Tabla I Distribución Binomial p .01 .05 .10 .15 .20 .25 .30. 1/3 .35 .40 .45 .49 .50.
n r. 2 0 .9801 .9025 .8100 .7225 .6400 .5625 .4900 .4444 .4225 .3600 .3025 ...
Tabla I Distribución Binomial
n 2
3
4
5
6
7
8
p r 0 1 2 0 1 2 3 0 1 2 3 4 0 1 2 3 4 5 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 8
.01
.05
.10
.15
.20
.25
.30
1/3
.35
.40
.45
.49
.50
.9801 .0198 .0001 .9703 .0294 .0003 .0000 .9606 .0388 .0006 .0000 .0000 .9510 .0480 .0010 .0000 .0000 .0000 .9415 .0571 .0014 .0000 .0000 .0000 .0000 .9321 .0659 .0020 .0000 .0000 .0000 .0000 .0000 .9227 .0746 .0026 .0001 .0000 .0000 .0000 .0000 .0000
.9025 .0950 .0025 .8574 .1354 .0071 .0001 .8145 .1715 .0135 .0005 .0000 .7738 .2036 .0214 .0011 .0000 .0000 .7351 .2321 .0305 .0021 .0001 .0000 .0000 .6983 .2573 .0406 .0036 .0002 .0000 .0000 .0000 .6634 .2793 .0515 .0054 .0004 .0000 .0000 .0000 .0000
.8100 .1800 .0100 .7290 .2430 .0270 .0010 .6561 .2916 .0486 .0036 .0001 .5905 .3280 .0729 .0081 .0004 .0000 .5314 .3543 .0984 .0146 .0012 .0001 .0000 .4783 .3720 .1240 .0230 .0026 .0002 .0000 .0000 .4305 .3826 .1488 .0331 .0046 .0004 .0000 .0000 .0000
.7225 .2550 .0225 .6141 .3251 .0574 .0034 .5220 .3685 .0975 .0115 .0005 .4437 .3915 .1382 .0244 .0022 .0001 .3771 .3993 .1762 .0415 .0055 .0004 .0000 .3206 .3960 .2097 .0617 .0109 .0012 .0001 .0000 .2725 .3847 .2376 .0839 .0185 .0026 .0002 .0000 .0000
.6400 .3200 .0400 .5120 .3840 .0960 .0080 .4096 .4096 .1636 .0256 .0016 .3277 .4096 .2048 .0512 .0064 .0003 .2621 .3932 .2458 .0819 .0154 .0015 .0001 .2097 .3670 .2753 .1147 .0287 .0043 .0004 .0000 .1678 .3355 .2936 .1468 .0459 .0092 .0011 .0001 .0000
.5625 .3750 .0625 .4219 .4219 .1406 .0156 .3164 .4219 .2109 .4609 .0039 .2373 .3855 .2637 .0879 .0146 .0010 .1780 .3560 .2966 .1318 .0330 .0044 .0002 .1335 .3115 .3115 .1730 .0577 .0115 .0013 .0001 .1001 .2670 .3115 .2076 .0865 .0231 .0038 .0004 .0000
.4900 .4200 .0900 .3430 .4410 .1890. .0270 .2401 .4116 .2646 .0756 .0081 .1681 .3602 .3087 .1323 .0284 .0024 .1176 .3025 .3241 .1852 .0595 .0102 .0007 .0824 .2471 .3177 .2269 .0972 .0250 .0036 .0002 .0576 .1977 .2965 .2541 .1361 .0467 .0100 .0012 .0001
.4444 .4444 .1111 .2963 .4444 .2222 .0370 .1975 .3951 .2963 .0988 .0123 .1317 .3292 .3292 .1646 .0412 .0041 .0878 .2634 .3292 .2195 .0823 .0165 .0014 .0585 .2048 .3073 .2561 .1280 .0384 .0064 .0005 .0390 .1561 .2731 .2731 .1707 .0683 .0171 .0024 .0002
.4225 .4550 .1225 .2746 .4436 .2389 .0429 .1785 .3845 .3105 .1115 .0150 .1160 .3124 .3364 .1811 .0488 .0053 .0754 .2437 .3280 .2355 .0951 .0205 .0018 .0490 .1848 .2985 .2679 .1442 .0466 .0084 .0006 .0319 .1373 .2587 .2786 .1875 .0808 .0217 .0033 .0002
.3600 .4800 .1600 .2160 .4320 .2880 .0640 .1296 .3456 .3456 .1536 .0256 .0778 .2592 .3456 .2304 .0768 .0102 .0467 .1866 .3110 .2765 .1382 .0369 .0041 .0280 .1306 .2613 .2903 .1935 .0774 .0172 .0016 .0168 .0896 .2090 .2787 .2322 .1239 .0413 .0079 .0007
.3025 .4950 .2025 .1664 .4084 .3341 .0911 .0915 .2995 .3675 .2005 .0410 .0503 .2059 .3369 .2757 .1128 .0185 .0277 .1359 .2780 .3032 .1861 .0609 .0083 .0152 .0872 .2140 .2918 .2388 .1172 .0320 .0037 .0084 .0548 .1569 .2568 .2627 .1719 .0703 .0164 .0017
.2601 .4998 .2401 .1327 .3823 3674 .1176 .0677 .2600 .3747 .2400 .0576 .0345 .1657 .3185 .3060 .1470 .0283 .0176 .1014 .2437 .3121 .2249 .0864 .0139 .0090 .0603 .1740 .2786 .2676 .1543 .0494 .0068 .0046 .0352 .1183 .2273 .2730 .2098 .1008 .0277 .0033
.2500 .5000 .2500 .1250 .3750 .3750 .1250 .0625 .2500 .3750 .2500 .0625 .0312 .1562 .3125 .3125 .1562 .0312 .0156 .0938 .2344 .3125 .2344 .0938 .0156 .0078 .0574 .1641 .2734 .2734 .1641 .0547 .0078 .0039 .0312 .1094 .2188 .2734 .2188 .1094 .0312 .0039
Tabla I Distribución Binomial (Continuación)
n 9
10
p r 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 10
.01
.05
.10
.15
.20
.25
.30
1/3
.35
.40
.45
.49
.50
.9135 .0830 .0034 .0001 .0000 .0000 .0000 .0000 .0000 .0000 .9044 .0914 .0042 .0001 .0000 .0000 .0000 .0000 .0000 .0000 .0000
.6302 .2985 .0629 .0077 .0006 .0000 .0000 .0000 .0000 .0000 .5987 .3151 .0746 .0105 .0010 .0001 .0000 .0000 .0000 .0000 .0000
.3874 .3874 .1722 .0446 .0074 .0008 .0001 .0000 .0000 .0000 .3487 .3874 .1937 .0574 .0112 .0015 .0001 .0000 .0000 .0000 .0000
.2316 .3679 .2597 .1069 .0283 .0050 .0006 .0000 .0000 .0000 .1969 .3474 .2759 .1298 .0401 .0085 .0012 .0001 .0000 .0000 .0000
.1342 .3020 .3020 .1762 .0661 .0165 .0028 .0003 .0000 .0000 .1074 .2684 .3020 .2013 .0881 .0264 .0055 .0008 .0001 .0000 .0000
.0751 .2253 .3003 .2336 .1168 .0389 .0087 .0012 .0001 .0000 .0563 .1877 .2816 .2503 .1460 .0584 .0162 .0031 .0004 .0000 .0000
.0404 .1556 .2688 .2668 .1715 .0735 .0210 .0039 .0004 .0000 .0282 .1211 .2335 .2668 .2001 .1029 .0368 .0090 .0014 .0001 .0000
.0260 .1171 .2341 .2731 .2048 .1024 .0341 .0073 .0009 .0001 .0173 .0867 .1951 .2601 .2276 .1366 .0596 .0163 .0030 .0003 .0000
.0207 .1004 .2162 .2716 .2194 .1181 .0424 .0098 .0013 .0001 .0135 .0725 .1757 .2522 .2377 .1536 .0689 .0212 .0043 .0005 .0000
.0101 .0605 .1612 .2508 .2508 .1672 .0743 .0212 .0035 .0003 .0060 .0403 .1209 .2150 .2508 .2007 .1115 .0425 .0106 .0016 .0001
.0046 .0339 .1110 .2119 .2600 .2128 .1160 .0407 .0083 .0008 .0025 .0207 .0763 .1665 .2384 .2340 .1596 .0746 .0229 .0042 .0003
.0023 .0202 .0776 .1739 .2506 .2408 .1542 .0635 .0153 .0016 .0012 .0114 .0495 .1267 .2130 .2456 .1966 .1080 .0389 .0083 .0008
.0020 .0176 .0703 .1641 .2461 .2461 .1641 .0703 .0176 .0020 .0010 .0098 .0439 .1172 .2051 .2461 .2051 .1172 .0439 .0098 .0010
Tabla II Distribución de Poisson r λ .l .2 .3 .4 .5 .6 .7 .8 .9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 5.0 6.0 7.0 8.0 9.0 10.0 r λ 5.0 6.0 7.0 8.0 9.0 10.0
0
1
2
3
4
5
6
7
8
9
10
11
12
.9048 .8187 .7408 .6703 .6065 .5488 .4966 .4493 .4066 .3679 .3329 .3012 .2725 .2466 .2231 .2019 .1827 .1653 .1496 .1353 .1108 .0907 .0743 .0608 .0498 .0408 .0334 .0273 .0224 .0183 .0067 .0025 .0009 .0003 .0001 .0000 13
.0905 .1637 .2222 .2681 .3033 .3293 .3476 .3595 .3659 .3679 .3662 .3614 .3543 .3452 .3347 .3230 .3106 .2975 .2842 .2707 .2438 .2177 .1931 .1703 .1494 .1304 .1135 .0984 .0850 .0733 .0337 .0149 .0064 .0027 .0011 .0005 14
.0045 .0164 .0333 .0536 .0758 .0988 .1217 .1438 .1647 .1839 .2014 .2169 .2303 .2417 .2510 .2584 .2640 .2678 .2700 .2707 .2681 .2613 .2510 .2384 .2240 .2087 .1929 .1771 .1615 .1465 .0842 .0446 .0223 .0107 .0050 .0023 15
.0002 .0011 .0033 .0072 .0126 .0198 .0284 .0383 .0494 .0613 .0738 .0867 .0998 .1128 .1255 .1378 .1496 .1607 .1710 .1804 .1966 .2090 .2176 .2225 .2240 .2226 .2186 .2125 .2046 .1954 .1404 .0892 .0521 .0286 .0150 .0076 16
.0000 .0001 .0002 .0007 .0016 .0030 .0050 .0077 .0111 .0153 .0203 .0260 .0324 .0395 .0471 .0551 .0636 .0723 .0812 .0902 l082 .1254 .1414 .1557 .1680 .1781 .1858 .1912 .1944 .1954 .1755 .1339 .0912 .0573 .0337 .0189 17
.0000 .0000 .0001 .0002 .0004 .0007 .0012 .0020 .0031 .0045 .0062 .0084 .0111 .0141 .0176 .0216 .0260 .0309 .0361 .0476 .0602 .0735 .0872 .1008 .1140 .1264 .1377 .1477 .1563 .1755 .1606 .1277 .0916 .0607 .0378 18
.0000 .0000 .0000 .0001 .0002 .0003 .0005 .0008 .0012 .0018 .0026 .0035 .0047 .0061 .0078 .0098 .0120 .0174 .0241 .0319 .0407 .0504 .0608 .0716 .0826 .0936 .1042 .1462 .1606 .1490 .1221 .0911 .0631 19
.0000 .0000 .0000 .0001 .0001 .0002 .0003 .0005 .0008 .0011 .0015 .0020 .0027 .0034 .0055 .0083 .0118 .0163 .0216 .0278 .0348 .0425 .0508 .0595 .1044 .1377 .1490 .1396 .1171 .0901 20
.0000 .0000 .0000 .0001 .0001 .0001 .0002 .0003 .0005 .0006 .0009 .0015 .0025 .0038 .0057 .0081 .0111 .0148 .0191 .0241 .0298 .0653 .1033 .1304 .1396 .1318 .1126 21
.0000 .0000 .0000 .0000 .0001 .0001 .0001 .0002 .0004 .0007 .0011 .0018 .0027 .0040 .0056 .0076 .0102 .0132 .0363 .0688 .1014 .1241 .1318 .1251 22
.0000 .0000 .0000 .0000 .0001 .0002 .0003 .0005 .0008 .0013 .0019 .0028 .0039 .0053 .0181 .0413 .0710 .0993 .1186 .1251 23
.0000 .0000 .0001 .0001 .0002 .0004 .0006 .0009 .0013 .0019 .0082 .0225 .0452 .0722 .0970 .1137 24
.0000 .0000 .0001 .0001 .0002 .0003 .0004 .0006 .0034 .0113 .0264 .0481 .0728 .0948
.0013 .0052 .0142 .0296 .0504 .0729
.0005 .0022 .0071 .0169 .0324 .0521
.0002 .0009 .0033 .0090 .0194 .0347
.0003 .0014 .0045 .0109 .0217
.0001 .0006 .0021 .0058 .0128
.0002 .0009 .0029 .0071
.0001 .0004 .0014 .0037
.0002 .0006 .0019
.0001 .0003 .0009
.0001 .0004
.0002
.0001
z 0.0 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
0.00 0.5000 0.4602 0.4207 0.3821 0.3446 0.3085 0.2743 0.2420 0.2119 0.1841 0.1597 0.1357 0.1151 0.0968 0.0808 0.0668 0.0548 0.0446 0.0359 0.0287 0.0228 0.0179 0.0139 0.0107 0.0082 0.00621 0.00466 0.00347 0.00256 0.00187 0.00135 0.00097 0.00069 0.00048 0.00034 0.00023 0.00016 0.00011 0.00007 0.00005
Tabla III. Valores críticos de la distribución Normal estándar R∞ 2 P [Z > Zα ] = Zα √12π exp−z /2 dz = α
0.01 0.4960 0.4562 0.4168 0.3783 0.3409 0.3050 0.2709 0.2389 0.2090 0.1814 0.1562 0.1335 0.1131 0.0951 0.0793 0.0655 0.0537 0.0436 0.0351 0.0281 0.0222 0.0174 0.0136 0.0104 0.00798 0.00604 0.00453 0.00336 0.00248 0.00181 0.00131 0.00094 0.00066 0.00047 0.00032 0.00022 0.00015 0.00010 0.00007 0.00005
0.02 0.4920 0.4522 0.4129 0.3745 0.3372 0.3015 0.2676 0.2358 0.2061 0.1788 0.1539 0.1314 0.1112 0.0934 0.0778 0.0643 0.0526 0.0427 0.0344 0.0274 0.0217 0.0170 0.0132 0.0102 0.00776 0.00587 0.00440 0.00326 0.00240 0.00175 0.00126 0.00091 0.00064 0.00045 0.00031 0.00022 0.00015 0.00010 0.00007 0.00004
0.03 0.4880 0.4483 0.4090 0.3707 0.3336 0.2981 0.2643 0.2327 0.2033 0.1762 0.1515 0.1292 0.1093 0.0918 0.0764 0.0630 0.0516 0.0418 0.0336 0.0268 0.0212 0.0166 0.0129 0.0099 0.00755 0.00570 0.00427 0.00317 0.00233 0.00169 0.00122 0.00087 0.00062 0.00043 0.0003 0.00021 0.00014 0.00010 0.00006 0.00004
0.04 0.4840 0.4443 0.4052 0.3669 0.3300 0.2946 0.2611 0.2296 0.2005 0.1736 0.1492 0.1271 0.1075 0.0901 0.0749 0.0618 0.0505 0.0409 0.0329 0.0262 0.0207 0.0162 0.0125 0.0096 0.00734 0.00554 0.00415 0.00307 0.00226 0.00164 0.00118 0.00084 0.0006 0.00042 0.00029 0.00020 0.00014 0.00009 0.00006 0.00004
0.05 0.4801 0.4404 0.4013 0.3632 0.3264 0.2912 0.2578 0.2266 0.1977 0.1711 0.1469 0.1251 0.1056 0.0885 0.0735 0.0606 0.0495 0.0401 0.0322 0.0256 0.0202 0.0158 0.0122 0.0094 0.00714 0.00539 0.00402 0.00298 0.00219 0.00159 0.00114 0.00082 0.00058 0.00041 0.00028 0.00019 0.00013 0.00009 0.00006 0.00004
0.06 0.4761 0.4364 0.3974 0.3594 0.3228 0.2877 0.2546 0.2236 0.1949 0.1685 0.1446 0.1230 0.1038 0.0869 0.0721 0.0594 0.0485 0.0392 0.0314 0.0250 0.0197 0.0154 0.0119 0.0091 0.00695 0.00523 0.00391 0.00289 0.00212 0.00154 0.00111 0.00079 0.00056 0.00032 0.00027 0.00019 0.00013 0.00009 0.00006 0.00004
0.07 0.4721 0.4325 0.3936 0.3557 0.3192 0.2843 0.2514 0.2206 0.1922 0.1660 0.1423 0.1210 0.1020 0.0853 0.0708 0.0582 0.0475 0.0394 0.0307 0.0244 0.0192 0.0150 0.0116 0.0089 0.00676 0.00508 0.00379 0.00280 0.00205 0.00149 0.00107 0.00076 0.00054 0.00038 0.00026 0.00018 0.00012 0.00008 0.00005 0.00004
0.08 0.4681 0.4286 0.3897 0.3520 0.3156 0.2910 0.2483 0.2177 0.1894 0.1635 0.1401 0.1190 0.1003 0.0838 0.0694 0.0571 0.0465 0.0375 0.0301 0.0239 0.0188 0.0146 0.0113 0.0087 0.00657 0.00494 0.00368 0.00272 0.00199 0.00144 0.00103 0.00074 0.00052 0.00036 0.00025 0.00017 0.00012 0.00008 0.00005 0.00003
0.09 0.4641 0.4247 0.3859 0.3483 0.3121 0.2776 0.2451 0.2148 0.1867 0.1611 0.1379 0.1170 0.0995 0.0823 0.0681 0.0559 0.0455 0.0367 0.0294 0.0233 0.0183 0.0143 0.0110 0.0084 0.00639 0.00480 0.00357 0.00264 0.00193 0.00139 0.00100 0.00071 0.00050 0.00035 0.00024 0.00017 0.00011 0.00008 0.00005 0.00003
Tabla IV. Valores críticos de la distribución t de Student: Abcisas tα;ν que dejan a su derecha un área α en una t con ν grados de libertad.
ν 1 2 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 40 60 120 ∞
0.4 0.325 0.289 0.277 0.271 0.267 0.265 0.263 0.262 0.261 0.260 0.260 0.259 0.259 0.258 0.258 0.258 0.257 0.257 0.257 0.257 0.257 0.256 0.256 0.256 0.256 0.256 0.256 0.256 0.256 0.256 0.255 0.254 0.254 0.253
0.25 1.000 0.816 0.765 0.741 0.727 0.718 0.711 0.706 0.703 0.700 0.697 0.695 0.694 0.692 0.691 0.690 0.689 0.688 0.688 0.687 0.686 0.686 0.685 0.685 0.684 0.684 0.684 0.683 0.683 0.683 0.681 0.679 0.677 0.674
0.1 3.078 1.886 1.638 1.533 1.476 1.440 1.415 1.397 1.383 1.372 1.363 1.356 1.350 1.345 1.341 1.337 1.333 1.330 1.328 1.325 1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.310 1.303 1.296 1.289 1.282
0.05 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697 1.684 1.671 1.658 1.645
0.025 12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042 2.021 2.000 1.980 1.960
0.01 31.821 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.423 2.390 2.358 2.326
0.005 63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.704 2.660 2.617 2.576
0.0025 127.32 14.089 7.453 5.598 4.773 4.317 4.029 3.833 3.690 3.581 3.497 3.428 3.372 3.326 3.286 3.252 3.222 3.197 3.174 3.153 3.135 3.119 3.104 3.091 3.078 3.067 3.057 3.047 3.038 3.030 2.971 2.915 2.860 2.807
0.001 318.31 22.326 10.213 7.173 5.893 5.208 4.785 4.501 4.297 4.144 4.025 3.930 3.852 3.787 3.733 3.686 3.646 3.610 3.579 3.552 3.527 3.505 3.485 3.467 3.450 3.435 3.421 3.408 3.396 3.385 3.307 3.232 3.160 3.090
0.0005 636.62 31.598 12.924 8.610 6.869 5.959 5.408 5.041 4.781 4.587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 3.883 3.850 3.819 3.792 3.767 3.745 3.725 3.707 3.690 3.674 3.659 3.646 3.551 3.460 3.373 3.291
Tabla V. Valores críticos de la distribución χ2 de Pearson: Abcisas χ2α;ν que dejan a su derecha un área α bajo la χ2 con ν grados de libertad.
ν 1 2 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
0.995 0.010 0.072 0.207 0.412 0.676 0.989 1.34 1.73 2.16 2.60 3.07 3.57 4.07 4.60 5.14 5.70 6.26 6.84 7.43 8.03 8.64 9.26 9.89 10.5 11.2 11.8 12.5 13.1 13.8
0.99 0.020 0.115 0.297 0.554 0.872 1.24 1.65 2.09 2.56 3.05 3.57 4.11 4.66 5.23 5.81 6.41 7.01 7.63 8.26 8.90 9.54 10.2 10.9 11.5 12.2 12.9 13.6 14.3 15.0
0.975 0.051 0.216 0.484 0.831 1.24 1.69 2.18 2.70 3.25 3.82 4.40 5.01 5.63 6.26 6.91 7.56 8.23 8.91 9.59 10.3 11.0 11.7 12.4 13.1 13.8 14.6 15.3 16.0 16.8
0.95 0.103 0.352 0.711 1.15 1.64 2.17 2.73 3.33 3.94 4.57 5.23 5.89 6.57 7.26 7.96 8.67 9.39 10.1 10.9 11.6 12.3 13.1 13.8 14.6 15.4 16.2 16.9 17.7 18.5
0.9 0.016 0.211 0.584 1.06 1.61 2.20 2.83 3.49 4.17 4.87 5.58 6.30 7.04 7.79 8.55 9.31 10.1 10.9 11.7 12.4 13.2 14.0 14.8 15.7 16.5 17.3 18.1 18.9 19.8 20.6
0.75 0.102 0.575 1.21 1.92 2.67 3.45 4.25 5.07 5.90 6.74 7.58 8.44 9.30 10.2 11.0 11.9 12.8 13.7 14.6 15.5 16.3 17.2 18.1 19.0 19.9 20.8 21.7 22.7 23.6 24.5
0.5 0.455 1.39 2.37 3.36 4.35 5.35 6.35 7.34 8.34 9.34 10.3 11.3 12.3 13.3 14.3 15.3 16.3 17.3 18.3 19.3 20.3 21.3 22.3 23.3 24.3 25.3 26.3 27.3 28.3 29.3
0.25 1.32 2.77 4.11 5.39 6.63 7.84 9.04 10.2 11.4 12.5 13.7 14.8 16.0 17.1 18.2 19.4 20.5 21.6 22.7 23.8 24.9 26.0 27.1 28.2 29.3 30.4 31.5 32.6 33.7 34.8
0.1 2.71 4.61 6.25 7.78 9.24 10.6 12.0 13.4 14.7 16.0 17.3 18.5 19.8 21.1 22.3 23.5 24.8 26.0 27.2 28.4 29.6 30.8 32.0 33.2 34.4 35.6 36.7 37.9 39.1 40.3
0.05 3.84 5.99 7.81 9.49 11.1 12.6 14.1 15.5 16.9 18.3 19.7 21.0 22.4 23.7 25.0 26.3 27.6 28.9 30.1 31.4 32.7 33.9 35.2 36.4 37.7 38.9 40.1 41.3 42.6 43.8
0.025 5.02 7.38 9.35 11.1 12.8 14.4 16.0 17.5 19.0 20.5 21.9 23.3 24.7 26.1 27.5 28.8 30.2 31.5 32.9 34.2 35.5 36.8 38.1 39.4 40.6 41.9 43.2 44.5 45.7 47.0
0.01 6.63 9.21 11.3 13.3 15.1 16.8 18.5 20.1 21.7 23.2 24.7 26.2 27.7 29.1 30.6 32.0 33.4 34.8 36.2 37.6 38.9 40.3 41.6 43.0 44.3 45.6 47.0 48.3 49.6 50.9
0.005 7.88 10.6 12.8 14.9 16.7 18.5 20.3 22.0 23.6 25.2 26.8 28.3 29.8 31.3 32.8 34.3 35.7 37.2 38.6 40.0 41.4 42.8 44.2 45.6 46.9 48.3 49.6 51.0 52.3 53.7
0.001 10.8 13.8 16.3 18.5 20.5 22.5 24.3 26.1 21.9 29.6 31.3 32.9 34.5 36.1 37.7 39.3 40.8 42.3 43.8 45.3 46.8 48.3 49.7 51.2 52.6 54.1 55.5 56.9 58.3 59.7
Tabla VI. Valores críticos de la distribución F de Snedecor: Abcisas Fα;ν 1 ,ν 2 que dejan a su derecha un área α bajo la F con ν 1 y ν 2 grados de libertad.
ν2 1 2 3 4 5 6 7 8 9 l0 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 ∞
1 5.83 2.57 2.02 1.81 1.69 1.62 1.57 1.54 1.51 1.49 1.47 1.46 1.45 1.44 1.43 1.42 1.42 1.41 1.41 1.40 1.40 1.40 1.39 1,39 1,39 1.38 1.38 1.38 1.38 1.38 1.36 1.35 1.34 1.32
2 7.50 3.00 2.28 2.00 1.85 1.76 1,70 1.66 1.62 1.60 1.58 1.56 1.55 1.53 1.52 1.51 1.51 1.50 1.49 1.49 1.48 1.48 1.47 1.47 1.47 1.46 1.46 1.46 1.45 1.45 1.44 1.42 1.40 1.39
3 8.20 3.15 2.36 2.05 1.88 1.78 1.72 1.67 1.63 1.60 1.58 1.56 1.55 1.53 1.52 1.51 1,50 1.49 1.49 1.48 1.48 1.47 1.47 1.46 1.46 1.45 1.45 1.45 1.45 1.44 1.42 1.41 1.39 1.37
4 8.58 3.23 2.39 2.06 1.89 1.79 1.72 1.66 1.63 1.59 1.57 1.55 1.53 1.52 1.51 1.50 1.49 1.48 1.47 1.47 1.46 1.45 1.45 1.44 1.44 1.44 1.43 1.43 1.43 1.42 1.40 1.38 1.37 1.35
5 8.82 3.28 2.41 2.07 1.89 1.79 1.71 1.66 1,62 1.59 1.56 1.54 1.52 1.51 1.49 1.48 1.47 1.46 1.46 1.45 1.44 1.44 1.43 1.43 1.42 1.42 1.42 1.41 1.41 1.41 1.39 1.37 1.35 1.33
6 8.98 3.31 2.42 2.08 1.89 1.78 1.71 1.65 1.61 1.58 1.55 1.53 1.51 1.50 1.48 1.47 1.46 1.45 l.44 1.44 1.43 1.42 1.42 1.41 1.41 1.41 1.40 1.40 1.40 1.39 1.37 1.35 1.33 1.31
7 9.10 3.34 2.43 2.08 1.89 1.78 1.70 1.64 1.60 1.57 1.54 1.52 1.50 1.49 1.47 1.46 1.45 1.44 1.43 1.43 1.42 1.41 1.41 1.40 1.40 1.39 1.39 1.39 1.38 1.38 1.36 1.33 1.31 1.29
8 9.19 3.35 2.44 2.09 1.89 1.78 1.70 1.64 1.60 1.56 1.53 1,51 1.49 1.48 1.46 1.45 1.44 1.43 1.42 1.42 1.41 1.40 1.40 1.39 1.39 1.38 1.38 1.38 1.37 1.37 1.35 1.32 1.30 1.28
α = 0,25 ν1 9 10 9.26 9.32 3.37 3.38 2.44 2.44 2.08 2.08 1.89 1.89 1.77 1.77 1.69 1.69 1.63 1.63 1.59 1.59 1.56 1.55 1.53 1.52 1.51 1.50 1.49 1.48 1.47 1.46 1.46 1.45 1.44 l.44 1.43 1.43 1.42 1.42 1.41 1.41 1.41 1.40 1.40 1.39 1.39 1.39 1.39 1.38 1.38 1.38 1.38 1.37 1.37 1.37 1.37 1.36 1.37 1.36 1.36 1.35 1.36 1.35 1.34 1.33 1.31 1.30 1.29 1.28 1.27 1.25
12 9.41 3.39 2.45 2.08 1.89 1.77 1.68 1.62 1.58 1.54 1.51 1.49 1.47 1.45 1.44 1.43 1.41 1.40 1.40 1.39 1.38 1.37 1.37 1.36 1.36 1.35 1.35 1.34 1.34 1.34 1.31 1.29 1.26 1.24
15 9.49 3.41 2.46 2.08 1.89 1.76 1.68 1.62 1.57 1.53 1.50 1.48 1.46 1.44 1.43 1.41 1.40 1.39 1.38 1.37 1.37 1.36 1.35 1.35 1.34 1.34 1.33 1.33 1.32 1.32 1.30 1.27 1.24 1.22
20 9.58 3.43 2.46 2.08 1.88 1.76 1.67 1.61 1.56 1.52 1.49 1.47 1.45 1.43 1.41 1.40 1.39 1.38 1,37 1.36 1.35 1.34 1.34 1.33 1.33 1.32 1.32 1.31 1.31 1.30 1.28 1.25 1.22 1.19
24 9.63 3.43 2,46 2.08 1.88 1.75 1.67 1.60 1.56 1.52 1.49 1.46 1.44 1.42 1.41 1.39 1.38 1.37 1.36 1.35 1.34 1.33 1.33 1.32 1.32 1.31 1.31 1.30 1.30 1.29 1.26 1.24 1.21 1.18
30 9.67 3.44 2.47 2.08 1.88 1.75 1.66 1.60 1.55 1.51 1.48 1.45 1.43 1.41 1.40 1.38 1.37 1.36 1.35 1.34 1.33 1.32 1.32 1.31 1.31 1.30 1.30 1.29 1.29 1.28 1.25 1.22 1.19 1.16
40 9.71 3.45 2.47 2.08 1.88 1.75 1.66 1.59 1.54 1.51 1.47 1.45 1.42 1.41 1.39 l.37 1.36 1.35 1.34 1.33 1.32 1.31 1.31 1.30 1.29 1.29 1.28 1.28 1.27 1.27 1.24 1.21 1.18 1.14
60 9.76 3.46 2.47 2.08 1.87 1.74 1.65 1.59 1.54 1.50 1.47 1.44 1.42 1.40 1.38 1.36 1.35 1.34 1.33 1.32 1.31 1.30 1.30 1.29 1.28 1.28 1.27 1.27 1.26 1.26 1.22 1.19 1.16 1.12
120 9.80 3.47 2.47 2.08 1.87 1.74 1.65 1.58 1.53 1.49 1.46 1.43 1.41 1,39 1.37 1.35 1.34 1.33 1.32 1.31 1.30 1.29 1.28 1.28 1.27 1,26 1.26 1.25 1.25 1.24 1.21 1.17 1.13 1.08
∞ 9.85 3.48 2.47 2.08 1.87 1.74 1.65 1.58 1.53 1.48 1.45 1.42 1.40 1.38 1.36 1.34 1.33 1.32 1.30 1.29 1.28 1.28 1.27 1.26 1.25 1.25 1.24 1.24 1.23 1.23 1.19 1.15 1.10 1.00
Tabla VI. Valores críticos de la distribución F de Snedecor: Abcisas Fα;ν 1 ,ν 2 que dejan a su derecha un área α bajo la F con ν 1 y ν 2 grados de libertad.
ν2 1 2 3 4 5 6 7 8 9 l0 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 ∞
1 39.86 8.53 5.54 4.54 4.06 3.78 3.59 3.46 3.36 3.29 3.23 3.18 3.14 3.10 3.07 3.05 3.03 3.01 2.99 2.97 2.96 2.95 2.94 2.93 2.92 2.91 2.90 2.89 2.89 2.88 2.84 2.79 2.75 2.71
2 49.50 9.00 5.46 4.32 3.78 3.46 3.26 3.11 3.01 2.92 2.86 2.81 2.76 2.73 2.70 2.67 2.64 2.62 2.61 2.59 2.57 2.56 2.55 2.54 2.53 2.52 2.51 2.50 2.50 2.49 2.44 2.39 2.35 2.30
3 53.59 9.16 5.39 4.19 3.62 3.29 3.07 2.92 2.81 2.73 2.66 2.61 2.56 2.52 2.49 2.46 2.44 2.42 2.40 2.38 2.36 2.35 2.34 2.33 2.32 2.31 2.30 2.29 2.28 2.28 2.23 2.18 2.13 2.08
4 55.83 9.24 5.34 4.11 3.52 3.18 2.96 2.81 2.69 2.61 2.54 2.48 2.43 2.39 2.36 2.33 2.31 2.29 2.27 2.25 2.23 2.22 2.21 2.19 2.18 2.17 2.17 2.16 2.15 2.14 2.09 2.04 1.99 1.94
5 57.24 9.29 5.31 4.05 3.45 3.11 2.88 2.73 2.61 2.52 2.45 2.39 2.35 2.31 2.27 2.24 2.22 2.20 2.18 2.16 2.14 2.13 2.11 2.10 2.09 2.08 2.07 2.06 2.06 2.05 2.00 1.95 1.90 1.85
6 58.20 9.33 5.28 4.01 3.40 3.05 2.83 2.67 2.55 2.46 2.39 2.33 2.28 2.24 2.21 2.18 2.15 2.13 2.11 2.09 2.08 2.06 2.05 2.04 2.02 2.01 2.00 2.00 1.99 1.98 1.93 1.87 1.82 1.77
7 58.91 9.35 5.27 3.98 3.37 3.01 2.78 2.62 2.51 2.41 2.34 2.28 2.23 2.19 2.16 2.13 2.10 2.08 2.06 2.04 2.02 2.01 1.99 1.98 1.97 1.96 1.95 1.94 1.93 1.93 1.87 1.82 1.77 1.72
8 59.44 9.37 5.25 3.95 3.34 2.98 2.75 2.59 2.47 2.38 2.30 2.24 2.20 2.15 2.12 2.09 2.06 2.04 2.02 2.00 1.98 1.97 1.95 1.94 1.93 1.92 1.91 1.90 1.89 1.88 1.83 1.77 1.72 1.67
α = 0,10 ν1 9 10 59.86 60.19 9.38 9.39 5.24 5.23 3.94 3.92 3.32 3.30 2.96 2.94 2.72 2.70 2.56 2.54 2.44 2.42 2.35 2.32 2.27 2.25 2.21 2.19 2.16 2.14 2.12 2.10 2.09 2.06 2.06 2.03 2.03 2.00 2.00 1.98 1.98 1.96 1.96 1.94 1.95 1.92 1.93 1.90 1.92 1.89 1.91 1.88 1.89 1.87 1.88 1.86 1.87 1.85 1.87 1.84 1.86 1.83 1.85 1.82 1.79 1.76 1.74 1.71 1.68 1.65 1.63 1.60
12 60.71 9.41 5.22 3.90 3.27 2.90 2.67 2.50 2.38 2.28 2.21 2.15 2.10 2.05 2.02 1.99 1.96 1.93 1.91 1.89 1.87 1.86 1.84 1.83 1.82 1.81 1.80 1.79 1.78 1.77 1.71 1.66 1.60 1.55
15 61.22 9.42 5.20 3.87 3.24 2.87 2.63 2.46 2.34 2.24 2.17 2.10 2.05 2.01 1.97 1.94 1.91 1.89 1.86 1.84 1.83 1.81 1.80 1.78 1.77 1.76 1.75 1.74 1.73 1.72 1.66 1.60 1.55 1.49
20 61.74 9.44 5.18 3.84 3.21 2.84 2.59 2.42 2.30 2.20 2.12 2.06 2.01 1.96 1.92 1.89 1.86 1.84 1.81 1.79 1.78 1.76 1.74 1.73 1.72 1.71 1.70 1.69 1.68 1.67 1.61 1.54 1.48 1.42
24 62.00 9.45 5.18 3.83 3.19 2.82 2.58 2.40 2.28 2.18 2.10 2.04 1.98 1.94 1,90 1.87 1.84 1.81 1.79 1.77 1.75 1.73 1.72 1.70 1.69 1.68 1.67 1.66 1.65 1.64 1.57 1.51 1.45 1.38
30 62.26 9.46 5.17 3.82 3.17 2.80 2.56 2.38 2.25 2.16 2.08 2.01 1.96 1.91 1.87 1.84 1.81 1.78 1.76 1.74 1.72 1.70 1.69 1.67 1.66 1.65 1.64 1.63 1.62 1.61 1.54 1.48 1.41 1.34
40 62.53 9.47 5.16 3.80 3.16 2.78 2.54 2.36 2.23 2.13 2.05 1.99 1.93 1.89 1.85 1.81 1.78 1.75 1.73 1.71 1.69 1.67 1.66 1.64 1.63 1.61 1.60 1.59 1.58 1.57 1.51 1.44 1.37 1.30
60 62.79 9.47 5.15 3.79 3.14 2.76 2.51 2.34 2.21 2.11 2.03 1.96 1.90 1.86 1.82 1.78 1.75 1.72 1.70 1.68 1.66 1.64 1.62 1.61 1.59 1.58 1.57 1.56 1.55 1.54 1.47 1.40 1.32 1.24
120 63.06 9.48 5.14 3.78 3.12 2.74 2.49 2.32 2.18 2.08 2.00 1.93 1.88 1.83 1.79 1.75 1.72 1.69 1,67 1.64 1.62 1.60 1.59 1.57 1.56 1.54 1.53 1.52 1.51 1.50 1.42 1.35 1.26 1.17
∞ 63.33 9.49 5.13 3.76 3.10 2.72 2.47 2.29 2.16 2.06 1.97 1.90 1.85 1.80 1.76 1.72 1.69 1.66 1.63 1.61 1.59 1.57 1.55 1.53 1.52 1.50 1.49 1.48 1.47 1.46 1.38 1.29 1.19 1.00
Tabla VI. Valores críticos de la distribución F de Snedecor: Abcisas Fα;ν 1 ,ν 2 que dejan a su derecha un área α bajo la F con ν 1 y ν 2 grados de libertad.
ν2 1 2 3 4 5 6 7 8 9 l0 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 ∞
1 161.4 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 4.41 4.38 4.35 4.32 4.30 4.28 4.26 4.24 4.23 4.21 4.20 4.18 4.17 4.08 4.00 3.92 3.84
2 199.5 19.00 9.55 6.94 5.79 5.14 4.74 4.46 4.26 4.10 3.98 3.89 3.81 3.74 3.68 3.63 3.59 3.55 3.52 3.49 3.47 3.44 3.42 3.40 3.39 3.37 3.35 3.34 3.33 3.32 3.23 3.15 3.07 3.00
3 215.7 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 3.16 3.13 3.10 3.07 3.05 3.03 3.01 2.99 2.98 2.96 2.95 2.93 2.92 2.84 2.76 2.68 2.60
4 224.6 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 2.93 2.90 2.87 2.84 2.82 2.80 2.78 2.76 2.74 2.73 2.71 2.70 2.69 2.61 2.53 2.45 2.37
5 230.2 19.30 9.01 6.26 5.05 4.39 3.97 3.69 3.48 3.33 3.20 3.11 3.03 2.96 2.90 2.85 2.81 2.77 2.74 2.71 2.68 2.66 2.64 2.62 2.60 2.59 2.57 2.56 2.55 2.53 2.45 2.37 2.29 2.21
6 234.0 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 2.66 2.63 2.60 2.57 2.55 2.53 2.51 2.49 2.47 2.46 2.45 2.43 2.42 2.34 2.25 2.17 2.10
7 236.8 19.35 8.89 6.09 4.88 4.21 3.79 3.50 3.29 3.14 3.01 2.91 2.83 2.76 2.71 2.66 2.61 2.58 2.54 2.51 2.49 2.46 2.44 2.42 2.40 2.39 2.37 2.36 2.35 2.33 2.25 2.17 2.09 2.01
8 238.9 19.37 8.85 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 2.51 2.48 2.45 2.42 2.40 2.37 2.36 2.34 2.32 2.31 2.29 2.28 2.27 2.18 2.10 2.02 1.94
α = 0,05 ν1 9 10 240.5 241.9 19.38 19.40 8.81 8.79 6.00 5.96 4.77 4.74 4.10 4.06 3.68 3.64 3.39 3.35 3.18 3.14 3.02 2.98 2.90 2.85 2.80 2.75 2.71 2.67 2.65 2.60 2.59 2.54 2.54 2,49 2.49 2.45 2.46 2.41 2.42 2.38 2.39 2.35 2.37 2.32 2.34 2.30 2.32 2.27 2.30 2.25 2.28 2.24 2.27 2.22 2.25 2.20 2.24 2.19 2.22 2.18 2.21 2.16 2.12 2.08 2.04 1.99 1.96 1.91 1.88 1.83
12 243.9 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 2.34 2.31 2.28 2.25 2.23 2.20 2.18 2.16 2.15 2.13 2,12 2.10 2.09 2.00 1.92 1.83 1.75
15 245.9 19.43 8.70 5.86 4.62 3.94 3.51 3.22 3.01 2.85 2.72 2.62 2.53 2.46 2.40 2.35 2.31 2.27 2.23 2.20 2.18 2.15 2.13 2.11 2.09 2.07 2.06 2.04 2.03 2.01 1.92 1.84 1.75 1.67
20 248.0 19.45 8.66 5.80 4.56 3.87 3.44 3.15 2.94 2.77 2.65 2.54 2.46 2.39 2.33 2.28 2.23 2.19 2.16 2.12 2.10 2.07 2.05 2.03 2.01 1.99 1.97 1.96 1.94 1.93 1.84 1.75 1.66 1.57
24 249.1 19.45 8,64 5.77 4.53 3.84 3.41 3.12 2.90 2.74 2.61 2.51 2.42 2.35 2.29 2.24 2.19 2.15 2.11 2.08 2.05 2.03 2.01 1.98 1.96 1.95 1.93 1.91 1.90 1.89 1.79 1.70 1.61 1.52
30 250.1 19.46 8.62 5.75 4.50 3.81 3.38 3.08 2.86 2.70 2.57 2.47 2.38 2.31 2.25 2.19 2.15 2.11 2.07 2.04 2.01 1.98 1.96 1.94 1.92 1.90 1.88 1.87 1.85 1.84 1.74 1.65 1.55 1.46
40 251.1 19.47 8.59 5.72 4.46 3.77 3.34 3.04 2.83 2.66 2.53 2.43 2.34 2.27 2.20 2.15 2.10 2.06 2.03 1.99 1.96 1.94 1.91 1.89 1.87 1.85 1.84 1.82 1.81 1.79 1.69 1.59 1.50 1.39
60 252.2 19.48 8.57 5.69 4.43 3.74 3.30 3.01 2 79 2.62 2.49 2.38 2.30 1.22 2.16 2.11 2.06 2.02 1.98 1.95 1.92 1.89 1.86 1.84 1.82 1.80 1.79 1.77 1.75 1.74 1.64 1.53 1.43 1.32
120 253.3 19.49 8.55 5.66 4.40 3.70 3.27 2.97 2.75 2.58 2.45 2.34 2.25 2.18 2.11 2.06 2.01 1.97 1.93 1.90 1.87 1.84 1.81 1.79 1.77 1.75 1.73 1.71 1.70 1.68 1.58 1.47 1.35 1.22
∞ 254.3 19.50 8.53 5.63 4.36 3.67 3.23 2.93 2.71 2.54 2.40 2.30 2.21 2.13 2.07 2.01 1.96 1.92 1.88 1.84 1.81 1.78 1.76 1.73 1.71 1.69 1.67 1.65 1.64 1.62 1.51 1.39 1.25 1.00
Tabla VI. Valores críticos de la distribución F de Snedecor: Abcisas Fα;ν 1 ,ν 2 que dejan a su derecha un área α bajo la F con ν 1 y ν 2 grados de libertad.
ν2 1 2 3 4 5 6 7 8 9 l0 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 ∞
1 647.8 38.51 17.44 12.22 10.01 8.81 8.07 7.57 7.21 6.94 6.72 6.55 6.41 6.30 6.20 6.12 6.04 5.98 5.92 5.87 5.83 5.79 5.75 5.72 5.69 5.66 5.63 5.61 5.59 5.57 5.42 5.29 5.15 5.02
2 799.5 39.00 16.04 10.65 8.43 7.26 6.54 6.06 5.71 5.46 5.26 5.10 4.97 4.86 4.77 4.69 4.62 4.56 4.51 4.46 4.42 4.38 4.35 4.32 4.29 4.27 4.24 4.22 4.20 4.18 4.05 3.93 3.80 3.69
3 864.2 39.17 15.44 9.98 7.76 6.60 5.89 5.42 5.00 4.83 4.63 4.47 4.35 4.24 4.15 4.08 4.01 3.95 3.90 3.86 3.82 3.78 3.75 3.72 3.69 3.67 3.63 3.63 3.61 3.59 3.46 3.34 3.23 3.12
4 899.6 39.25 15.10 9.60 7.39 6.23 5.52 5.05 4.72 4.47 4.28 4.12 4.00 3.89 3.80 3.73 3.66 3.61 3.56 3.51 3.48 3.44 3.41 3.38 3.35 3.33 3.31 3.29 3.27 3.25 3.13 3.01 2.89 2.79
5 921.8 39.30 14.88 9.36 7.15 5.99 5.29 4.82 4.48 4.24 4.04 3.89 3.77 3.66 3.58 3.50 3.44 3.38 3.33 3.29 3.25 3.22 3.18 3.15 3.13 3.10 3.06 3.06 3.04 3.03 2.90 2.79 2.67 2.57
6 937.1 39.33 14.73 9.20 6.98 5.82 5.12 4.65 4.32 4.07 3.88 3.73 3.60 3.50 3.41 3.34 3.28 3.22 3.17 3.13 3.09 3.05 3.02 2.99 2.97 2.94 2.92 2.90 2.88 2.87 2.74 2.63 2.52 2.41
7 948.2 39.36 14.62 9.07 6.85 5.70 4.99 4.53 4.20 3.95 3.76 3.61 3.48 3.38 3.29 3.22 3.16 3.10 3.05 3.01 2.97 2.93 2.90 2.87 2.85 2.82 2.80 2.78 2.76 2.75 2.62 2.51 2.39 2.29
8 956.7 39.37 14.54 8.98 6.76 5.60 4.90 4.43 4.10 3.85 3.66 3.51 3.39 3.29 3.20 3.12 3.06 3.01 2.96 2.91 2.87 2.84 2.81 2.78 2.75 2.73 2.71 2.69 2.67 2.65 2.53 2.41 2.30 2.19
α = 0,025 ν1 9 10 963.3 968.6 39.39 39.40 14.47 14.42 8.90 8.84 6.68 6.62 5.52 5.46 4.82 4.76 4.36 4.30 4.03 3.96 3.78 3.72 3.59 3.53 3.44 3.37 3.31 3.25 3.21 3.15 3.12 3 06 3.05 2.99 2.98 2.92 2.93 2.87 2.88 2.82 2.84 2.77 2.80 2.73 2,76 2.70 2.73 2.67 2.70 2.64 2.68 2.61 2.65 2.59 2.63 2.57 2.61 2.55 2.59 2.53 2.57 2.51 2.45 2.39 2.33 2.27 2.22 2.16 2.11 2.05
12 976.7 39.41 14.34 8.75 6.52 5.37 4.67 4.20 3.87 3.62 3.43 3.28 3.15 3.05 2.96 2.89 2.82 2.77 2.72 2.68 2.64 2.60 2.57 2.54 2.51 2.49 2.47 2.45 2.43 2.41 2.29 2.17 2.05 1.94
15 984.9 39.43 14.25 8.66 6.43 5.27 4.57 4.10 3.77 3.52 3.33 3.18 3.05 2.95 2.86 2.79 2.72 2.67 2.62 2.57 2.53 2.50 2.47 2.44 2.41 2.39 2.36 2.34 2.32 2.31 2.18 2.06 1.94 1.83
20 993.1 39.45 14.17 8.56 6.33 5.17 4.47 4.00 3.67 3.42 3.23 3.07 2.95 2.84 2.76 2.68 2.62 2.56 2.51 2.46 2.42 2.39 2.36 2.33 2.30 2.28 2.25 2.23 2.21 2.20 2.07 1.94 1.82 1.71
24 997.2 39.46 14.12 8.51 6.28 5.12 4.42 3.95 3.61 3.37 3.17 3.02 2.89 2.79 2.70 2.63 2.56 2.50 2.45 2.41 2.37 2.33 2.30 2.27 2.24 2.22 2.19 2.17 2.15 2.14 2.01 1.88 1.76 1.64
30 1001 39.46 14.08 8.46 6.23 5.07 4.36 3.89 3.56 3.31 3.12 2.96 2.84 2.73 2.64 2.57 2.50 2.44 2.39 2.35 2.31 2.27 2.24 2.21 2.18 2.16 2.13 2.11 2.09 2.07 1.94 1.82 1.69 1.57
40 1006 39.47 14.04 8.41 6.18 5.01 4.31 3.84 3.51 3.26 3.06 2.91 2.78 2.67 2.59 2.51 2.44 2.38 2.33 2.29 2.25 2.21 2.18 2.15 2.12 2.09 2.07 2.05 2.03 2.01 1.88 1.74 1.61 1.48
60 1010 39.48 13.99 8.36 6.12 4.96 4.25 3.78 3.45 3.20 3.00 2.85 2.72 2.61 2.52 2.45 2.38 2.32 2.27 2.22 2.18 2.14 2.11 2.08 2.05 2.03 2.00 l.98 l.96 1.94 1.80 1.67 1.53 1.39
120 1014 39.49 13.95 8.31 6.07 4.90 4.20 3.73 3.39 3.14 2.94 2.79 2.66 2.55 2.46 2.38 2.32 2.26 2.20 2.16 2.11 2.08 2.04 2.01 1.98 1.95 1.93 1.91 1.89 1.87 1.72 1.58 1.43 1.27
∞ 1018 39.50 13.90 8.26 6.02 4.85 4.14 3.67 3.33 3.08 2.88 2.72 2.60 2.49 2.40 2.32 2.25 2.19 2.13 2.09 2.04 2.00 1.97 1.94 1.91 1.88 1.85 1.83 1.81 1.79 1.64 1.48 1.31 1.00
Tabla VI. Valores críticos de la distribución F de Snedecor: Abcisas Fα;ν 1 ,ν 2 que dejan a su derecha un área α bajo la F con ν 1 y ν 2 grados de libertad.
ν2 1 2 3 4 5 6 7 8 9 l0 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 ∞
1 4052 98.50 34.12 21.20 16.26 13.75 12.25 11.26 10.56 10.04 9.65 9.33 9.07 8.86 8.68 8.53 8.40 8.29 8.18 8.10 8.02 7.95 7.88 7.82 7.77 7.72 7.68 7.64 7.60 7.56 7.31 7.08 6.85 6.63
2 4999.50 99.00 30.82 18,00 13.27 10.92 9.55 8.65 8.02 7.56 7.21 6.93 6.70 6.51 6.36 6.23 6.11 6.01 5.93 5.85 5.78 5.72 5.66 5.61 5.57 5.53 5.49 5.45 5.42 5.39 5.18 4.98 4.79 4.61
3 5403 99.17 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 5.09 5.01 4.94 4.87 4.82 4.76 4.72 4.68 4.64 4.60 4.57 4.54 4.51 4.31 4.13 3.95 3.78
4 5625 99.25 28.71 15.98 11.39 9.15 7.85 7.01 6.42 5.99 5.67 5.41 5.21 5.04 4.89 4.77 4.67 4.58 4.50 4.43 4.37 4.31 4.26 4.22 4.18 4.14 4.11 4.07 4.04 4.02 3.83 3.65 3.48 3.32
5 5764 99.30 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 4.25 4.17 4.10 4.04 3.99 3.94 3.90 3.85 3.82 3.78 3.75 3.73 3.70 3.51 3.34 3.17 3.02
6 5859 99.33 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 4.01 3.94 3.87 3.81 3.76 3.71 3.67 3.63 3.59 3.56 3.53 3.50 3.47 3.29 3.12 2.96 2.80
7 5928 99.36 27.67 14.98 10.46 8.26 6.99 6.18 5.61 5.20 4.89 4.64 4.44 4.28 4.14 4.03 3.93 3.84 3.77 3.70 3.64 3.59 3.54 3.50 3.46 3.42 3.39 3.36 3.33 3.30 3.12 2.95 2.79 2.64
8 5982 99.37 27.49 14.80 10.29 8.10 6.84 6.03 5.47 5.06 4.74 4.50 4.30 4.14 4.00 3.89 3.79 3.71 3.63 3,56 3.51 3.45 3.41 3.36 3.32 3.29 3.26 3.23 3.20 3.17 2.99 2.82 2.66 2.51
α = 0,01 ν1 9 10 6022 6056 99.39 99.40 27.35 27.23 14.66 14.55 10.16 10.05 7.98 7.87 6.72 6.62 5.91 5.81 5.35 5.26 4.94 4.85 4.63 4.54 4.39 4.30 4.19 4.10 4.03 3.94 3.89 3.80 3.78 3.69 3.68 3.59 3.60 3.51 3.52 3.43 3.46 3.37 3.40 3.31 3.35 3.26 3.30 3,21 3.26 3.17 3.22 3.13 3.18 3.09 3.15 3.06 3.12 3.03 3.09 3.00 3.07 2.98 2.89 2.80 2.72 2.63 2.56 2.47 2.41 2.32
12 6106 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 3.37 3.30 3.23 3.17 3.12 3.07 3.03 2.99 2.96 2.93 2.90 2.87 2.84 2.66 2.50 2.34 2.18
15 6157 99.43 26.87 14.20 9.72 7.56 6.31 5.52 4.96 4.56 4.25 4.01 3.82 3.66 3.52 3.41 3.31 3.23 3.15 3.09 3.03 2.98 2.93 2.89 2.85 2,81 2.78 2.75 2.73 2.70 2.52 2.35 2.19 2.04
20 6209 99.45 26.69 14.02 9.55 7.40 6.16 5.36 4.81 4.41 4.10 3.86 3.66 3.51 3.37 3.26 3.16 3.08 3.00 2.94 2.88 2.83 2.78 2.74 2.70 2.66 2.63 2.60 2.57 2.55 2.37 2.20 2.03 1.88
24 6235 99.46 26.60 13.93 9.47 7.31 6.07 5.28 4.73 4.33 4.02 3.78 3.59 3.43 3.29 3.18 3.08 3.00 2.92 2.86 2.80 2.75 2.70 2.66 2.62 2.58 2.55 2.52 2.49 2.47 2.29 2.12 1.95 1.79
30 6261 99.47 26.50 13.84 9.38 7.23 5.99 5.20 4.65 4.25 3.94 3.70 3.51 3.35 3.21 3.10 3.00 2.92 2.84 2.78 2.72 2.67 2.62 2.58 2.54 2.50 2.47 2.44 2.41 2.39 2.20 2.03 1.86 1.70
40 6287 99.47 26.41 13.75 9.29 7.14 5.91 5.12 4.57 4.17 3.86 3.62 3.43 3.27 3.13 3.02 2.92 2.84 2.76 2.69 2.64 2.58 2.54 2.49 2.45 2.42 2.38 2.35 2.33 2.30 2.11 1.94 1.76 1.59
60 6313 99.48 26.32 13.65 9.20 7.06 5.82 5.03 4.48 4.08 3.78 3.54 3.34 3.18 3.05 2.93 2.83 2.75 2.67 2.61 2.55 2.50 2.45 2.40 2.36 2.33 2.29 2.26 2.23 2.21 2.02 1.84 1.66 1.47
120 6339 99.49 26.22 13.56 9.11 6.97 5.74 4.95 4.40 4.00 3.69 3.45 3.25 3.09 2.96 2.84 2.75 2.66 2.58 2.52 2.46 2.40 2.35 2.31 2.27 2.23 2.20 2.17 2.14 2.11 1.92 1.73 1.53 1.32
∞ 6366 99.50 26.13 13.46 9.02 6.88 5.65 4.86 4.31 3.91 3.60 3.36 3.17 3.00 2.87 2.75 2.65 2.57 2.49 2.42 2.36 2.31 2.26 2.21 2.17 2.13 2.10 2.06 2.03 2.01 1.80 1.60 1.38 1.00
Tabla VI. Valores críticos de la distribución F de Snedecor: Abcisas Fα;ν 1 ,ν 2 que dejan a su derecha un área α bajo la F con ν 1 y ν 2 grados de libertad.
ν2 1 2 3 4 5 6 7 8 9 l0 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 ∞
1 16211 198.5 55.55 31.33 22.78 18.64 16.24 14.69 13.61 12.83 12.23 11.75 11.37 11.06 10.80 10.58 10.38 10.22 10.07 9.94 9.83 9.73 9.63 9.55 9.48 9.41 9.34 9.28 9.23 9.18 8.83 8.49 8.18 7.88
2 20000 199.0 49.80 26.28 18.31 14.54 12.40 11.04 10.11 9.43 8.91 8.51 8.19 7.92 7.70 7.51 7.35 7.21 7.09 6.99 6.89 6.81 6.73 6.66 6.60 6.54 6.49 6.44 6.40 6.35 6.07 5.79 5.54 5.30
3 21615 199.2 47.46 24.25 16.53 12.92 10.88 9.60 8.72 8.08 7.60 7.23 6.93 6.68 6.48 6.30 6.16 6.06 5.92 5.82 5.73 5.65 5.58 5.52 5.46 5.41 5.36 5.32 5.28 5.24 4.94 4.73 4.50 4.28
4 22500 199.2 46.17 23.15 15.56 12.03 10.05 8.81 7.96 7.34 6.88 6.52 6.23 6.00 5.80 5.64 5.50 5.37 5.27 5.17 5.09 5.02 4.95 4.89 4.84 4.79 4.74 4.70 4.66 4.62 4.37 4.14 3.92 3.72
5 23056 199.3 45.42 22.46 14.94 11.46 9.52 8.30 7.47 6.87 6.42 6.07 5.79 5.56 5.37 5.21 5.07 4.96 4.85 4.76 4.68 4.61 4.54 4.49 4.43 4.38 4.34 4.30 4.26 4.23 3.99 3.76 3.55 3.35
6 23437 199.3 44.85 21.98 14.51 11.07 9.16 7.95 7.13 6.54 6.10 5.76 5.48 5.26 5.07 4.91 4.78 4.66 4.56 4.47 4.39 4.32 4.26 4.20 4.15 4.10 4.06 4.02 3.98 3.95 3.71 3.49 3.28 3.09
7 23715 199.4 44.40 21.62 14.20 10.79 8.89 7.69 6.89 6.30 5.86 5.52 5.25 5.03 4.85 4.69 4.56 4.44 4.34 4.26 4.18 4.11 4.05 3.99 3.94 3.89 3.85 3.81 3.77 3.74 3.51 3.29 3.09 2.90
8 23925 199.4 44.11 21.35 13.96 10.57 6.68 7.50 6.69 6.12 5.68 5.34 5.08 4.86 4.67 4.52 4.39 4.28 4.18 4.09 4.01 3.94 3.88 3.83 3.78 3.73 3.69 3.65 3.61 3.58 3.35 3.13 2.93 2.74
α = 0,005 ν1 9 10 24091 24224 199.4 199.4 43.84 43.73 21.14 20.97 13.77 13.62 10.39 10.25 8.51 8.38 7.34 7.21 6.54 6.42 5.97 5.85 5.54 5.42 5.20 5.09 4.94 4.82 4.72 4.60 4.54 4.42 4.38 4.27 4.25 4.14 4.14 4.03 4.04 3.93 3.96 3.85 3.88 3.77 3.81 3.70 3.75 3.64 3.69 3.59 3.64 3.54 3.60 3.49 3.56 3.45 3.52 3.41 3.48 3.38 3.45 3.34 3.22 3.12 3.01 2.90 2.81 2.71 2.62 2.52
12 24426 199.4 43.38 20.70 13.39 10.03 8.18 7.02 6.23 5.66 5.24 4.91 4.64 4.43 4.25 4.10 3.97 3.86 3.76 3.68 3.60 3.53 3.47 3.42 3.37 3.33 3.28 3.25 3.21 3.18 2.95 2.74 2.54 2.36
15 24630 199.4 43.13 20.43 13.15 9.81 7.97 6.82 6.03 5.47 5.05 4.72 4.46 4.25 4.07 3.92 3.79 3.68 3.59 3.50 3.43 3.36 3.30 3.25 3.20 3.15 3.11 3.07 3.04 3.01 2.78 2.57 2.37 2.19
20 24836 199.5 42.87 20.17 12.90 9.59 7.75 6.61 5.83 5.27 4.86 4.53 4.27 4.06 3.88 3.73 3.61 3.50 3.40 3.32 3.24 3.18 3.12 3.06 3.01 2.97 2.93 2.89 2.86 2.82 2.60 2.39 2.19 2.00
24 24940 199.5 42.65 20.04 12.78 9.48 7.64 6.50 5.73 5.17 4.76 4.43 4.17 3.96 3.79 3.64 3.51 3.40 3.31 3.22 3.15 3.08 3.02 2.97 2.92 2.87 2.83 2.79 2.76 2.73 2.50 2.29 2.09 1.90
30 25044 199.5 42.47 19.89 12.66 9.36 7.53 6.40 5.62 5.07 4.65 4.33 4.07 3.86 3.69 3.54 3.41 3.30 3.21 3.12 3.05 2.98 2.92 2.87 2.82 2.77 2.73 2.69 2.66 2.63 2.40 2.19 1.98 1.79
40 25148 199.5 42.31 19.75 12.53 9.24 7.42 6.29 5.52 4.97 4.55 4.23 3.97 3.76 3.58 3.44 3.31 3.20 3.11 3.02 2.95 2.88 2.82 2.77 2.72 2.67 2.63 2.59 2.56 2.52 2.30 2.08 1.87 1.67
60 25253 199.5 42.15 19.61 12.40 9.12 7.31 6.18 5.41 4.86 4.45 4.12 3.87 3.86 3.48 3.33 3.21 3.10 3.00 2.92 2.84 2.77 2.71 2.66 2.61 2.56 2.52 2.48 2.45 2.42 2.18 1.96 1.75 1.53
120 25359 19.49 41.99 19.47 12.27 9.00 7.19 6.06 5.30 4.75 4.34 4.02 3.76 3.55 3.37 3.22 3.10 2.99 2.89 2.81 2.73 2.66 2.60 2.55 2.50 2.45 2.41 2.37 2.33 2.30 2.06 1.83 1.61 1.36
∞ 25465 19.50 41.83 19.32 12.14 8.88 7.08 5.95 5.19 4.64 4.23 3.90 3.65 3.44 3.26 3.11 2.98 2.87 2.78 2.69 2.61 2.55 2.48 2.43 2.38 2.33 2.29 2.25 2.21 2.18 1.93 1.69 1.43 1.00
Tabla VI. Valores críticos de la distribución F de Snedecor: Abcisas Fα;ν 1 ,ν 2 que dejan a su derecha un área α bajo la F con ν 1 y ν 2 grados de libertad.
ν2 1 1 4053* 998.5 2 167.0 3 74.14 4 47.18 5 35.51 6 29.25 7 25.42 8 22.86 9 21.04 l0 19.69 11 18.64 12 17.81 13 17.14 14 16.59 15 16.12 16 15.72 17 15.38 18 15.08 19 14.82 20 14.59 21 14.38 22 14.19 23 14.03 24 13.88 25 13.74 26 13.61 27 13.50 28 13.39 29 13.29 30 12.61 40 11.97 60 120 11.38 10.83 ∞ * Multiplicar
2 3 5000* 5404* 999.0 999.2 148.5 141.1 61.25 56.18 37.12 33.20 27.00 23.70 21.69 18.77 18.49 15.83 16.39 13.90 14.91 12.55 13.81 11.56 12.97 10.80 12.31 10.21 11.78 9.73 11.34 9.34 10.97 9.00 10.66 8.73 10.39 8.49 10.16 8.28 9.95 8.10 9.77 7,94 9.61 7.80 9.47 7.67 9.34 7.55 9.22 7.45 9.12 7.36 9.02 7.27 8.93 7.19 8.85 7.12 8.77 7,05 8.25 6.60 7.76 6.17 7.32 5.79 6.91 5.42 estas celdas por
4 5625* 999.2 137.1 53.44 31.09 21.92 17.19 14.39 12.56 11.28 10.35 9.63 9.07 8.62 8.25 7.94 7.68 7.46 7.26 7.10 6.95 6.81 6.69 6.59 6.49 6.41 6.33 6.25 6.19 6.12 5.70 5.31 4.95 4.621 100
5 5764* 999.3 134.6 51.71 29.75 20.81 16.21 13.49 11.71 10.48 9.58 8.89 8.35 7.92 7.57 7.27 7.02 6.81 6.62 6.46 6.32 6.19 6.08 5.98 5.88 5.80 5.73 5.66 5.59 5.53 5.13 4.76 4.42 4.10
6 5859* 999.3 132.8 50.53 28.84 20.03 15.52 12.86 11.13 9.92 9.05 8.38 7.86 7.43 7.09 6.81 6.56 6.35 6.18 6.02 5.88 5.76 5.65 5.55 5.46 5.38 5.31 5.24 5.18 5.12 4.73 4.37 4.04 3.74
7 5929* 999.4 131.6 49.66 28.16 19.46 15.02 12.40 10.70 9.52 8.66 8.00 7.49 7.08 6.74 6.46 6.22 6.02 5.85 5.69 5.56 5.44 5.33 5.23 5.15 5.07 5.00 4.93 4.87 4.82 4.44 4.09 3.77 3.47
8 5981* 999.4 130.6 49.00 27.64 19.03 14.63 12.04 10.37 9.20 8.35 7.71 7.21 6.80 6.47 6.19 5.96 5.76 5.59 5.44 5.31 5.19 5.09 4.99 4.91 4.83 4.76 4.69 4.64 4.58 4.21 3.87 3.55 3.27
α = 0,001 ν1 9 10 6023* 6056* 999.4 999.4 129.9 129.2 48.47 48.05 27.24 26.92 18.69 18.41 14.33 14.08 11.77 11.54 10.11 9.89 8.96 8.75 8.12 7.92 7.48 7.29 6.98 6.80 6.58 6.40 6.26 6.08 5.98 5.81 5.75 5.58 5.56 5.39 5.39 5.22 5.24 5.08 5.11 4.95 4.99 4.83 4.89 4.73 4.80 4.64 4.71 4.56 4.64 4.48 4.57 4.41 4.50 4.35 4.45 4.29 4.39 4.24 4.02 3.87 3.69 3.54 3.38 3.24 3.10 2.96
12 6107* 999.4 128.3 47.41 26.42 17.99 13.71 11.19 9.57 8.45 7.63 7.00 6.52 6.13 5.81 5.55 5.32 5.13 4.97 4.82 4.70 4.58 4.48 4.39 4.31 4.24 4.17 4.11 4.05 4.00 3.64 3.31 3.02 2.74
15 6158* 999.4 127.4 46.76 25.91 17.56 13.32 10.84 9.24 8.13 7.32 6.71 6.23 5.85 5.54 5.27 5.05 4.87 4.70 4.56 4.44 4.33 4.23 4.14 4.06 3.99 3.92 3.86 3.80 3.75 3.40 3,08 2.78 2.51
20 6209* 999.4 126.4 46.10 25.39 17.12 12.93 10.48 8.90 7.80 7.01 6.40 5.93 5.56 5.25 4.99 4.78 4.59 4.43 4.29 4.17 4.06 3.96 3.87 3.79 3.72 3.66 3.60 3.54 3.49 3.15 2.83 2.53 2.27
24 6235* 999.5 125.9 45.77 25.14 16.89 12.73 10.30 8.72 7.64 6.85 6.25 5.78 5.41 5.10 4.85 4.63 4.45 4.29 4.15 4.03 3.92 3.82 3.74 3.66 3.59 3.52 3.46 3.41 3.36 3.01 2.69 2.40 2.13
30 6261* 999.5 125.4 45.43 24.87 16.67 12.53 10.11 8.55 7.47 6.68 6.09 5.63 5.25 4.95 4.70 4.48 4.30 4.14 4.00 3.88 3.78 3.68 3.59 3.52 3.44 3.38 3.32 3.27 3.22 2.87 2.55 2.26 1.99
40 6287* 999.5 125.0 45.09 24.60 16.44 12.33 9.92 8.37 7.30 6.52 5.93 5.47 5.10 4.80 4.54 4.33 4.15 3.99 3.86 3.74 3.63 3.53 3.45 3.37 3.30 3.23 3.18 3.12 3.07 2.73 2.41 2.11 1.84
60 6313* 999.5 124.5 44.75 24.33 16.21 12.12 9.73 8.19 7.12 6.35 5.76 5.30 4.94 4.64 4.39 4.18 4.00 3.84 3.70 3.58 3.48 3.38 3.29 3.22 3.15 3.08 3.02 2.97 2.92 2.57 2.25 1.95 1.66
120 6340* 999.5 124.0 44.40 24.06 15.99 11.91 9.53 8.00 6.94 6.17 5.59 5.14 4.77 4.47 4.23 4.02 3.84 3.68 3.54 3.42 3.32 3.22 3.14 3.06 2.99 2.92 2.86 2,81 2.76 2.41 2.08 1.76 1.45
∞ 6366* 999.5 123.5 44.05 23.79 15.75 11.70 9.33 7.81 6.76 6.00 5.42 4.97 4.60 4.31 4.06 3.85 3.67 3.51 3.38 3.26 3.15 3.05 2.97 2.89 2.82 2.75 2.69 2.64 2.59 2.23 1.89 1.54 1.00
