) con n suficientemente grande, Pr(X ≤ 3.78) ≈ 0.99. Fuente: Tabla construida utilizando la función @qfdist de EViews® 3.1.
vii
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
-3.0
0.001350 0.001306 0.001264 0.001223 0.001183 0.001144 0.001107 0.001070 0.001035 0.001001
-2.9
0.001866 0.001807 0.001750 0.001695 0.001641 0.001589 0.001538 0.001489 0.001441 0.001395
-2.8
0.002555 0.002477 0.002401 0.002327 0.002256 0.002186 0.002118 0.002052 0.001988 0.001926
-2.7
0.003467 0.003364 0.003264 0.003167 0.003072 0.002980 0.002890 0.002803 0.002718 0.002635
-2.6
0.004661 0.004527 0.004396 0.004269 0.004145 0.004025 0.003907 0.003793 0.003681 0.003573
-2.5
0.006210 0.006037 0.005868 0.005703 0.005543 0.005386 0.005234 0.005085 0.004940 0.004799
-2.4
0.008198 0.007976 0.007760 0.007549 0.007344 0.007143 0.006947 0.006756 0.006569 0.006387
-2.3
0.010724 0.010444 0.010170 0.009903 0.009642 0.009387 0.009137 0.008894 0.008656 0.008424
-2.2
0.013903 0.013553 0.013209 0.012874 0.012545 0.012224 0.011911 0.011604 0.011304 0.011011
-2.1
0.017864 0.017429 0.017003 0.016586 0.016177 0.015778 0.015386 0.015003 0.014629 0.014262
-2.0
0.022750 0.022216 0.021692 0.021178 0.020675 0.020182 0.019699 0.019226 0.018763 0.018309
-1.9
0.028717 0.028067 0.027429 0.026803 0.026190 0.025588 0.024998 0.024419 0.023852 0.023295
-1.8
0.035930 0.035148 0.034380 0.033625 0.032884 0.032157 0.031443 0.030742 0.030054 0.029379
-1.7
0.044565 0.043633 0.042716 0.041815 0.040930 0.040059 0.039204 0.038364 0.037538 0.036727
-1.6
0.054799 0.053699 0.052616 0.051551 0.050503 0.049471 0.048457 0.047460 0.046479 0.045514
-1.5
0.066807 0.065522 0.064255 0.063008 0.061780 0.060571 0.059380 0.058208 0.057053 0.055917
-1.4
0.080757 0.079270 0.077804 0.076359 0.074934 0.073529 0.072145 0.070781 0.069437 0.068112
-1.3
0.096800 0.095098 0.093418 0.091759 0.090123 0.088508 0.086915 0.085343 0.083793 0.082264
-1.2
0.115070 0.113139 0.111232 0.109349 0.107488 0.105650 0.103835 0.102042 0.100273 0.098525
-1.1
0.135666 0.133500 0.131357 0.129238 0.127143 0.125072 0.123024 0.121000 0.119000 0.117023
-1.0
0.158655 0.156248 0.153864 0.151505 0.149170 0.146859 0.144572 0.142310 0.140071 0.137857
-0.9
0.184060 0.181411 0.178786 0.176186 0.173609 0.171056 0.168528 0.166023 0.163543 0.161087
-0.8
0.211855 0.208970 0.206108 0.203269 0.200454 0.197663 0.194895 0.192150 0.189430 0.186733
-0.7
0.241964 0.238852 0.235762 0.232695 0.229650 0.226627 0.223627 0.220650 0.217695 0.214764
-0.6
0.274253 0.270931 0.267629 0.264347 0.261086 0.257846 0.254627 0.251429 0.248252 0.245097
-0.5
0.308538 0.305026 0.301532 0.298056 0.294599 0.291160 0.287740 0.284339 0.280957 0.277595
-0.4
0.344578 0.340903 0.337243 0.333598 0.329969 0.326355 0.322758 0.319178 0.315614 0.312067
-0.3
0.382089 0.378280 0.374484 0.370700 0.366928 0.363169 0.359424 0.355691 0.351973 0.348268
-0.2
0.420740 0.416834 0.412936 0.409046 0.405165 0.401294 0.397432 0.393580 0.389739 0.385908
-0.1
0.460172 0.456205 0.452242 0.448283 0.444330 0.440382 0.436441 0.432505 0.428576 0.424655
-0.0
0.500000 0.496011 0.492022 0.488034 0.484047 0.480061 0.476078 0.472097 0.468119 0.464144
0.0
0.500000 0.503989 0.507978 0.511966 0.515953 0.519939 0.523922 0.527903 0.531881 0.535856
0.1
0.539828 0.543795 0.547758 0.551717 0.555670 0.559618 0.563559 0.567495 0.571424 0.575345
0.2
0.579260 0.583166 0.587064 0.590954 0.594835 0.598706 0.602568 0.606420 0.610261 0.614092
0.3
0.617911 0.621720 0.625516 0.629300 0.633072 0.636831 0.640576 0.644309 0.648027 0.651732
0.4
0.655422 0.659097 0.662757 0.666402 0.670031 0.673645 0.677242 0.680822 0.684386 0.687933
0.5
0.691462 0.694974 0.698468 0.701944 0.705401 0.708840 0.712260 0.715661 0.719043 0.722405
0.6
0.725747 0.729069 0.732371 0.735653 0.738914 0.742154 0.745373 0.748571 0.751748 0.754903
0.7
0.758036 0.761148 0.764238 0.767305 0.770350 0.773373 0.776373 0.779350 0.782305 0.785236
0.8
0.788145 0.791030 0.793892 0.796731 0.799546 0.802337 0.805105 0.807850 0.810570 0.813267
0.9
0.815940 0.818589 0.821214 0.823814 0.826391 0.828944 0.831472 0.833977 0.836457 0.838913
1.0
0.841345 0.843752 0.846136 0.848495 0.850830 0.853141 0.855428 0.857690 0.859929 0.862143
1.1
0.864334 0.866500 0.868643 0.870762 0.872857 0.874928 0.876976 0.879000 0.881000 0.882977
1.2
0.884930 0.886861 0.888768 0.890651 0.892512 0.894350 0.896165 0.897958 0.899727 0.901475
1.3
0.903200 0.904902 0.906582 0.908241 0.909877 0.911492 0.913085 0.914657 0.916207 0.917736
1.4
0.919243 0.920730 0.922196 0.923641 0.925066 0.926471 0.927855 0.929219 0.930563 0.931888
1.5
0.933193 0.934478 0.935745 0.936992 0.938220 0.939429 0.940620 0.941792 0.942947 0.944083
1.6
0.945201 0.946301 0.947384 0.948449 0.949497 0.950529 0.951543 0.952540 0.953521 0.954486
1.7
0.955435 0.956367 0.957284 0.958185 0.959070 0.959941 0.960796 0.961636 0.962462 0.963273
1.8
0.964070 0.964852 0.965620 0.966375 0.967116 0.967843 0.968557 0.969258 0.969946 0.970621
i
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
1.9
0.971283 0.971933 0.972571 0.973197 0.973810 0.974412 0.975002 0.975581 0.976148 0.976705
2.0
0.977250 0.977784 0.978308 0.978822 0.979325 0.979818 0.980301 0.980774 0.981237 0.981691
2.1
0.982136 0.982571 0.982997 0.983414 0.983823 0.984222 0.984614 0.984997 0.985371 0.985738
2.2
0.986097 0.986447 0.986791 0.987126 0.987455 0.987776 0.988089 0.988396 0.988696 0.988989
2.3
0.989276 0.989556 0.989830 0.990097 0.990358 0.990613 0.990863 0.991106 0.991344 0.991576
2.4
0.991802 0.992024 0.992240 0.992451 0.992656 0.992857 0.993053 0.993244 0.993431 0.993613
2.5
0.993790 0.993963 0.994132 0.994297 0.994457 0.994614 0.994766 0.994915 0.995060 0.995201
2.6
0.995339 0.995473 0.995604 0.995731 0.995855 0.995975 0.996093 0.996207 0.996319 0.996427
2.7
0.996533 0.996636 0.996736 0.996833 0.996928 0.997020 0.997110 0.997197 0.997282 0.997365
2.8
0.997445 0.997523 0.997599 0.997673 0.997744 0.997814 0.997882 0.997948 0.998012 0.998074
2.9
0.998134 0.998193 0.998250 0.998305 0.998359 0.998411 0.998462 0.998511 0.998559 0.998605
3.0
0.998650 0.998694 0.998736 0.998777 0.998817 0.998856 0.998893 0.998930 0.998965 0.998999
Ejemplos: Si X ∼ N(0,1), entonces Pr(X ≤ −1.96) = 0.024998 y Pr(X ≤ 2.00) = 0.977250. Fuente: Tabla construida utilizando la función @cnorm de EViews® 3.1.
ii
Tabla 2: Valores Críticos de la Distribución t de Student. FUNCION DE DISTRIBUCION 0.005
0.010
0.025
0.050
1
-63.657
-31.821
-12.706
-6.314
2
-9.925
-6.965
-4.303
-2.920
3
-5.841
-4.541
-3.182
-2.353
4
-4.604
-3.747
-2.776
5
-4.032
-3.365
6
-3.707
7
-3.499
8 9
0.100
0.900
0.950
0.975
0.990
0.995
-3.078
3.078
6.314
12.706
31.821
63.657
-1.886
1.886
2.920
4.303
6.965
9.925
-1.638
1.638
2.353
3.182
4.541
5.841
-2.132
-1.533
1.533
2.132
2.776
3.747
4.604
-2.571
-2.015
-1.476
1.476
2.015
2.571
3.365
4.032
-3.143
-2.447
-1.943
-1.440
1.440
1.943
2.447
3.143
3.707
-2.998
-2.365
-1.895
-1.415
1.415
1.895
2.365
2.998
3.499
-3.355
-2.896
-2.306
-1.860
-1.397
1.397
1.860
2.306
2.896
3.355
-3.250
-2.821
-2.262
-1.833
-1.383
1.383
1.833
2.262
2.821
3.250
10
-3.169
-2.764
-2.228
-1.812
-1.372
1.372
1.812
2.228
2.764
3.169
G
11
-3.106
-2.718
-2.201
-1.796
-1.363
1.363
1.796
2.201
2.718
3.106
R
12
-3.055
-2.681
-2.179
-1.782
-1.356
1.356
1.782
2.179
2.681
3.055
A
13
-3.012
-2.650
-2.160
-1.771
-1.350
1.350
1.771
2.160
2.650
3.012
D
14
-2.977
-2.624
-2.145
-1.761
-1.345
1.345
1.761
2.145
2.624
2.977
O
15
-2.947
-2.602
-2.131
-1.753
-1.341
1.341
1.753
2.131
2.602
2.947
S 16
-2.921
-2.583
-2.120
-1.746
-1.337
1.337
1.746
2.120
2.583
2.921
D
17
-2.898
-2.567
-2.110
-1.740
-1.333
1.333
1.740
2.110
2.567
2.898
E
18
-2.878
-2.552
-2.101
-1.734
-1.330
1.330
1.734
2.101
2.552
2.878
19
-2.861
-2.539
-2.093
-1.729
-1.328
1.328
1.729
2.093
2.539
2.861
L
20
-2.845
-2.528
-2.086
-1.725
-1.325
1.325
1.725
2.086
2.528
2.845
B
21
-2.831
-2.518
-2.080
-1.721
-1.323
1.323
1.721
2.080
2.518
2.831
E
22
-2.819
-2.508
-2.074
-1.717
-1.321
1.321
1.717
2.074
2.508
2.819
R
23
-2.807
-2.500
-2.069
-1.714
-1.319
1.319
1.714
2.069
2.500
2.807
T
24
-2.797
-2.492
-2.064
-1.711
-1.318
1.318
1.711
2.064
2.492
2.797
A
25
-2.787
-2.485
-2.060
-1.708
-1.316
1.316
1.708
2.060
2.485
2.787
26
-2.779
-2.479
-2.056
-1.706
-1.315
1.315
1.706
2.056
2.479
2.779
27
-2.771
-2.473
-2.052
-1.703
-1.314
1.314
1.703
2.052
2.473
2.771
28
-2.763
-2.467
-2.048
-1.701
-1.313
1.313
1.701
2.048
2.467
2.763
29
-2.756
-2.462
-2.045
-1.699
-1.311
1.311
1.699
2.045
2.462
2.756
30
-2.750
-2.457
-2.042
-1.697
-1.310
1.310
1.697
2.042
2.457
2.750
40
-2.704
-2.423
-2.021
-1.684
-1.303
1.303
1.684
2.021
2.423
2.704
I
D
60
-2.660
-2.390
-2.000
-1.671
-1.296
1.296
1.671
2.000
2.390
2.660
90
-2.632
-2.368
-1.987
-1.662
-1.291
1.291
1.662
1.987
2.368
2.632
120
-2.617
-2.358
-1.980
-1.658
-1.289
1.289
1.658
1.980
2.358
2.617
INF
-2.576
-2.327
-1.960
-1.645
-1.282
1.282
1.645
1.960
2.327
2.576
Ejemplos: Si X ∼ t(20), entonces Pr(X ≤ −2.528) = 0.01 y Pr(X ≤ 1.725) = 0.95; si X ∼ t(n) con n suficientemente grande, entonces Pr(X ≤ −1.960) ≈ 0.025 y Pr(X ≤ 2.327) ≈ 0.99. Fuente: Tabla construida utilizando la función @qtdist de EViews® 3.1.
iii
Tabla 3: Valores Críticos de la Distribución Chi-Cuadrado. FUNCION DE DISTRIBUCION 0.005
0.010
0.025
0.050
0.100
0.900
0.950
0.975
0.990
0.995
1
0.000039 0.000157 0.000982 0.003932 0.0158
2.71
3.84
5.02
6.63
7.88
2
0.0100
0.0201
0.0506
0.10
0.21
4.61
5.99
7.38
9.21
10.60
3
0.0717
0.11
0.22
0.35
0.58
6.25
7.81
9.35
11.34
12.84
4
0.21
0.30
0.48
0.71
1.06
7.78
9.49
11.14
13.28
14.86
5
0.41
0.55
0.83
1.15
1.61
9.24
11.07
12.83
15.09
16.75
6
0.68
0.87
1.24
1.64
2.20
10.64
12.59
14.45
16.81
18.55
7
0.99
1.24
1.69
2.17
2.83
12.02
14.07
16.01
18.48
20.28
8
1.34
1.65
2.18
2.73
3.49
13.36
15.51
17.53
20.09
21.95
R
9
1.73
2.09
2.70
3.33
4.17
14.68
16.92
19.02
21.67
23.59
A
10
2.16
2.56
3.25
3.94
4.87
15.99
18.31
20.48
23.21
25.19
O
11
2.60
3.05
3.82
4.57
5.58
17.28
19.68
21.92
24.72
26.76
S
12
3.07
3.57
4.40
5.23
6.30
18.55
21.03
23.34
26.22
28.30
13
3.57
4.11
5.01
5.89
7.04
19.81
22.36
24.74
27.69
29.82
D
14
4.07
4.66
5.63
6.57
7.79
21.06
23.68
26.12
29.14
31.32
E
15
4.60
5.23
6.26
7.26
8.55
22.31
25.00
27.49
30.58
32.80
G
D
16
5.14
5.81
6.91
7.96
9.31
23.54
26.30
28.85
32.00
34.27
L
17
5.70
6.41
7.56
8.67
10.09
24.77
27.59
30.19
33.41
35.72
I
18
6.26
7.01
8.23
9.39
10.86
25.99
28.87
31.53
34.81
37.16
B
19
6.84
7.63
8.91
10.12
11.65
27.20
30.14
32.85
36.19
38.58
E
20
7.43
8.26
9.59
10.85
12.44
28.41
31.41
34.17
37.57
40.00
T
21
8.03
8.90
10.28
11.59
13.24
29.62
32.67
35.48
38.93
41.40
A
22
8.64
9.54
10.98
12.34
14.04
30.81
33.92
36.78
40.29
42.80
D
23
9.26
10.20
11.69
13.09
14.85
32.01
35.17
38.08
41.64
44.18
24
9.89
10.86
12.40
13.85
15.66
33.20
36.42
39.36
42.98
45.56
25
10.52
11.52
13.12
14.61
16.47
34.38
37.65
40.65
44.31
46.93
26
11.16
12.20
13.84
15.38
17.29
35.56
38.89
41.92
45.64
48.29
27
11.81
12.88
14.57
16.15
18.11
36.74
40.11
43.19
46.96
49.64
28
12.46
13.56
15.31
16.93
18.94
37.92
41.34
44.46
48.28
50.99
29
13.12
14.26
16.05
17.71
19.77
39.09
42.56
45.72
49.59
52.34
30
13.79
14.95
16.79
18.49
20.60
40.26
43.77
46.98
50.89
53.67
R
2
Ejemplos: Si X ∼ χ (20), entonces Pr(X ≤ 9.59) = 0.025 y Pr(X ≤ 34.17) = 0.975. Fuente: Tabla construida utilizando la función @qchisq de EViews® 3.1.
iv
Tabla 4-1: Valores Críticos de la Distribución F - Función de Distribución = 0.90. GRADOS DE LIBERTAD DEL NUMERADOR 1
2
3
4
5
6
7
8
9
10
1
39.86
49.50
53.59
55.83
57.24
58.20
58.91
59.44
59.86
60.19
2
8.53
9.00
9.16
9.24
9.29
9.33
9.35
9.37
9.38
9.39
3
5.54
5.46
5.39
5.34
5.31
5.28
5.27
5.25
5.24
5.23
G
4
4.54
4.32
4.19
4.11
4.05
4.01
3.98
3.95
3.94
3.92
R
5
4.06
3.78
3.62
3.52
3.45
3.40
3.37
3.34
3.32
3.30
D
6
3.78
3.46
3.29
3.18
3.11
3.05
3.01
2.98
2.96
2.94
O
7
3.59
3.26
3.07
2.96
2.88
2.83
2.78
2.75
2.72
2.70
S
8
3.46
3.11
2.92
2.81
2.73
2.67
2.62
2.59
2.56
2.54
9
3.36
3.01
2.81
2.69
2.61
2.55
2.51
2.47
2.44
2.42
10
3.29
2.92
2.73
2.61
2.52
2.46
2.41
2.38
2.35
2.32
A
D E
11
3.23
2.86
2.66
2.54
2.45
2.39
2.34
2.30
2.27
2.25
L
12
3.18
2.81
2.61
2.48
2.39
2.33
2.28
2.24
2.21
2.19
I
13
3.14
2.76
2.56
2.43
2.35
2.28
2.23
2.20
2.16
2.14
B
14
3.10
2.73
2.52
2.39
2.31
2.24
2.19
2.15
2.12
2.10
E
15
3.07
2.70
2.49
2.36
2.27
2.21
2.16
2.12
2.09
2.06
T
16
3.05
2.67
2.46
2.33
2.24
2.18
2.13
2.09
2.06
2.03
A
17
3.03
2.64
2.44
2.31
2.22
2.15
2.10
2.06
2.03
2.00
D
18
3.01
2.62
2.42
2.29
2.20
2.13
2.08
2.04
2.00
1.98
19
2.99
2.61
2.40
2.27
2.18
2.11
2.06
2.02
1.98
1.96
20
2.97
2.59
2.38
2.25
2.16
2.09
2.04
2.00
1.96
1.94
21
2.96
2.57
2.36
2.23
2.14
2.08
2.02
1.98
1.95
1.92
R
D E L
22
2.95
2.56
2.35
2.22
2.13
2.06
2.01
1.97
1.93
1.90
D
23
2.94
2.55
2.34
2.21
2.11
2.05
1.99
1.95
1.92
1.89
E
24
2.93
2.54
2.33
2.19
2.10
2.04
1.98
1.94
1.91
1.88
N
25
2.92
2.53
2.32
2.18
2.09
2.02
1.97
1.93
1.89
1.87
M
26
2.91
2.52
2.31
2.17
2.08
2.01
1.96
1.92
1.88
1.86
I
27
2.90
2.51
2.30
2.17
2.07
2.00
1.95
1.91
1.87
1.85
N
28
2.89
2.50
2.29
2.16
2.06
2.00
1.94
1.90
1.87
1.84
A
29
2.89
2.50
2.28
2.15
2.06
1.99
1.93
1.89
1.86
1.83
D
30
2.88
2.49
2.28
2.14
2.05
1.98
1.93
1.88
1.85
1.82
40
2.84
2.44
2.23
2.09
2.00
1.93
1.87
1.83
1.79
1.76
60
2.79
2.39
2.18
2.04
1.95
1.87
1.82
1.77
1.74
1.71
90
2.76
2.36
2.15
2.01
1.91
1.84
1.78
1.74
1.70
1.67
120
2.75
2.35
2.13
1.99
1.90
1.82
1.77
1.72
1.68
1.65
INF
2.71
2.30
2.08
1.95
1.85
1.77
1.72
1.67
1.63
1.60
O
O R
Ejemplos: Si X ∼ F(2,20), Pr(X ≤ 2.59) = 0.90; si X ∼ F(3,n) con n suficientemente grande, Pr(X ≤ 2.08) ≈ 0.90. Fuente: Tabla construida utilizando la función @qfdist de EViews® 3.1.
v
Tabla 4-2: Valores Críticos de la Distribución F - Función de Distribución = 0.95. GRADOS DE LIBERTAD DEL NUMERADOR 1 1
2
3
4
5
6
7
8
9
10
161.45 199.50 215.71 224.58 230.16 233.99 236.77 238.88 240.54 241.88
2
18.51
19.00
19.16
19.25
19.30
19.33
19.35
19.37
19.38
19.40
3
10.13
9.55
9.28
9.12
9.01
8.94
8.89
8.85
8.81
8.79
G
4
7.71
6.94
6.59
6.39
6.26
6.16
6.09
6.04
6.00
5.96
R
5
6.61
5.79
5.41
5.19
5.05
4.95
4.88
4.82
4.77
4.74
D
6
5.99
5.14
4.76
4.53
4.39
4.28
4.21
4.15
4.10
4.06
O
7
5.59
4.74
4.35
4.12
3.97
3.87
3.79
3.73
3.68
3.64
S
8
5.32
4.46
4.07
3.84
3.69
3.58
3.50
3.44
3.39
3.35
9
5.12
4.26
3.86
3.63
3.48
3.37
3.29
3.23
3.18
3.14
10
4.96
4.10
3.71
3.48
3.33
3.22
3.14
3.07
3.02
2.98
A
D E
11
4.84
3.98
3.59
3.36
3.20
3.09
3.01
2.95
2.90
2.85
L
12
4.75
3.89
3.49
3.26
3.11
3.00
2.91
2.85
2.80
2.75
I
13
4.67
3.81
3.41
3.18
3.03
2.92
2.83
2.77
2.71
2.67
B
14
4.60
3.74
3.34
3.11
2.96
2.85
2.76
2.70
2.65
2.60
E
15
4.54
3.68
3.29
3.06
2.90
2.79
2.71
2.64
2.59
2.54
T
16
4.49
3.63
3.24
3.01
2.85
2.74
2.66
2.59
2.54
2.49
A
17
4.45
3.59
3.20
2.96
2.81
2.70
2.61
2.55
2.49
2.45
D
18
4.41
3.55
3.16
2.93
2.77
2.66
2.58
2.51
2.46
2.41
19
4.38
3.52
3.13
2.90
2.74
2.63
2.54
2.48
2.42
2.38
20
4.35
3.49
3.10
2.87
2.71
2.60
2.51
2.45
2.39
2.35
21
4.32
3.47
3.07
2.84
2.68
2.57
2.49
2.42
2.37
2.32
R
D E L
22
4.30
3.44
3.05
2.82
2.66
2.55
2.46
2.40
2.34
2.30
D
23
4.28
3.42
3.03
2.80
2.64
2.53
2.44
2.37
2.32
2.27
E
24
4.26
3.40
3.01
2.78
2.62
2.51
2.42
2.36
2.30
2.25
N
25
4.24
3.39
2.99
2.76
2.60
2.49
2.40
2.34
2.28
2.24
M
26
4.23
3.37
2.98
2.74
2.59
2.47
2.39
2.32
2.27
2.22
I
27
4.21
3.35
2.96
2.73
2.57
2.46
2.37
2.31
2.25
2.20
N
28
4.20
3.34
2.95
2.71
2.56
2.45
2.36
2.29
2.24
2.19
A
29
4.18
3.33
2.93
2.70
2.55
2.43
2.35
2.28
2.22
2.18
D
30
4.17
3.32
2.92
2.69
2.53
2.42
2.33
2.27
2.21
2.16
40
4.08
3.23
2.84
2.61
2.45
2.34
2.25
2.18
2.12
2.08
60
4.00
3.15
2.76
2.53
2.37
2.25
2.17
2.10
2.04
1.99
90
3.95
3.10
2.71
2.47
2.32
2.20
2.11
2.04
1.99
1.94
120
3.92
3.07
2.68
2.45
2.29
2.18
2.09
2.02
1.96
1.91
INF
3.84
3.00
2.61
2.37
2.21
2.10
2.01
1.94
1.88
1.83
O
O R
Ejemplos: Si X ∼ F(2,20), Pr(X ≤ 3.49) = 0.95; si X ∼ F(3,n) con n suficientemente grande, Pr(X ≤ 2.61) ≈ 0.95. Fuente: Tabla construida utilizando la función @qfdist de EViews® 3.1.
vi
Tabla 4-3: Valores Críticos de la Distribución F - Función de Distribución = 0.99. GRADOS DE LIBERTAD DEL NUMERADOR 1
2
3
4
5
6
7
8
9
10
1
4052
5000
5403
5625
5764
5859
5928
5981
6022
6056
2
98.50
99.00
99.17
99.25
99.30
99.33
99.36
99.37
99.39
99.40
3
34.12
30.82
29.46
28.71
28.24
27.91
27.67
27.49
27.35
27.23
G
4
21.20
18.00
16.69
15.98
15.52
15.21
14.98
14.80
14.66
14.55
R
5
16.26
13.27
12.06
11.39
10.97
10.67
10.46
10.29
10.16
10.05
D
6
13.75
10.92
9.78
9.15
8.75
8.47
8.26
8.10
7.98
7.87
O
7
12.25
9.55
8.45
7.85
7.46
7.19
6.99
6.84
6.72
6.62
S
8
11.26
8.65
7.59
7.01
6.63
6.37
6.18
6.03
5.91
5.81
9
10.56
8.02
6.99
6.42
6.06
5.80
5.61
5.47
5.35
5.26
10
10.04
7.56
6.55
5.99
5.64
5.39
5.20
5.06
4.94
4.85
A
D E
11
9.65
7.21
6.22
5.67
5.32
5.07
4.89
4.74
4.63
4.54
L
12
9.33
6.93
5.95
5.41
5.06
4.82
4.64
4.50
4.39
4.30
I
13
9.07
6.70
5.74
5.21
4.86
4.62
4.44
4.30
4.19
4.10
B
14
8.86
6.51
5.56
5.04
4.69
4.46
4.28
4.14
4.03
3.94
E
15
8.68
6.36
5.42
4.89
4.56
4.32
4.14
4.00
3.89
3.80
T
16
8.53
6.23
5.29
4.77
4.44
4.20
4.03
3.89
3.78
3.69
A
17
8.40
6.11
5.18
4.67
4.34
4.10
3.93
3.79
3.68
3.59
D
18
8.29
6.01
5.09
4.58
4.25
4.01
3.84
3.71
3.60
3.51
19
8.18
5.93
5.01
4.50
4.17
3.94
3.77
3.63
3.52
3.43
20
8.10
5.85
4.94
4.43
4.10
3.87
3.70
3.56
3.46
3.37
21
8.02
5.78
4.87
4.37
4.04
3.81
3.64
3.51
3.40
3.31
R
D E L
22
7.95
5.72
4.82
4.31
3.99
3.76
3.59
3.45
3.35
3.26
D
23
7.88
5.66
4.76
4.26
3.94
3.71
3.54
3.41
3.30
3.21
E
24
7.82
5.61
4.72
4.22
3.90
3.67
3.50
3.36
3.26
3.17
N
25
7.77
5.57
4.68
4.18
3.85
3.63
3.46
3.32
3.22
3.13
M
26
7.72
5.53
4.64
4.14
3.82
3.59
3.42
3.29
3.18
3.09
I
27
7.68
5.49
4.60
4.11
3.78
3.56
3.39
3.26
3.15
3.06
N
28
7.64
5.45
4.57
4.07
3.75
3.53
3.36
3.23
3.12
3.03
A
29
7.60
5.42
4.54
4.04
3.73
3.50
3.33
3.20
3.09
3.00
D
30
7.56
5.39
4.51
4.02
3.70
3.47
3.30
3.17
3.07
2.98
40
7.31
5.18
4.31
3.83
3.51
3.29
3.12
2.99
2.89
2.80
60
7.08
4.98
4.13
3.65
3.34
3.12
2.95
2.82
2.72
2.63
90
6.93
4.85
4.01
3.53
3.23
3.01
2.84
2.72
2.61
2.52
120
6.85
4.79
3.95
3.48
3.17
2.96
2.79
2.66
2.56
2.47
INF
6.64
4.61
3.78
3.32
3.02
2.80
2.64
2.51
2.41
2.32
O
O R
Ejemplos: Si X ∼ F(2,20), Pr(X ≤ 5.85) = 0.99; si X ∼ F(3,n) con n suficientemente grande, Pr(X ≤ 3.78) ≈ 0.99. Fuente: Tabla construida utilizando la función @qfdist de EViews® 3.1.
vii
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