Tablas estadisticas

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Tablas estadisticas

  1. 1. Curso: Estadística Aplicada APÉNDICE TABLAS ESTADÍSTICAS
  2. 2. Curso: Estadística Aplicada Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 .0279 .0319 .0359 .1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 .0714 .0753 .2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 .1064 .1103 .1141 .3 .1179 .1217 .1255 .1293 .1331 .1368 .1406 .1443 .1480 .1879 .4 .1554 .1591 .1628 .1664 .1700 .1736 .1772 .1808 .1844 .1879 .5 .1915 .1950 .1985 .2019 .2054 .2088 .2123 .2157 .2190 .2224 .6 .2257 .2291 .2324 .2357 .2389 .2422 .2454 .2486 .2518 .2549 .7 .2580 .2612 .2642 .2673 .2704 .2734 .2764 .2794 .2823 .2852 .8 .2881 .2910 .2939 .2967 .2995 .3023 .3051 .3078 .3106 .3133 .9 .3159 .3186 .3212 .3238 .3264 .3289 .3315 .3340 .3365 .3389 1.0 .3413 .3438 .3461 .3485 .3508 .3531 .3554 .3577 .3599 .3621 1.1 .3643 .3665 .3686 .3708 .3729 .3749 .3770 .3790 .3810 .3830 1.2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 .3980 .3997 .4015 1.3 .4032 .4049 .4066 .4082 .4099 .4115 .4131 .4147 .4162 .4177 1.4 .4192 .4207 .4222 .4236 .4251 .4265 .4279 .4292 .4306 .4319 1.5 .4332 .4345 .4357 .4370 .4382 .4394 .4406 .4418 .4429 .4441 1.6 .4452 .4463 .4474 .4484 .4495 .4505 .4515 .4525 .4535 .4545 1.7 .4554 .4564 .4573 .4582 .4591 .4599 .4608 .4616 .4625 .4633 1.8 .4641 .4649 .4656 .4664 .4671 .4678 .4686 .4693 .4699 .4706 1.9 .4713 .4719 .4726 .4732 .4738 .4744 .4750 .4756 .4761 .4767 2.0 .4772 .4778 .4783 .4788 .4793 .4798 .4803 .4808 .4812 .4817 2.1 .4821 .4826 .4830 .4834 .4838 .4842 .4846 .4850 .4854 .4857 2.2 .4861 .4864 .4868 .4871 .4875 .4878 .4881 .4884 .4887 .4890 2.3 .4893 .4896 .4898 .4901 .4909 .4906 .4909 .4911 .4913 .4916 2.4 .4918 .4920 .4922 .4925 .4927 .4929 .4931 .4932 .4934 .4936 2.5 .4938 .4940 .4941 .4943 .4945 .4946 .4948 .4949 .4951 .4952 2.6 .4953 .4955 .4956 .4957 .4959 .4960 .4961 .4962 .4963 .4964 2.7 .4965 .4966 .4967 .4968 .4969 .4970 .4971 .4972 .4973 .4974 2.8 .4974 .4975 .4976 .4977 .4977 .4978 .4979 .4979 .4980 .4981 2.9 .4981 .4982 .4982 .4983 .4984 .4984 .4985 .4985 .4986 .4986 3.0 .4986 .4987 .4987 .4988 .4988 .4989 .4989 .4989 .4990 .4990 3.1 .4990 .4991 .4991 .4991 .4992 .4992 .4992 .4992 .4993 .4993 3.2 .4993 .4993 .4994 .4994 .4994 .4994 .4994 .4995 .4995 .4995 3.3 .4995 .4995 .4995 .4996 .4996 .4996 .4996 .4996 .4996 .4997 3.4 .4997 .4997 .4997 .4997 .4997 .4997 .4997 .4997 .4997 .4998 3.6 .4998 .4998 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999 3.9 .5000 Fuente: The Nacional Bureau of Standards, Tables of Normal Probability Functions, Serie de Matemáticas Aplicadas, Nro. 23 (Washington, D.C; U. S. Government Printing Office, 1953). El original contiene valores de z de 0 a 8.285, principalmente en incrementos de 0.0001 y para áreas de µ -z a µ + z.
  3. 3. Curso: Estadística Aplicada Grados de Libertad Áreas de cola crítica ( = α para prueba de una cola, = α/2 para prueba de dos colas) .4 .25 .1 .05 .025 .01 .005 .0025 .001 .0005 1 0.325 1.000 3.078 6.314 12.706 31.821 63.657 127.32 318.31 636.62 2 .289 .816 .1886 2.920 4.303 6.965 9.925 14.089 22.327 31.598 3 .277 .765 1.638 2.353 3.182 4.541 5.841 7.453 10.214 12.924 4 .271 .741 1.533 2.132 2.776 3.747 4.604 5.598 7.173 8.610 5 0.267 0.727 1.476 2.015 2.571 3.365 4.032 4.773 5.893 6.869 6 .265 .718 1.440 1.943 2.447 3.143 3.707 4.317 5.208 5.959 7 .263 .711 1.415 1.895 2.365 2.998 3.499 4.029 4.785 5.408 8 .262 .706 1.397 1.860 2.306 2.896 3.355 3.833 4.501 5.041 9 .261 .703 1.383 1.833 2.262 2.821 3.250 3.690 4.297 4.781 10 0.260 0.700 1.372 1.812 2.228 2.764 3.169 3.581 4.144 4.587 11 .260 .697 1.363 1.796 2.201 2.718 3.106 3.497 4.025 4.437 12 .259 .695 1.356 1.782 2.179 2.681 3.055 3.428 3.930 4.318 13 .259 .694 1.350 1.771 2.160 2.650 3.012 3.372 3.852 4.221 14 .258 .692 1.345 1.761 2.145 2.624 2.977 3.326 3.787 4.140 15 0.258 0.691 1.341 1.753 2.131 2.602 2.947 3.286 3.733 4.073 16 .258 .690 1.337 1.746 2.120 2.583 2.921 3.252 3.686 4.015 17 .257 .689 1.333 1.740 2.110 2.567 2.898 3.222 3.646 3.965 18 .257 .688 1.330 1.734 2.101 2.552 2.878 3.197 3.610 3.922 19 .257 .688 1.328 1.729 2.093 2.539 2.861 3.174 3.579 3.883 20 0.257 0.687 1.325 1.725 2.086 2.528 2.845 3.153 3.552 3.850 21 .257 .686 1.323 1.721 2.080 2.518 2.831 3.135 3.527 3.819 22 .256 .686 1.321 1.717 2.074 2.508 2.819 3.119 3.505 3.792 23 .256 .685 1.319 1.714 2.069 2.500 2.807 3.104 3.485 3.767 24 .256 .685 1.318 1.711 2.064 2.492 2.797 3.091 3.467 3.745 25 0.256 0.684 1.316 1.708 2.060 2.485 2.787 3.078 3.450 3.725 26 .256 .684 1.315 1.706 2.056 2.479 2.779 3.067 3.435 3.707 27 .256 .684 1.314 1.703 2.052 2.473 2.771 3.057 3.421 3.690 28 .256 .683 1.313 1.701 2.048 2.467 2.763 3.047 3.408 3.674 29 .256 .683 1.311 1.699 2.045 2.462 2.756 3.038 3.396 3.659 30 0.256 0.683 1.310 1.697 2.042 2.457 2.750 3.030 3.385 3.646 40 .255 .681 1.303 1.684 2.021 2.423 2.704 2.971 3.307 3.551 60 .254 .679 1.296 1.671 2.000 2.390 2.660 2.915 3.232 3.460 120 .254 .677 1.289 1.658 1.980 2.358 2.617 2.860 3.160 3.373 ∞ .253 .674 1.282 1.645 1.960 2.326 2.576 2.807 3.090 3.291 Nivel de confianza C = 1 - α Prueba de una cola .60 .75 .90 .95 .975 .99 .995 .9975 .999 .9995 Prueba de dos colas .20 .50 .80 .90 .95 .98 .99 .995 .998 .999 Nota: Un nivel de significancia de α se asocia, por ejemplo, con un área de cola superior α en una prueba de cola superior, pero con un área tanto superior como inferior de α/2 en una prueba de dos colas. El nivel de confianza siempre es igual a C = 1 – α. Por tanto, un nivel de significancia de α = .05, por ejemplo, irá con un área de cola superior de .05 en una prueba de cola superior (C = 0.95), pero con un área de cola superior de .025 en una prueba de dos colas (C = .95). Fuente: E. S. Pearson y H. O. Hartley, Biométrica Tables for Statisticians, vol. 1 (Cambridge University Press, 1966), p. 146. Reimpreso con licencia de Biometika Trustes (fiduciarios). TABLA 2: DISTRIBUCIONES t DE STUDENT La siguiente tabla contiene los valores de tα que corresponden a un área α de cola superior dada y un número especificado de grados de libertad. Por ejemplo, para un área de cola superior de .05 y 9 grados de libertad, el valor de tα = 1.833
  4. 4. Curso: Estadística Aplicada Grados de libertad Valores críticos para área de cola superior α .99 .98 .95 .90 .80 .70 .50 .30 .20 .10 .05 .02 .01 .001 1 .0 3 157 .0 3 628 .00393 .0158 .0642 .148 .455 1.074 1.642 2.706 3.841 5.412 6.635 10.827 2 .0201 .0404 .103 .211 .446 .713 1.386 2.408 3.219 4.605 5.991 7.824 9.210 13.815 3 .115 .185 .352 .584 1.005 1.424 2.366 3.665 4.642 6.251 7.815 9.837 11.345 16.266 4 .297 .429 .711 1.064 1.649 2.195 3.357 4.878 5.989 7.779 9.488 11.668 13.277 18.467 5 .554 .752 1.145 1.610 2.343 3.000 4.351 6.064 7.289 9.236 11.070 13.388 15.086 20.515 6 .872 1.134 1.635 2.204 3.070 3.828 5.348 7.231 8.558 10.645 12.592 15.033 16.812 22.457 7 1.239 1.564 2.167 2.833 3.822 4.671 6.346 8.383 9.803 12.017 14.067 16.622 18.475 24.322 8 1.646 2.032 2.733 3.490 4.594 5.527 7.344 9.524 11.030 13.362 15.507 18.168 20.090 26.125 9 2.088 2.532 3.325 4.168 5.380 6.393 8.343 10.656 12.242 14.684 16.919 19.679 21.666 27.877 10 2.558 3.059 3.940 4.865 6.179 7.267 9.342 11.781 13.442 15.987 18.307 21.161 23.209 29.588 11 3.053 3.609 4.575 5.578 6.989 8.148 10.341 12.899 14.631 17.275 19.675 22.618 24.725 31.264 12 3.571 4.178 5.226 6.304 7.807 9.034 11.340 14.011 15.812 18.549 21.026 24.054 26.217 32.909 13 4.107 4.765 5.892 7.042 8.634 9.926 12.340 15.119 16.151 19.812 22.362 25.472 27.688 34.528 14 4.660 5.368 6.571 7.790 9.467 10.821 13.339 16.222 18.151 21.064 23.685 26.873 29.141 36.123 15 5.229 5.985 7.261 8.547 10.307 11.721 14.339 17.322 19.311 22.307 24.996 28.259 30.578 37.697 16 5.812 6.614 7.962 9.312 11.152 12.624 15.338 18.418 20.465 23.542 26.296 29.633 32.000 39.252 17 6.408 7.255 8.672 10.085 12.002 13.531 16.338 19.511 21.615 24.769 27.587 30.995 33.409 40.790 18 7.015 7.906 9.390 10.865 12.857 14.440 17.338 20.601 22.760 25.989 28.869 32.346 34.805 42.312 19 7.633 8.567 10.117 11.651 13.716 15.352 18.338 21.689 23.900 27.204 30.144 33.687 36.191 43.820 20 8.260 9.237 10.851 12.443 14.578 16.266 19.337 22.775 25.038 28.412 31.410 35.020 37.566 45.315 21 8.897 9.915 11.591 13.240 15.445 17.182 20.337 23.858 26.171 29.615 32.671 36.343 38.932 46.797 22 9.542 10.600 12.338 14.041 16.314 18.101 21.337 24.939 27.301 30.813 33.924 37.659 40.289 48.268 23 10.196 11.293 13.848 14.848 17.187 19.021 22.337 26.018 28.429 32.007 35.172 38.968 41.638 49.728 24 10.856 11.992 13.848 15.659 18.062 19.943 23.337 27.096 29.553 33.196 36.415 40.270 42.980 51.179 25 11.524 12.697 14.611 16.473 18.940 20.867 24.337 28.172 30.675 34.382 37.652 41.566 44.314 52.620 26 12.198 13.409 15.379 17.292 19.820 21.792 25.336 29.246 31.795 35.563 38.885 42.856 45.642 54.052 27 12.879 14.125 16.151 18.114 20.703 22.719 26.336 30.319 32.912 36.741 40.113 44.140 46.963 55.476 28 13.565 14.847 16.928 18.939 21.588 23.647 27.336 31.391 34.027 37.916 41.337 45.419 48.278 56.893 29 14.256 15.574 17.708 19.768 22.475 24.577 28.336 32.461 35.139 39.087 42.557 46.693 49.588 58.302 30 14.953 16.306 18.493 20.599 23.364 25.508 29.336 33.530 36.250 40.256 43.773 47.962 50.892 59.703 Nota: Cuando el número de grados de libertad excede de 30, la distribución 2  puede ser aproximada por la distribución normal, pero la tabla original de Fisher/Yates contiene valores hasta 70 grados de libertad. Fuente: Ronald A. Fisher y Frank Yates, Statistical Tables for Biological, Agricultural and Medical Research, 6ª edición, (Nueva York, Hafner, 1963), p.47 TABLA 3: DISTRIBUCIÓN CHI CUADRADO Esta tabla contiene los valores de 2  α que corresponden a un área dada de la cola superior, , y a un número específico de grados de libertad. Por ejemplo, para un área de cola superior de .05 y 4 grados de libertad, el valor crítico de 2  .05 es 9.488
  5. 5. Curso: Estadística Aplicada TABLA 4: Números aleatorios 71274 84346 75444 85690 35384 87841 97411 78698 46796 33552 64017 01373 14665 31891 80997 14321 47741 59980 87739 38174 43747 17686 11045 15549 52779 65135 00275 95434 36337 24041 59688 48689 41591 47042 83615 93034 25077 64835 67798 30547 95016 73467 11447 59500 94921 15166 69217 26267 11316 22651 65207 30591 65947 58339 00952 32111 45459 14986 57395 34492 34510 78657 08883 49489 85619 52912 01662 49854 78354 30631 56299 60624 91572 31734 18159 18927 31314 59682 41320 88602 02113 12579 86172 03819 69968 02616 72687 42699 04792 16510 00884 87979 45184 61572 20086 14498 29640 94263 90964 29278 89367 53577 97412 19603 57234 63055 49059 35761 72007 22751 99781 56740 42659 46617 21828 99831 45987 63450 66919 78252 92024 12100 76013 12587 86340 74880 79979 35906 38122 64917 82861 09215 87342 72789 76132 24468 93065 78968 03321 48081 11286 13011 67982 74101 44961 25468 14247 95934 50711 24492 68674 24686 14460 61242 92310 86810 87702 69811 53996 99517 24882 20749 94139 28785 74402 18561 79069 56838 30020 99707 21740 51134 39298 92203 66230 30636 58169 78982 50057 39908 46901 34825 28673 10404 97777 30782 04680 15319 84125 40937 92686 81702 74149 76326 01101 96278 90855 55145 89705 51199 98743 59366 94797 96803 69876 87533 19675 59246 65348 06606 11463 25619 38107 91053 58416 02720 86563 27443 99598 04074 76975 18636 54975 67422 57101 68857 35389 35641 34505 71552 67359 50379 81053 97357 00717 59504 34480 77127 23243 48682 34084 48031 27227 48912 10797 88917 93126 52945 79457 66528 94553 44441 83166 40056 73935 52103 13972 56781 31900 95037 20545 43211 34500 92233 53497 39401 78535 82360 57410 32060 05646 01152 13235 39168 69214 83852 00144 08105 94247 37189 54022 58295 96122 87620 74774 06884 81689 68392 25776 08748 32291 30700 32561 83579 94582 77930 06826 96855 97751 42664 66212 75061 65891 96896 15107 12985 97616 64241 08592 81036 98059 44951 23078 92793 80756 52799 20340 62969 81775 31065 23157 52179 24394 39833 89427 58771 26992 00649 25475 50888 28911 81929 91368 49372 43335 44465 43257 66893 34761 60423 85959 90369 02100 28727 83001 84166 20473 35305 38088 54795 34459 31400 58760 17157 73816 55527 54133 24605 56153 35354 04073 57781 36894 93000 57834 29343 98195 58425 97275 71392 22126 91330 95667 75737 36869 55209 41663 04943 59401 17039 10288 61685 25302 84097 13088 86840 04020 43046 01043 43157 75431 32853 72907 99432 65482 23011 70466 87386 67471 77629 90800 17425 28042 53770 98924 31863 84115 82488 23239 82185 19083 89475 05207 41284 83405 55825 31117 59821 96455 63796 10405 67911 77238 46262 42766 07215 02391 47316 78724 41170 34711 77325 99768 63455 44335 91028 27740 86163 81474 08159 73334 61941 16883 05012 63191 35763 60157 09617 25501 44989 79452 68381 71937 23274 60273 47091 82876 24641 03825 50894 13864 28746 32434 88325 99996 96130 39471 74020 56077 22133 73082 50271 83240 80065 09328 02940 41686 32758 89467 73553 43060 88221 35010 79829 71520 80453 95049 66352 77495 83256 15172 42061 33264 63832 48528 23258 13520 83222 45659 39074 Fuente: The Rand Corporation, A million Random Digits with 100,000 Normal Deviates (Glencoe, III,: The Free Press, 1955), p.377.Copyright C 1955 por la Rand Corporation. Reimpreso con licencia.

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