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Probability Tables: Normal, t, & Chi-Squared Distributions
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Probabilidad Probabilidad El valor de la tabla para z es el área bajo la curva de la normal estándar a la izquierda de z El valor de la tabla para z es el área bajo la curva de la normal estándar a la izquierda de z z z TABLA A: Probabilidades de la normal estándar (cont. ) TABLA A: Probabilidades de la normal estándar z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 ⫺3.4 ⫺3.3 ⫺3.2 ⫺3.1 ⫺3.0 ⫺2.9 ⫺2.8 ⫺2.7 ⫺2.6 ⫺2.5 ⫺2.4 ⫺2.3 ⫺2.2 ⫺2.1 ⫺2.0 ⫺1.9 ⫺1.8 ⫺1.7 ⫺1.6 ⫺1.5 ⫺1.4 ⫺1.3 ⫺1.2 ⫺1.1 ⫺1.0 ⫺0.9 ⫺0.8 ⫺0.7 ⫺0.6 ⫺0.5 ⫺0.4 ⫺0.3 ⫺0.2 ⫺0.1 ⫺0.0 .0003 .0005 .0007 .0010 .0013 .0019 .0026 .0035 .0047 .0062 .0082 .0107 .0139 .0179 .0228 .0287 .0359 .0446 .0548 .0668 .0808 .0968 .1151 .1357 .1587 .1841 .2119 .2420 .2743 .3085 .3446 .3821 .4207 .4602 .5000 .0003 .0005 .0007 .0009 .0013 .0018 .0025 .0034 .0045 .0060 .0080 .0104 .0136 .0174 .0222 .0281 .0351 .0436 .0537 .0655 .0793 .0951 .1131 .1335 .1562 .1814 .2090 .2389 .2709 .3050 .3409 .3783 .4168 .4562 .4960 .0003 .0005 .0006 .0009 .0013 .0018 .0024 .0033 .0044 .0059 .0078 .0102 .0132 .0170 .0217 .0274 .0344 .0427 .0526 .0643 .0778 .0934 .1112 .1314 .1539 .1788 .2061 .2358 .2676 .3015 .3372 .3745 .4129 .4522 .4920 .0003 .0004 .0006 .0009 .0012 .0017 .0023 .0032 .0043 .0057 .0075 .0099 .0129 .0166 .0212 .0268 .0336 .0418 .0516 .0630 .0764 .0918 .1093 .1292 .1515 .1762 .2033 .2327 .2643 .2981 .3336 .3707 .4090 .4483 .4880 .0003 .0004 .0006 .0008 .0012 .0016 .0023 .0031 .0041 .0055 .0073 .0096 .0125 .0162 .0207 .0262 .0329 .0409 .0505 .0618 .0749 .0901 .1075 .1271 .1492 .1736 .2005 .2296 .2611 .2946 .3300 .3669 .4052 .4443 .4840 .0003 .0004 .0006 .0008 .0011 .0016 .0022 .0030 .0040 .0054 .0071 .0094 .0122 .0158 .0202 .0256 .0322 .0401 .0495 .0606 .0735 .0885 .1056 .1251 .1469 .1711 .1977 .2266 .2578 .2912 .3264 .3632 .4013 .4404 .4801 .0003 .0004 .0006 .0008 .0011 .0015 .0021 .0029 .0039 .0052 .0069 .0091 .0119 .0154 .0197 .0250 .0314 .0392 .0485 .0594 .0721 .0869 .1038 .1230 .1446 .1685 .1949 .2236 .2546 .2877 .3228 .3594 .3974 .4364 .4761 .0003 .0004 .0005 .0008 .0011 .0015 .0021 .0028 .0038 .0051 .0068 .0089 .0116 .0150 .0192 .0244 .0307 .0384 .0475 .0582 .0708 .0853 .1020 .1210 .1423 .1660 .1922 .2206 .2514 .2843 .3192 .3557 .3936 .4325 .4721 .0003 .0004 .0005 .0007 .0010 .0014 .0020 .0027 .0037 .0049 .0066 .0087 .0113 .0146 .0188 .0239 .0301 .0375 .0465 .0571 .0694 .0838 .1003 .1190 .1401 .1635 .1894 .2177 .2483 .2810 .3156 .3520 .3897 .4286 .4681 .0002 .0003 .0005 .0007 .0010 .0014 .0019 .0026 .0036 .0048 .0064 .0084 .0110 .0143 .0183 .0233 .0294 .0367 .0455 .0559 .0681 .0823 .0985 .1170 .1379 .1611 .1867 .2148 .2451 .2776 .3121 .3483 .3859 .4247 .4641 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 .5000 .5398 .5793 .6179 .6554 .6915 .7257 .7580 .7881 .8159 .8413 .8643 .8849 .9032 .9192 .9332 .9452 .9554 .9641 .9713 .9772 .9821 .9861 .9893 .9918 .9938 .9953 .9965 .9974 .9981 .9987 .9990 .9993 .9995 .9997 .5040 .5438 .5832 .6217 .6591 .6950 .7291 .7611 .7910 .8186 .8438 .8665 .8869 .9049 .9207 .9345 .9463 .9564 .9649 .9719 .9778 .9826 .9864 .9896 .9920 .9940 .9955 .9966 .9975 .9982 .9987 .9991 .9993 .9995 .9997 .5080 .5478 .5871 .6255 .6628 .6985 .7324 .7642 .7939 .8212 .8461 .8686 .8888 .9066 .9222 .9357 .9474 .9573 .9656 .9726 .9783 .9830 .9868 .9898 .9922 .9941 .9956 .9967 .9976 .9982 .9987 .9991 .9994 .9995 .9997 .5120 .5517 .5910 .6293 .6664 .7019 .7357 .7673 .7967 .8238 .8485 .8708 .8907 .9082 .9236 .9370 .9484 .9582 .9664 .9732 .9788 .9834 .9871 .9901 .9925 .9943 .9957 .9968 .9977 .9983 .9988 .9991 .9994 .9996 .9997 .5160 .5557 .5948 .6331 .6700 .7054 .7389 .7704 .7995 .8264 .8508 .8729 .8925 .9099 .9251 .9382 .9495 .9591 .9671 .9738 .9793 .9838 .9875 .9904 .9927 .9945 .9959 .9969 .9977 .9984 .9988 .9992 .9994 .9996 .9997 .5199 .5596 .5987 .6368 .6736 .7088 .7422 .7734 .8023 .8289 .8531 .8749 .8944 .9115 .9265 .9394 .9505 .9599 .9678 .9744 .9798 .9842 .9878 .9906 .9929 .9946 .9960 .9970 .9978 .9984 .9989 .9992 .9994 .9996 .9997 .5239 .5636 .6026 .6406 .6772 .7123 .7454 .7764 .8051 .8315 .8554 .8770 .8962 .9131 .9279 .9406 .9515 .9608 .9686 .9750 .9803 .9846 .9881 .9909 .9931 .9948 .9961 .9971 .9979 .9985 .9989 .9992 .9994 .9996 .9997 .5279 .5675 .6064 .6443 .6808 .7157 .7486 .7794 .8078 .8340 .8577 .8790 .8980 .9147 .9292 .9418 .9525 .9616 .9693 .9756 .9808 .9850 .9884 .9911 .9932 .9949 .9962 .9972 .9979 .9985 .9989 .9992 .9995 .9996 .9997 .5319 .5714 .6103 .6480 .6844 .7190 .7517 .7823 .8106 .8365 .8599 .8810 .8997 .9162 .9306 .9429 .9535 .9625 .9699 .9761 .9812 .9854 .9887 .9913 .9934 .9951 .9963 .9973 .9980 .9986 .9990 .9993 .9995 .9996 .9997 .5359 .5753 .6141 .6517 .6879 .7224 .7549 .7852 .8133 .8389 .8621 .8830 .9015 .9177 .9319 .9441 .9545 .9633 .9706 .9767 .9817 .9857 .9890 .9916 .9936 .9952 .9964 .9974 .9981 .9986 .9990 .9993 .9995 .9997 .9998 Probabilidad p El valor de la tabla para p y C es el valor crítico t* que deja una probabilidad p a la derecha y una probabilidad C entre -t* y t* Probabilidad p t* X2* TABLA B Valores críticos de la distribución t de Student El valor de la tabla para p es el valor crítico X 2ⴱ que deja la probabilidad p a la derecha Probabilidad de la cola p gl 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 50 60 80 100 1000 zⴱ .25 .20 .15 .10 .05 .025 .02 .01 .005 .0025 .001 .0005 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 0.679 0.678 0.677 0.675 0.674 1.376 1.061 0.978 0.941 0.920 0.906 0.896 0.889 0.883 0.879 0.876 0.873 0.870 0.868 0.866 0.865 0.863 0.862 0.861 0.860 0.859 0.858 0.858 0.857 0.856 0.856 0.855 0.855 0.854 0.854 0.851 0.849 0.848 0.846 0.845 0.842 0.841 1.963 1.386 1.250 1.190 1.156 1.134 1.119 1.108 1.100 1.093 1.088 1.083 1.079 1.076 1.074 1.071 1.069 1.067 1.066 1.064 1.063 1.061 1.060 1.059 1.058 1.058 1.057 1.056 1.055 1.055 1.050 1.047 1.045 1.043 1.042 1.037 1.036 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 1.299 1.296 1.292 1.290 1.282 1.282 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 1.676 1.671 1.664 1.660 1.646 1.645 12.71 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 2.009 2.000 1.990 1.984 1.962 1.960 15.89 4.849 3.482 2.999 2.757 2.612 2.517 2.449 2.398 2.359 2.328 2.303 2.282 2.264 2.249 2.235 2.224 2.214 2.205 2.197 2.189 2.183 2.177 2.172 2.167 2.162 2.158 2.154 2.150 2.147 2.123 2.109 2.099 2.088 2.081 2.056 2.054 31.82 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 2.403 2.390 2.374 2.364 2.330 2.326 63.66 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 2.678 2.660 2.639 2.626 2.581 2.576 127.3 14.09 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 2.937 2.915 2.887 2.871 2.813 2.807 318.3 22.33 10.21 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 3.611 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 3.261 3.232 3.195 3.174 3.098 3.091 636.6 31.60 12.92 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 3.768 3.745 3.725 3.707 3.690 3.674 3.659 3.646 3.551 3.496 3.460 3.416 3.390 3.300 3.291 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% Nivel de confianza C TABLA C: Valores críticos de la distribución 2 de Pearson Probabilidad de la cola p gl 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 50 60 80 100 .25 .20 .15 .10 .05 .025 .02 .01 .005 .0025 .001 .0005 1.32 2.77 4.11 5.39 6.63 7.84 9.04 10.22 11.39 12.55 13.70 14.85 15.98 17.12 18.25 19.37 20.49 21.60 22.72 23.83 24.93 26.04 27.14 28.24 29.34 30.43 31.53 32.62 33.71 34.80 45.62 56.33 66.98 88.13 109.1 1.64 3.22 4.64 5.99 7.29 8.56 9.80 11.03 12.24 13.44 14.63 15.81 16.98 18.15 19.31 20.47 21.61 22.76 23.90 25.04 26.17 27.30 28.43 29.55 30.68 31.79 32.91 34.03 35.14 36.25 47.27 58.16 68.97 90.41 111.7 2.07 3.79 5.32 6.74 8.12 9.45 10.75 12.03 13.29 14.53 15.77 16.99 18.20 19.41 20.60 21.79 22.98 24.16 25.33 26.50 27.66 28.82 29.98 31.13 32.28 33.43 34.57 35.71 36.85 37.99 49.24 60.35 71.34 93.11 114.7 2.71 4.61 6.25 7.78 9.24 10.64 12.02 13.36 14.68 15.99 17.28 18.55 19.81 21.06 22.31 23.54 24.77 25.99 27.20 28.41 29.62 30.81 32.01 33.20 34.38 35.56 36.74 37.92 39.09 40.26 51.81 63.17 74.40 96.58 118.5 3.84 5.99 7.81 9.49 11.07 12.59 14.07 15.51 16.92 18.31 19.68 21.03 22.36 23.68 25.00 26.30 27.59 28.87 30.14 31.41 32.67 33.92 35.17 36.42 37.65 38.89 40.11 41.34 42.56 43.77 55.76 67.50 79.08 101.9 124.3 5.02 7.38 9.35 11.14 12.83 14.45 16.01 17.53 19.02 20.48 21.92 23.34 24.74 26.12 27.49 28.85 30.19 31.53 32.85 34.17 35.48 36.78 38.08 39.36 40.65 41.92 43.19 44.46 45.72 46.98 59.34 71.42 83.30 106.6 129.6 5.41 7.82 9.84 11.67 13.39 15.03 16.62 18.17 19.68 21.16 22.62 24.05 25.47 26.87 28.26 29.63 31.00 32.35 33.69 35.02 36.34 37.66 38.97 40.27 41.57 42.86 44.14 45.42 46.69 47.96 60.44 72.61 84.58 108.1 131.1 6.63 9.21 11.34 13.28 15.09 16.81 18.48 20.09 21.67 23.21 24.72 26.22 27.69 29.14 30.58 32.00 33.41 34.81 36.19 37.57 38.93 40.29 41.64 42.98 44.31 45.64 46.96 48.28 49.59 50.89 63.69 76.15 88.38 112.3 135.8 7.88 10.60 12.84 14.86 16.75 18.55 20.28 21.95 23.59 25.19 26.76 28.30 29.82 31.32 32.80 34.27 35.72 37.16 38.58 40.00 41.40 42.80 44.18 45.56 46.93 48.29 49.64 50.99 52.34 53.67 66.77 79.49 91.95 116.3 140.2 9.14 11.98 14.32 16.42 18.39 20.25 22.04 23.77 25.46 27.11 28.73 30.32 31.88 33.43 34.95 36.46 37.95 39.42 40.88 42.34 43.78 45.20 46.62 48.03 49.44 50.83 52.22 53.59 54.97 56.33 69.70 82.66 95.34 120.1 144.3 10.83 13.82 16.27 18.47 20.51 22.46 24.32 26.12 27.88 29.59 31.26 32.91 34.53 36.12 37.70 39.25 40.79 42.31 43.82 45.31 46.80 48.27 49.73 51.18 52.62 54.05 55.48 56.89 58.30 59.70 73.40 86.66 99.61 124.8 149.4 12.12 15.20 17.73 20.00 22.11 24.10 26.02 27.87 29.67 31.42 33.14 34.82 36.48 38.11 39.72 41.31 42.88 44.43 45.97 47.50 49.01 50.51 52.00 53.48 54.95 56.41 57.86 59.30 60.73 62.16 76.09 89.56 102.7 128.3 153.2 Probabilidad p Probabilidad p F* F* El valor de la tabla para p es el valor crítico F* que deja la probabilidad p a la derecha El valor de la tabla para p es el valor crítico F* que deja la probabilidad p a la derecha TABLA D Valores críticos de la distribución F de Fisher TABLA D Valores críticos de la distribución F de Fisher (cont.) Grados de libertad en el denominador Grados de libertad en el numerador Grados de libertad del numerador p 1 2 3 4 5 6 7 8 9 10 12 15 20 25 30 40 50 60 120 1000 1 .100 .050 .025 .010 .001 39.86 161.45 647.79 4052.2 405284 49.50 199.50 799.50 4999.5 500000 53.59 215.71 864.16 5403.4 540379 55.83 224.58 899.58 5624.6 562500 57.24 230.16 921.85 5763.6 576405 58.20 233.99 937.11 5859.0 585937 58.91 236.77 948.22 5928.4 592873 59.44 238.88 956.66 5981.1 598144 59.86 240.54 963.28 6022.5 602284 60.19 241.88 968.63 6055.8 605621 60.71 243.91 976.71 6106.3 610668 61.22 245.95 984.87 6157.3 615764 61.74 248.01 993.10 6208.7 620908 62.05 249.26 998.08 6239.8 624017 62.26 250.10 1001.4 6260.6 626099 62.53 251.14 1005.6 6286.8 628712 62.69 251.77 1008.1 6302.5 630285 62.79 252.20 1009.8 6313.0 631337 63.06 253.25 1014.0 6339.4 633972 63.30 254.19 1017.7 6362.7 636301 2 .100 .050 .025 .010 .001 8.53 18.51 38.51 98.50 998.50 9.00 19.00 39.00 99.00 999.00 9.16 19.16 39.17 99.17 999.17 9.24 19.25 39.25 99.25 999.25 9.29 19.30 39.30 99.30 999.30 9.33 19.33 39.33 99.33 999.33 9.35 19.35 39.36 99.36 999.36 9.37 19.37 39.37 99.37 999.37 9.38 19.38 39.39 99.39 999.39 9.39 19.40 39.40 99.40 999.40 9.41 19.41 39.41 99.42 999.42 9.42 19.43 39.43 99.43 999.43 9.44 19.45 39.45 99.45 999.45 9.45 19.46 39.46 99.46 999.46 9.46 19.46 39.46 99.47 999.47 9.47 19.47 39.47 99.47 999.47 9.47 19.48 39.48 99.48 999.48 9.47 19.48 39.48 99.48 999.48 9.48 19.49 39.49 99.49 999.49 9.49 19.49 39.50 99.50 999.50 3 .100 .050 .025 .010 .001 5.54 10.13 17.44 34.12 167.03 5.46 9.55 16.04 30.82 148.50 5.39 9.28 15.44 29.46 141.11 5.34 9.12 15.10 28.71 137.10 5.31 9.01 14.88 28.24 134.58 5.28 8.94 14.73 27.91 132.85 5.27 8.89 14.62 27.67 131.58 5.25 8.85 14.54 27.49 130.62 5.24 8.81 14.47 27.35 129.86 5.23 8.79 14.42 27.23 129.25 5.22 8.74 14.34 27.05 128.32 5.20 8.70 14.25 26.87 127.37 5.18 8.66 14.17 26.69 126.42 5.17 8.63 14.12 26.58 125.84 5.17 8.62 14.08 26.50 125.45 5.16 8.59 14.04 26.41 124.96 5.15 8.58 14.01 26.35 124.66 5.15 8.57 13.99 26.32 124.47 5.14 8.55 13.95 26.22 123.97 5.13 8.53 13.91 26.14 123.53 4 .100 .050 .025 .010 .001 4.54 7.71 12.22 21.20 74.14 4.32 6.94 10.65 18.00 61.25 4.19 6.59 9.98 16.69 56.18 4.11 6.39 9.60 15.98 53.44 4.05 6.26 9.36 15.52 51.71 4.01 6.16 9.20 15.21 50.53 3.98 6.09 9.07 14.98 49.66 3.95 6.04 8.98 14.80 49.00 3.94 6.00 8.90 14.66 48.47 3.92 5.96 8.84 14.55 48.05 3.90 5.91 8.75 14.37 47.41 3.87 5.86 8.66 14.20 46.76 3.84 5.80 8.56 14.02 46.10 3.83 5.77 8.50 13.91 45.70 3.82 5.75 8.46 13.84 45.43 3.80 5.72 8.41 13.75 45.09 3.80 5.70 8.38 13.69 44.88 3.79 5.69 8.36 13.65 44.75 3.78 5.66 8.31 13.56 44.40 3.76 5.63 8.26 13.47 44.09 5 .100 .050 .025 .010 .001 4.06 6.61 10.01 16.26 47.18 3.78 5.79 8.43 13.27 37.12 3.62 5.41 7.76 12.06 33.20 3.52 5.19 7.39 11.39 31.09 3.45 5.05 7.15 10.97 29.75 3.40 4.95 6.98 10.67 28.83 3.37 4.88 6.85 10.46 28.16 3.34 4.82 6.76 10.29 27.65 3.32 4.77 6.68 10.16 27.24 3.30 4.74 6.62 10.05 26.92 3.27 4.68 6.52 9.89 26.42 3.24 4.62 6.43 9.72 25.91 3.21 4.56 6.33 9.55 25.39 3.19 4.52 6.27 9.45 25.08 3.17 4.50 6.23 9.38 24.87 3.16 4.46 6.18 9.29 24.60 3.15 4.44 6.14 9.24 24.44 3.14 4.43 6.12 9.20 24.33 3.12 4.40 6.07 9.11 24.06 3.11 4.37 6.02 9.03 23.82 6 .100 .050 .025 .010 .001 3.78 5.99 8.81 13.75 35.51 3.46 5.14 7.26 10.92 27.00 3.29 4.76 6.60 9.78 23.70 3.18 4.53 6.23 9.15 21.92 3.11 4.39 5.99 8.75 20.80 3.05 4.28 5.82 8.47 20.03 3.01 4.21 5.70 8.26 19.46 2.98 4.15 5.60 8.10 19.03 2.96 4.10 5.52 7.98 18.69 2.94 4.06 5.46 7.87 18.41 2.90 4.00 5.37 7.72 17.99 2.87 3.94 5.27 7.56 17.56 2.84 3.87 5.17 7.40 17.12 2.81 3.83 5.11 7.30 16.85 2.80 3.81 5.07 7.23 16.67 2.78 3.77 5.01 7.14 16.44 2.77 3.75 4.98 7.09 16.31 2.76 3.74 4.96 7.06 16.21 2.74 3.70 4.90 6.97 15.98 2.72 3.67 4.86 6.89 15.77 7 .100 .050 .025 .010 .001 3.59 5.59 8.07 12.25 29.25 3.26 4.74 6.54 9.55 21.69 3.07 4.35 5.89 8.45 18.77 2.96 4.12 5.52 7.85 17.20 2.88 3.97 5.29 7.46 16.21 2.83 3.87 5.12 7.19 15.52 2.78 3.79 4.99 6.99 15.02 2.75 3.73 4.90 6.84 14.63 2.72 3.68 4.82 6.72 14.33 2.70 3.64 4.76 6.62 14.08 2.67 3.57 4.67 6.47 13.71 2.63 3.51 4.57 6.31 13.32 2.59 3.44 4.47 6.16 12.93 2.57 3.40 4.40 6.06 12.69 2.56 3.38 4.36 5.99 12.53 2.54 3.34 4.31 5.91 12.33 2.52 3.32 4.28 5.86 12.20 2.51 3.30 4.25 5.82 12.12 2.49 3.27 4.20 5.74 11.91 2.47 3.23 4.15 5.66 11.72 TABLA D TABLA D Valores críticos de la distribución F de Fisher (cont.) Valores críticos de la distribución F de Fisher (cont.) Grados de libertad en el numerador Grados de libertad en el denominador Grados de libertad en el numerador p 1 2 3 4 5 6 7 8 9 10 12 15 20 25 30 40 50 60 120 1000 8 .100 .050 .025 .010 .001 3.46 5.32 7.57 11.26 25.41 3.11 4.46 6.06 8.65 18.49 2.92 4.07 5.42 7.59 15.83 2.81 3.84 5.05 7.01 14.39 2.73 3.69 4.82 6.63 13.48 2.67 3.58 4.65 6.37 12.86 2.62 3.50 4.53 6.18 12.40 2.59 3.44 4.43 6.03 12.05 2.56 3.39 4.36 5.91 11.77 2.54 3.35 4.30 5.81 11.54 2.50 3.28 4.20 5.67 11.19 2.46 3.22 4.10 5.52 10.84 2.42 3.15 4.00 5.36 10.48 2.40 3.11 3.94 5.26 10.26 2.38 3.08 3.89 5.20 10.11 2.36 3.04 3.84 5.12 9.92 2.35 3.02 3.81 5.07 9.80 2.34 3.01 3.78 5.03 9.73 2.32 2.97 3.73 4.95 9.53 2.30 2.93 3.68 4.87 9.36 9 .100 .050 .025 .010 .001 3.36 5.12 7.21 10.56 22.86 3.01 4.26 5.71 8.02 16.39 2.81 3.86 5.08 6.99 13.90 2.69 3.63 4.72 6.42 12.56 2.61 3.48 4.48 6.06 11.71 2.55 3.37 4.32 5.80 11.13 2.51 3.29 4.20 5.61 10.70 2.47 3.23 4.10 5.47 10.37 2.44 3.18 4.03 5.35 10.11 2.42 3.14 3.96 5.26 9.89 2.38 3.07 3.87 5.11 9.57 2.34 3.01 3.77 4.96 9.24 2.30 2.94 3.67 4.81 8.90 2.27 2.89 3.60 4.71 8.69 2.25 2.86 3.56 4.65 8.55 2.23 2.83 3.51 4.57 8.37 2.22 2.80 3.47 4.52 8.26 2.21 2.79 3.45 4.48 8.19 2.18 2.75 3.39 4.40 8.00 2.16 2.71 3.34 4.32 7.84 10 .100 .050 .025 .010 .001 3.29 4.96 6.94 10.04 21.04 2.92 4.10 5.46 7.56 14.91 2.73 3.71 4.83 6.55 12.55 2.61 3.48 4.47 5.99 11.28 2.52 3.33 4.24 5.64 10.48 2.46 3.22 4.07 5.39 9.93 2.41 3.14 3.95 5.20 9.52 2.38 3.07 3.85 5.06 9.20 2.35 3.02 3.78 4.94 8.96 2.32 2.98 3.72 4.85 8.75 2.28 2.91 3.62 4.71 8.45 2.24 2.85 3.52 4.56 8.13 2.20 2.77 3.42 4.41 7.80 2.17 2.73 3.35 4.31 7.60 2.16 2.70 3.31 4.25 7.47 2.13 2.66 3.26 4.17 7.30 2.12 2.64 3.22 4.12 7.19 2.11 2.62 3.20 4.08 7.12 2.08 2.58 3.14 4.00 6.94 2.06 2.54 3.09 3.92 6.78 11 .100 .050 .025 .010 .001 3.23 4.84 6.72 9.65 19.69 2.86 3.98 5.26 7.21 13.81 2.66 3.59 4.63 6.22 11.56 2.54 3.36 4.28 5.67 10.35 2.45 3.20 4.04 5.32 9.58 2.39 3.09 3.88 5.07 9.05 2.34 3.01 3.76 4.89 8.66 2.30 2.95 3.66 4.74 8.35 2.27 2.90 3.59 4.63 8.12 2.25 2.85 3.53 4.54 7.92 2.21 2.79 3.43 4.40 7.63 2.17 2.72 3.33 4.25 7.32 2.12 2.65 3.23 4.10 7.01 2.10 2.60 3.16 4.01 6.81 2.08 2.57 3.12 3.94 6.68 2.05 2.53 3.06 3.86 6.52 2.04 2.51 3.03 3.81 6.42 2.03 2.49 3.00 3.78 6.35 2.00 2.45 2.94 3.69 6.18 1.98 2.41 2.89 3.61 6.02 12 .100 .050 .025 .010 .001 3.18 4.75 6.55 9.33 18.64 2.81 3.89 5.10 6.93 12.97 2.61 3.49 4.47 5.95 10.80 2.48 3.26 4.12 5.41 9.63 2.39 3.11 3.89 5.06 8.89 2.33 3.00 3.73 4.82 8.38 2.28 2.91 3.61 4.64 8.00 2.24 2.85 3.51 4.50 7.71 2.21 2.80 3.44 4.39 7.48 2.19 2.75 3.37 4.30 7.29 2.15 2.69 3.28 4.16 7.00 2.10 2.62 3.18 4.01 6.71 2.06 2.54 3.07 3.86 6.40 2.03 2.50 3.01 3.76 6.22 2.01 2.47 2.96 3.70 6.09 1.99 2.43 2.91 3.62 5.93 1.97 2.40 2.87 3.57 5.83 1.96 2.38 2.85 3.54 5.76 1.93 2.34 2.79 3.45 5.59 1.91 2.30 2.73 3.37 5.44 13 .100 .050 .025 .010 .001 3.14 4.67 6.41 9.07 17.82 2.76 3.81 4.97 6.70 12.31 2.56 3.41 4.35 5.74 10.21 2.43 3.18 4.00 5.21 9.07 2.35 3.03 3.77 4.86 8.35 2.28 2.92 3.60 4.62 7.86 2.23 2.83 3.48 4.44 7.49 2.20 2.77 3.39 4.30 7.21 2.16 2.71 3.31 4.19 6.98 2.14 2.67 3.25 4.10 6.80 2.10 2.60 3.15 3.96 6.52 2.05 2.53 3.05 3.82 6.23 2.01 2.46 2.95 3.66 5.93 1.98 2.41 2.88 3.57 5.75 1.96 2.38 2.84 3.51 5.63 1.93 2.34 2.78 3.43 5.47 1.92 2.31 2.74 3.38 5.37 1.90 2.30 2.72 3.34 5.30 1.88 2.25 2.66 3.25 5.14 1.85 2.21 2.60 3.18 4.99 14 .100 .050 .025 .010 .001 3.10 4.60 6.30 8.86 17.14 2.73 3.74 4.86 6.51 11.78 2.52 3.34 4.24 5.56 9.73 2.39 3.11 3.89 5.04 8.62 2.31 2.96 3.66 4.69 7.92 2.24 2.85 3.50 4.46 7.44 2.19 2.76 3.38 4.28 7.08 2.15 2.70 3.29 4.14 6.80 2.12 2.65 3.21 4.03 6.58 2.10 2.60 3.15 3.94 6.40 2.05 2.53 3.05 3.80 6.13 2.01 2.46 2.95 3.66 5.85 1.96 2.39 2.84 3.51 5.56 1.93 2.34 2.78 3.41 5.38 1.91 2.31 2.73 3.35 5.25 1.89 2.27 2.67 3.27 5.10 1.87 2.24 2.64 3.22 5.00 1.86 2.22 2.61 3.18 4.94 1.83 2.18 2.55 3.09 4.77 1.80 2.14 2.50 3.02 4.62 15 .100 .050 .025 .010 .001 3.07 4.54 6.20 8.68 16.59 2.70 3.68 4.77 6.36 11.34 2.49 3.29 4.15 5.42 9.34 2.36 3.06 3.80 4.89 8.25 2.27 2.90 3.58 4.56 7.57 2.21 2.79 3.41 4.32 7.09 2.16 2.71 3.29 4.14 6.74 2.12 2.64 3.20 4.00 6.47 2.09 2.59 3.12 3.89 6.26 2.06 2.54 3.06 3.80 6.08 2.02 2.48 2.96 3.67 5.81 1.97 2.40 2.86 3.52 5.54 1.92 2.33 2.76 3.37 5.25 1.89 2.28 2.69 3.28 5.07 1.87 2.25 2.64 3.21 4.95 1.85 2.20 2.59 3.13 4.80 1.83 2.18 2.55 3.08 4.70 1.82 2.16 2.52 3.05 4.64 1.79 2.11 2.46 2.96 4.47 1.76 2.07 2.40 2.88 4.33 16 .100 .050 .025 .010 .001 3.05 4.49 6.12 8.53 16.12 2.67 3.63 4.69 6.23 10.97 2.46 3.24 4.08 5.29 9.01 2.33 3.01 3.73 4.77 7.94 2.24 2.85 3.50 4.44 7.27 2.18 2.74 3.34 4.20 6.80 2.13 2.66 3.22 4.03 6.46 2.09 2.59 3.12 3.89 6.19 2.06 2.54 3.05 3.78 5.98 2.03 2.49 2.99 3.69 5.81 1.99 2.42 2.89 3.55 5.55 1.94 2.35 2.79 3.41 5.27 1.89 2.28 2.68 3.26 4.99 1.86 2.23 2.61 3.16 4.82 1.84 2.19 2.57 3.10 4.70 1.81 2.15 2.51 3.02 4.54 1.79 2.12 2.47 2.97 4.45 1.78 2.11 2.45 2.93 4.39 1.75 2.06 2.38 2.84 4.23 1.72 2.02 2.32 2.76 4.08 17 .100 .050 .025 .010 .001 3.03 4.45 6.04 8.40 15.72 2.64 3.59 4.62 6.11 10.66 2.44 3.20 4.01 5.19 8.73 2.31 2.96 3.66 4.67 7.68 2.22 2.81 3.44 4.34 7.02 2.15 2.70 3.28 4.10 6.56 2.10 2.61 3.16 3.93 6.22 2.06 2.55 3.06 3.79 5.96 2.03 2.49 2.98 3.68 5.75 2.00 2.45 2.92 3.59 5.58 1.96 2.38 2.82 3.46 5.32 1.91 2.31 2.72 3.31 5.05 1.86 2.23 2.62 3.16 4.78 1.83 2.18 2.55 3.07 4.60 1.81 2.15 2.50 3.00 4.48 1.78 2.10 2.44 2.92 4.33 1.76 2.08 2.41 2.87 4.24 1.75 2.06 2.38 2.83 4.18 1.72 2.01 2.32 2.75 4.02 1.69 1.97 2.26 2.66 3.87 TABLA D Valores críticos de la distribución F de Fisher (cont.) TABLA D Valores críticos de la distribución F de Fisher (cont.) Grados de libertad en el denominador Grados de libertad en el numerador Grados de libertad en el numerador p 1 2 3 4 5 6 7 8 9 10 12 15 20 25 30 40 50 60 120 1000 18 .100 .050 .025 .010 .001 3.01 4.41 5.98 8.29 15.38 2.62 3.55 4.56 6.01 10.39 2.42 3.16 3.95 5.09 8.49 2.29 2.93 3.61 4.58 7.46 2.20 2.77 3.38 4.25 6.81 2.13 2.66 3.22 4.01 6.35 2.08 2.58 3.10 3.84 6.02 2.04 2.51 3.01 3.71 5.76 2.00 2.46 2.93 3.60 5.56 1.98 2.41 2.87 3.51 5.39 1.93 2.34 2.77 3.37 5.13 1.89 2.27 2.67 3.23 4.87 1.84 2.19 2.56 3.08 4.59 1.80 2.14 2.49 2.98 4.42 1.78 2.11 2.44 2.92 4.30 1.75 2.06 2.38 2.84 4.15 1.74 2.04 2.35 2.78 4.06 1.72 2.02 2.32 2.75 4.00 1.69 1.97 2.26 2.66 3.84 1.66 1.92 2.20 2.58 3.69 19 .100 .050 .025 .010 .001 2.99 4.38 5.92 8.18 15.08 2.61 3.52 4.51 5.93 10.16 2.40 3.13 3.90 5.01 8.28 2.27 2.90 3.56 4.50 7.27 2.18 2.74 3.33 4.17 6.62 2.11 2.63 3.17 3.94 6.18 2.06 2.54 3.05 3.77 5.85 2.02 2.48 2.96 3.63 5.59 1.98 2.42 2.88 3.52 5.39 1.96 2.38 2.82 3.43 5.22 1.91 2.31 2.72 3.30 4.97 1.86 2.23 2.62 3.15 4.70 1.81 2.16 2.51 3.00 4.43 1.78 2.11 2.44 2.91 4.26 1.76 2.07 2.39 2.84 4.14 1.73 2.03 2.33 2.76 3.99 1.71 2.00 2.30 2.71 3.90 1.70 1.98 2.27 2.67 3.84 1.67 1.93 2.20 2.58 3.68 1.64 1.88 2.14 2.50 3.53 20 .100 .050 .025 .010 .001 2.97 4.35 5.87 8.10 14.82 2.59 3.49 4.46 5.85 9.95 2.38 3.10 3.86 4.94 8.10 2.25 2.87 3.51 4.43 7.10 2.16 2.71 3.29 4.10 6.46 2.09 2.60 3.13 3.87 6.02 2.04 2.51 3.01 3.70 5.69 2.00 2.45 2.91 3.56 5.44 1.96 2.39 2.84 3.46 5.24 1.94 2.35 2.77 3.37 5.08 1.89 2.28 2.68 3.23 4.82 1.84 2.20 2.57 3.09 4.56 1.79 2.12 2.46 2.94 4.29 1.76 2.07 2.40 2.84 4.12 1.74 2.04 2.35 2.78 4.00 1.71 1.99 2.29 2.69 3.86 1.69 1.97 2.25 2.64 3.77 1.68 1.95 2.22 2.61 3.70 1.64 1.90 2.16 2.52 3.54 1.61 1.85 2.09 2.43 3.40 21 .100 .050 .025 .010 .001 2.96 4.32 5.83 8.02 14.59 2.57 3.47 4.42 5.78 9.77 2.36 3.07 3.82 4.87 7.94 2.23 2.84 3.48 4.37 6.95 2.14 2.68 3.25 4.04 6.32 2.08 2.57 3.09 3.81 5.88 2.02 2.49 2.97 3.64 5.56 1.98 2.42 2.87 3.51 5.31 1.95 2.37 2.80 3.40 5.11 1.92 2.32 2.73 3.31 4.95 1.87 2.25 2.64 3.17 4.70 1.83 2.18 2.53 3.03 4.44 1.78 2.10 2.42 2.88 4.17 1.74 2.05 2.36 2.79 4.00 1.72 2.01 2.31 2.72 3.88 1.69 1.96 2.25 2.64 3.74 1.67 1.94 2.21 2.58 3.64 1.66 1.92 2.18 2.55 3.58 1.62 1.87 2.11 2.46 3.42 1.59 1.82 2.05 2.37 3.28 22 .100 .050 .025 .010 .001 2.95 4.30 5.79 7.95 14.38 2.56 3.44 4.38 5.72 9.61 2.35 3.05 3.78 4.82 7.80 2.22 2.82 3.44 4.31 6.81 2.13 2.66 3.22 3.99 6.19 2.06 2.55 3.05 3.76 5.76 2.01 2.46 2.93 3.59 5.44 1.97 2.40 2.84 3.45 5.19 1.93 2.34 2.76 3.35 4.99 1.90 2.30 2.70 3.26 4.83 1.86 2.23 2.60 3.12 4.58 1.81 2.15 2.50 2.98 4.33 1.76 2.07 2.39 2.83 4.06 1.73 2.02 2.32 2.73 3.89 1.70 1.98 2.27 2.67 3.78 1.67 1.94 2.21 2.58 3.63 1.65 1.91 2.17 2.53 3.54 1.64 1.89 2.14 2.50 3.48 1.60 1.84 2.08 2.40 3.32 1.57 1.79 2.01 2.32 3.17 23 .100 .050 .025 .010 .001 2.94 4.28 5.75 7.88 14.20 2.55 3.42 4.35 5.66 9.47 2.34 3.03 3.75 4.76 7.67 2.21 2.80 3.41 4.26 6.70 2.11 2.64 3.18 3.94 6.08 2.05 2.53 3.02 3.71 5.65 1.99 2.44 2.90 3.54 5.33 1.95 2.37 2.81 3.41 5.09 1.92 2.32 2.73 3.30 4.89 1.89 2.27 2.67 3.21 4.73 1.84 2.20 2.57 3.07 4.48 1.80 2.13 2.47 2.93 4.23 1.74 2.05 2.36 2.78 3.96 1.71 2.00 2.29 2.69 3.79 1.69 1.96 2.24 2.62 3.68 1.66 1.91 2.18 2.54 3.53 1.64 1.88 2.14 2.48 3.44 1.62 1.86 2.11 2.45 3.38 1.59 1.81 2.04 2.35 3.22 1.55 1.76 1.98 2.27 3.08 24 .100 .050 .025 .010 .001 2.93 4.26 5.72 7.82 14.03 2.54 3.40 4.32 5.61 9.34 2.33 3.01 3.72 4.72 7.55 2.19 2.78 3.38 4.22 6.59 2.10 2.62 3.15 3.90 5.98 2.04 2.51 2.99 3.67 5.55 1.98 2.42 2.87 3.50 5.23 1.94 2.36 2.78 3.36 4.99 1.91 2.30 2.70 3.26 4.80 1.88 2.25 2.64 3.17 4.64 1.83 2.18 2.54 3.03 4.39 1.78 2.11 2.44 2.89 4.14 1.73 2.03 2.33 2.74 3.87 1.70 1.97 2.26 2.64 3.71 1.67 1.94 2.21 2.58 3.59 1.64 1.89 2.15 2.49 3.45 1.62 1.86 2.11 2.44 3.36 1.61 1.84 2.08 2.40 3.29 1.57 1.79 2.01 2.31 3.14 1.54 1.74 1.94 2.22 2.99 25 .100 .050 .025 .010 .001 2.92 4.24 5.69 7.77 13.88 2.53 3.39 4.29 5.57 9.22 2.32 2.99 3.69 4.68 7.45 2.18 2.76 3.35 4.18 6.49 2.09 2.60 3.13 3.85 5.89 2.02 2.49 2.97 3.63 5.46 1.97 2.40 2.85 3.46 5.15 1.93 2.34 2.75 3.32 4.91 1.89 2.28 2.68 3.22 4.71 1.87 2.24 2.61 3.13 4.56 1.82 2.16 2.51 2.99 4.31 1.77 2.09 2.41 2.85 4.06 1.72 2.01 2.30 2.70 3.79 1.68 1.96 2.23 2.60 3.63 1.66 1.92 2.18 2.54 3.52 1.63 1.87 2.12 2.45 3.37 1.61 1.84 2.08 2.40 3.28 1.59 1.82 2.05 2.36 3.22 1.56 1.77 1.98 2.27 3.06 1.52 1.72 1.91 2.18 2.91 26 .100 .050 .025 .010 .001 2.91 4.23 5.66 7.72 13.74 2.52 3.37 4.27 5.53 9.12 2.31 2.98 3.67 4.64 7.36 2.17 2.74 3.33 4.14 6.41 2.08 2.59 3.10 3.82 5.80 2.01 2.47 2.94 3.59 5.38 1.96 2.39 2.82 3.42 5.07 1.92 2.32 2.73 3.29 4.83 1.88 2.27 2.65 3.18 4.64 1.86 2.22 2.59 3.09 4.48 1.81 2.15 2.49 2.96 4.24 1.76 2.07 2.39 2.81 3.99 1.71 1.99 2.28 2.66 3.72 1.67 1.94 2.21 2.57 3.56 1.65 1.90 2.16 2.50 3.44 1.61 1.85 2.09 2.42 3.30 1.59 1.82 2.05 2.36 3.21 1.58 1.80 2.03 2.33 3.15 1.54 1.75 1.95 2.23 2.99 1.51 1.70 1.89 2.14 2.84 27 .100 .050 .025 .010 .001 2.90 4.21 5.63 7.68 13.61 2.51 3.35 4.24 5.49 9.02 2.30 2.96 3.65 4.60 7.27 2.17 2.73 3.31 4.11 6.33 2.07 2.57 3.08 3.78 5.73 2.00 2.46 2.92 3.56 5.31 1.95 2.37 2.80 3.39 5.00 1.91 2.31 2.71 3.26 4.76 1.87 2.25 2.63 3.15 4.57 1.85 2.20 2.57 3.06 4.41 1.80 2.13 2.47 2.93 4.17 1.75 2.06 2.36 2.78 3.92 1.70 1.97 2.25 2.63 3.66 1.66 1.92 2.18 2.54 3.49 1.64 1.88 2.13 2.47 3.38 1.60 1.84 2.07 2.38 3.23 1.58 1.81 2.03 2.33 3.14 1.57 1.79 2.00 2.29 3.08 1.53 1.73 1.93 2.20 2.92 1.50 1.68 1.86 2.11 2.78 TABLA D Valores críticos de la distribución F de Fisher (cont.) TABLA D Valores críticos de la distribución F de Fisher (cont.) Grados de libertad en el numerador Grados de libertad en el denominador Grados de libertad en el numerador p 1 2 3 4 5 6 7 8 9 10 12 15 20 25 30 40 50 60 120 1000 28 .100 .050 .025 .010 .001 2.89 4.20 5.61 7.64 13.50 2.50 3.34 4.22 5.45 8.93 2.29 2.95 3.63 4.57 7.19 2.16 2.71 3.29 4.07 6.25 2.06 2.56 3.06 3.75 5.66 2.00 2.45 2.90 3.53 5.24 1.94 2.36 2.78 3.36 4.93 1.90 2.29 2.69 3.23 4.69 1.87 2.24 2.61 3.12 4.50 1.84 2.19 2.55 3.03 4.35 1.79 2.12 2.45 2.90 4.11 1.74 2.04 2.34 2.75 3.86 1.69 1.96 2.23 2.60 3.60 1.65 1.91 2.16 2.51 3.43 1.63 1.87 2.11 2.44 3.32 1.59 1.82 2.05 2.35 3.18 1.57 1.79 2.01 2.30 3.09 1.56 1.77 1.98 2.26 3.02 1.52 1.71 1.91 2.17 2.86 1.48 1.66 1.84 2.08 2.72 29 .100 .050 .025 .010 .001 2.89 4.18 5.59 7.60 13.39 2.50 3.33 4.20 5.42 8.85 2.28 2.93 3.61 4.54 7.12 2.15 2.70 3.27 4.04 6.19 2.06 2.55 3.04 3.73 5.59 1.99 2.43 2.88 3.50 5.18 1.93 2.35 2.76 3.33 4.87 1.89 2.28 2.67 3.20 4.64 1.86 2.22 2.59 3.09 4.45 1.83 2.18 2.53 3.00 4.29 1.78 2.10 2.43 2.87 4.05 1.73 2.03 2.32 2.73 3.80 1.68 1.94 2.21 2.57 3.54 1.64 1.89 2.14 2.48 3.38 1.62 1.85 2.09 2.41 3.27 1.58 1.81 2.03 2.33 3.12 1.56 1.77 1.99 2.27 3.03 1.55 1.75 1.96 2.23 2.97 1.51 1.70 1.89 2.14 2.81 1.47 1.65 1.82 2.05 2.66 30 .100 .050 .025 .010 .001 2.88 4.17 5.57 7.56 13.29 2.49 3.32 4.18 5.39 8.77 2.28 2.92 3.59 4.51 7.05 2.14 2.69 3.25 4.02 6.12 2.05 2.53 3.03 3.70 5.53 1.98 2.42 2.87 3.47 5.12 1.93 2.33 2.75 3.30 4.82 1.88 2.27 2.65 3.17 4.58 1.85 2.21 2.57 3.07 4.39 1.82 2.16 2.51 2.98 4.24 1.77 2.09 2.41 2.84 4.00 1.72 2.01 2.31 2.70 3.75 1.67 1.93 2.20 2.55 3.49 1.63 1.88 2.12 2.45 3.33 1.61 1.84 2.07 2.39 3.22 1.57 1.79 2.01 2.30 3.07 1.55 1.76 1.97 2.25 2.98 1.54 1.74 1.94 2.21 2.92 1.50 1.68 1.87 2.11 2.76 1.46 1.63 1.80 2.02 2.61 40 .100 .050 .025 .010 .001 2.84 4.08 5.42 7.31 12.61 2.44 3.23 4.05 5.18 8.25 2.23 2.84 3.46 4.31 6.59 2.09 2.61 3.13 3.83 5.70 2.00 2.45 2.90 3.51 5.13 1.93 2.34 2.74 3.29 4.73 1.87 2.25 2.62 3.12 4.44 1.83 2.18 2.53 2.99 4.21 1.79 2.12 2.45 2.89 4.02 1.76 2.08 2.39 2.80 3.87 1.71 2.00 2.29 2.66 3.64 1.66 1.92 2.18 2.52 3.40 1.61 1.84 2.07 2.37 3.14 1.57 1.78 1.99 2.27 2.98 1.54 1.74 1.94 2.20 2.87 1.51 1.69 1.88 2.11 2.73 1.48 1.66 1.83 2.06 2.64 1.47 1.64 1.80 2.02 2.57 1.42 1.58 1.72 1.92 2.41 1.38 1.52 1.65 1.82 2.25 50 .100 .050 .025 .010 .001 2.81 4.03 5.34 7.17 12.22 2.41 3.18 3.97 5.06 7.96 2.20 2.79 3.39 4.20 6.34 2.06 2.56 3.05 3.72 5.46 1.97 2.40 2.83 3.41 4.90 1.90 2.29 2.67 3.19 4.51 1.84 2.20 2.55 3.02 4.22 1.80 2.13 2.46 2.89 4.00 1.76 2.07 2.38 2.78 3.82 1.73 2.03 2.32 2.70 3.67 1.68 1.95 2.22 2.56 3.44 1.63 1.87 2.11 2.42 3.20 1.57 1.78 1.99 2.27 2.95 1.53 1.73 1.92 2.17 2.79 1.50 1.69 1.87 2.10 2.68 1.46 1.63 1.80 2.01 2.53 1.44 1.60 1.75 1.95 2.44 1.42 1.58 1.72 1.91 2.38 1.38 1.51 1.64 1.80 2.21 1.33 1.45 1.56 1.70 2.05 60 .100 .050 .025 .010 .001 2.79 4.00 5.29 7.08 11.97 2.39 3.15 3.93 4.98 7.77 2.18 2.76 3.34 4.13 6.17 2.04 2.53 3.01 3.65 5.31 1.95 2.37 2.79 3.34 4.76 1.87 2.25 2.63 3.12 4.37 1.82 2.17 2.51 2.95 4.09 1.77 2.10 2.41 2.82 3.86 1.74 2.04 2.33 2.72 3.69 1.71 1.99 2.27 2.63 3.54 1.66 1.92 2.17 2.50 3.32 1.60 1.84 2.06 2.35 3.08 1.54 1.75 1.94 2.20 2.83 1.50 1.69 1.87 2.10 2.67 1.48 1.65 1.82 2.03 2.55 1.44 1.59 1.74 1.94 2.41 1.41 1.56 1.70 1.88 2.32 1.40 1.53 1.67 1.84 2.25 1.35 1.47 1.58 1.73 2.08 1.30 1.40 1.49 1.62 1.92 100 .100 .050 .025 .010 .001 2.76 3.94 5.18 6.90 11.50 2.36 3.09 3.83 4.82 7.41 2.14 2.70 3.25 3.98 5.86 2.00 2.46 2.92 3.51 5.02 1.91 2.31 2.70 3.21 4.48 1.83 2.19 2.54 2.99 4.11 1.78 2.10 2.42 2.82 3.83 1.73 2.03 2.32 2.69 3.61 1.69 1.97 2.24 2.59 3.44 1.66 1.93 2.18 2.50 3.30 1.61 1.85 2.08 2.37 3.07 1.56 1.77 1.97 2.22 2.84 1.49 1.68 1.85 2.07 2.59 1.45 1.62 1.77 1.97 2.43 1.42 1.57 1.71 1.89 2.32 1.38 1.52 1.64 1.80 2.17 1.35 1.48 1.59 1.74 2.08 1.34 1.45 1.56 1.69 2.01 1.28 1.38 1.46 1.57 1.83 1.22 1.30 1.36 1.45 1.64 200 .100 .050 .025 .010 .001 2.73 3.89 5.10 6.76 11.15 2.33 3.04 3.76 4.71 7.15 2.11 2.65 3.18 3.88 5.63 1.97 2.42 2.85 3.41 4.81 1.88 2.26 2.63 3.11 4.29 1.80 2.14 2.47 2.89 3.92 1.75 2.06 2.35 2.73 3.65 1.70 1.98 2.26 2.60 3.43 1.66 1.93 2.18 2.50 3.26 1.63 1.88 2.11 2.41 3.12 1.58 1.80 2.01 2.27 2.90 1.52 1.72 1.90 2.13 2.67 1.46 1.62 1.78 1.97 2.42 1.41 1.56 1.70 1.87 2.26 1.38 1.52 1.64 1.79 2.15 1.34 1.46 1.56 1.69 2.00 1.31 1.41 1.51 1.63 1.90 1.29 1.39 1.47 1.58 1.83 1.23 1.30 1.37 1.45 1.64 1.16 1.21 1.25 1.30 1.43 1000 .100 .050 .025 .010 .001 2.71 3.85 5.04 6.66 10.89 2.31 3.00 3.70 4.63 6.96 2.09 2.61 3.13 3.80 5.46 1.95 2.38 2.80 3.34 4.65 1.85 2.22 2.58 3.04 4.14 1.78 2.11 2.42 2.82 3.78 1.72 2.02 2.30 2.66 3.51 1.68 1.95 2.20 2.53 3.30 1.64 1.89 2.13 2.43 3.13 1.61 1.84 2.06 2.34 2.99 1.55 1.76 1.96 2.20 2.77 1.49 1.68 1.85 2.06 2.54 1.43 1.58 1.72 1.90 2.30 1.38 1.52 1.64 1.79 2.14 1.35 1.47 1.58 1.72 2.02 1.30 1.41 1.50 1.61 1.87 1.27 1.36 1.45 1.54 1.77 1.25 1.33 1.41 1.50 1.69 1.18 1.24 1.29 1.35 1.49 1.08 1.11 1.13 1.16 1.22
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