Tablas de las Distribuciones Estadisticas Mas Usadas

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TABLAS DE LAS DISTRIBUCIONES ESTADISTICAS MÁS USADAS http://estadistica-spss.blogspot.com/ Clases Online de Estadistica, Analisis de Datos y SPSS [email protected]

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Transcript of Tablas de las Distribuciones Estadisticas Mas Usadas

Page 1: Tablas de las Distribuciones Estadisticas Mas Usadas

TABLAS DE LAS

DISTRIBUCIONES

ESTADISTICAS

MÁS USADAS

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BINOMIAL

TABLA DE DISTRIBUCION

α=P[B≤k]

(Probabilidad acumulada inferior o a la izquierda)

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Tables of the Binomial Cumulative Distribution

The table below gives the probability of obtaining at most x successes in n independent trials, each of which has a probability p of success. Thatis, if X denotes the number of successes, the table shows

0

( ) (1 )x

n r n rr

r

P X x C p p −

=

≤ = −∑p= 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5n= 2 x= 0 0.9801 0.9604 0.9409 0.9216 0.9025 0.8836 0.8649 0.8464 0.8281 0.8100 0.7225 0.6400 0.5625 0.4900 0.4225 0.3600 0.3025 0.2500

1 0.9999 0.9996 0.9991 0.9984 0.9975 0.9964 0.9951 0.9936 0.9919 0.9900 0.9775 0.9600 0.9375 0.9100 0.8775 0.8400 0.7975 0.75002 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

n= 3 x= 0 0.9703 0.9412 0.9127 0.8847 0.8574 0.8306 0.8044 0.7787 0.7536 0.7290 0.6141 0.5120 0.4219 0.3430 0.2746 0.2160 0.1664 0.12501 0.9997 0.9988 0.9974 0.9953 0.9928 0.9896 0.9860 0.9818 0.9772 0.9720 0.9393 0.8960 0.8438 0.7840 0.7183 0.6480 0.5748 0.50002 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9995 0.9993 0.9990 0.9966 0.9920 0.9844 0.9730 0.9571 0.9360 0.9089 0.87503 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

n= 4 x= 0 0.9606 0.9224 0.8853 0.8493 0.8145 0.7807 0.7481 0.7164 0.6857 0.6561 0.5220 0.4096 0.3164 0.2401 0.1785 0.1296 0.0915 0.06251 0.9994 0.9977 0.9948 0.9909 0.9860 0.9801 0.9733 0.9656 0.9570 0.9477 0.8905 0.8192 0.7383 0.6517 0.5630 0.4752 0.3910 0.31252 1.0000 1.0000 0.9999 0.9998 0.9995 0.9992 0.9987 0.9981 0.9973 0.9963 0.9880 0.9728 0.9492 0.9163 0.8735 0.8208 0.7585 0.68753 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9995 0.9984 0.9961 0.9919 0.9850 0.9744 0.9590 0.93754 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

n= 5 x= 0 0.9510 0.9039 0.8587 0.8154 0.7738 0.7339 0.6957 0.6591 0.6240 0.5905 0.4437 0.3277 0.2373 0.1681 0.1160 0.0778 0.0503 0.03131 0.9990 0.9962 0.9915 0.9852 0.9774 0.9681 0.9575 0.9456 0.9326 0.9185 0.8352 0.7373 0.6328 0.5282 0.4284 0.3370 0.2562 0.18752 1.0000 0.9999 0.9997 0.9994 0.9988 0.9980 0.9969 0.9955 0.9937 0.9914 0.9734 0.9421 0.8965 0.8369 0.7648 0.6826 0.5931 0.50003 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9995 0.9978 0.9933 0.9844 0.9692 0.9460 0.9130 0.8688 0.81254 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9990 0.9976 0.9947 0.9898 0.9815 0.96885 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

n= 6 x= 0 0.9415 0.8858 0.8330 0.7828 0.7351 0.6899 0.6470 0.6064 0.5679 0.5314 0.3771 0.2621 0.1780 0.1176 0.0754 0.0467 0.0277 0.01561 0.9985 0.9943 0.9875 0.9784 0.9672 0.9541 0.9392 0.9227 0.9048 0.8857 0.7765 0.6554 0.5339 0.4202 0.3191 0.2333 0.1636 0.10942 1.0000 0.9998 0.9995 0.9988 0.9978 0.9962 0.9942 0.9915 0.9882 0.9842 0.9527 0.9011 0.8306 0.7443 0.6471 0.5443 0.4415 0.34383 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9995 0.9992 0.9987 0.9941 0.9830 0.9624 0.9295 0.8826 0.8208 0.7447 0.65634 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.9984 0.9954 0.9891 0.9777 0.9590 0.9308 0.89065 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9993 0.9982 0.9959 0.9917 0.98446 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

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p= 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5n= 7 x= 0 0.9321 0.8681 0.8080 0.7514 0.6983 0.6485 0.6017 0.5578 0.5168 0.4783 0.3206 0.2097 0.1335 0.0824 0.0490 0.0280 0.0152 0.0078

1 0.9980 0.9921 0.9829 0.9706 0.9556 0.9382 0.9187 0.8974 0.8745 0.8503 0.7166 0.5767 0.4449 0.3294 0.2338 0.1586 0.1024 0.06252 1.0000 0.9997 0.9991 0.9980 0.9962 0.9937 0.9903 0.9860 0.9807 0.9743 0.9262 0.8520 0.7564 0.6471 0.5323 0.4199 0.3164 0.22663 1.0000 1.0000 1.0000 0.9999 0.9998 0.9996 0.9993 0.9988 0.9982 0.9973 0.9879 0.9667 0.9294 0.8740 0.8002 0.7102 0.6083 0.50004 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9988 0.9953 0.9871 0.9712 0.9444 0.9037 0.8471 0.77345 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.9987 0.9962 0.9910 0.9812 0.9643 0.93756 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9994 0.9984 0.9963 0.99227 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

n= 8 x= 0 0.9227 0.8508 0.7837 0.7214 0.6634 0.6096 0.5596 0.5132 0.4703 0.4305 0.2725 0.1678 0.1001 0.0576 0.0319 0.0168 0.0084 0.00391 0.9973 0.9897 0.9777 0.9619 0.9428 0.9208 0.8965 0.8702 0.8423 0.8131 0.6572 0.5033 0.3671 0.2553 0.1691 0.1064 0.0632 0.03522 0.9999 0.9996 0.9987 0.9969 0.9942 0.9904 0.9853 0.9789 0.9711 0.9619 0.8948 0.7969 0.6785 0.5518 0.4278 0.3154 0.2201 0.14453 1.0000 1.0000 0.9999 0.9998 0.9996 0.9993 0.9987 0.9978 0.9966 0.9950 0.9786 0.9437 0.8862 0.8059 0.7064 0.5941 0.4770 0.36334 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9997 0.9996 0.9971 0.9896 0.9727 0.9420 0.8939 0.8263 0.7396 0.63675 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9988 0.9958 0.9887 0.9747 0.9502 0.9115 0.85556 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.9987 0.9964 0.9915 0.9819 0.96487 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9993 0.9983 0.99618 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

n= 9 x= 0 0.9135 0.8337 0.7602 0.6925 0.6302 0.5730 0.5204 0.4722 0.4279 0.3874 0.2316 0.1342 0.0751 0.0404 0.0207 0.0101 0.0046 0.00201 0.9966 0.9869 0.9718 0.9522 0.9288 0.9022 0.8729 0.8417 0.8088 0.7748 0.5995 0.4362 0.3003 0.1960 0.1211 0.0705 0.0385 0.01952 0.9999 0.9994 0.9980 0.9955 0.9916 0.9862 0.9791 0.9702 0.9595 0.9470 0.8591 0.7382 0.6007 0.4628 0.3373 0.2318 0.1495 0.08983 1.0000 1.0000 0.9999 0.9997 0.9994 0.9987 0.9977 0.9963 0.9943 0.9917 0.9661 0.9144 0.8343 0.7297 0.6089 0.4826 0.3614 0.25394 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9995 0.9991 0.9944 0.9804 0.9511 0.9012 0.8283 0.7334 0.6214 0.50005 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9994 0.9969 0.9900 0.9747 0.9464 0.9006 0.8342 0.74616 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9987 0.9957 0.9888 0.9750 0.9502 0.91027 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.9986 0.9962 0.9909 0.98058 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9992 0.99809 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

n= 10 x= 0 0.9044 0.8171 0.7374 0.6648 0.5987 0.5386 0.4840 0.4344 0.3894 0.3487 0.1969 0.1074 0.0563 0.0282 0.0135 0.0060 0.0025 0.00101 0.9957 0.9838 0.9655 0.9418 0.9139 0.8824 0.8483 0.8121 0.7746 0.7361 0.5443 0.3758 0.2440 0.1493 0.0860 0.0464 0.0233 0.01072 0.9999 0.9991 0.9972 0.9938 0.9885 0.9812 0.9717 0.9599 0.9460 0.9298 0.8202 0.6778 0.5256 0.3828 0.2616 0.1673 0.0996 0.05473 1.0000 1.0000 0.9999 0.9996 0.9990 0.9980 0.9964 0.9942 0.9912 0.9872 0.9500 0.8791 0.7759 0.6496 0.5138 0.3823 0.2660 0.17194 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9994 0.9990 0.9984 0.9901 0.9672 0.9219 0.8497 0.7515 0.6331 0.5044 0.37705 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9986 0.9936 0.9803 0.9527 0.9051 0.8338 0.7384 0.62306 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9991 0.9965 0.9894 0.9740 0.9452 0.8980 0.82817 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.9984 0.9952 0.9877 0.9726 0.94538 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9995 0.9983 0.9955 0.98939 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.999010 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

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p= 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5n= 11 x= 0 0.8953 0.8007 0.7153 0.6382 0.5688 0.5063 0.4501 0.3996 0.3544 0.3138 0.1673 0.0859 0.0422 0.0198 0.0088 0.0036 0.0014 0.0005

1 0.9948 0.9805 0.9587 0.9308 0.8981 0.8618 0.8228 0.7819 0.7399 0.6974 0.4922 0.3221 0.1971 0.1130 0.0606 0.0302 0.0139 0.00592 0.9998 0.9988 0.9963 0.9917 0.9848 0.9752 0.9630 0.9481 0.9305 0.9104 0.7788 0.6174 0.4552 0.3127 0.2001 0.1189 0.0652 0.03273 1.0000 1.0000 0.9998 0.9993 0.9984 0.9970 0.9947 0.9915 0.9871 0.9815 0.9306 0.8389 0.7133 0.5696 0.4256 0.2963 0.1911 0.11334 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9995 0.9990 0.9983 0.9972 0.9841 0.9496 0.8854 0.7897 0.6683 0.5328 0.3971 0.27445 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9973 0.9883 0.9657 0.9218 0.8513 0.7535 0.6331 0.50006 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9980 0.9924 0.9784 0.9499 0.9006 0.8262 0.72567 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9988 0.9957 0.9878 0.9707 0.9390 0.88678 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9994 0.9980 0.9941 0.9852 0.96739 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9993 0.9978 0.994110 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.999511 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

n= 12 x= 0 0.8864 0.7847 0.6938 0.6127 0.5404 0.4759 0.4186 0.3677 0.3225 0.2824 0.1422 0.0687 0.0317 0.0138 0.0057 0.0022 0.0008 0.00021 0.9938 0.9769 0.9514 0.9191 0.8816 0.8405 0.7967 0.7513 0.7052 0.6590 0.4435 0.2749 0.1584 0.0850 0.0424 0.0196 0.0083 0.00322 0.9998 0.9985 0.9952 0.9893 0.9804 0.9684 0.9532 0.9348 0.9134 0.8891 0.7358 0.5583 0.3907 0.2528 0.1513 0.0834 0.0421 0.01933 1.0000 0.9999 0.9997 0.9990 0.9978 0.9957 0.9925 0.9880 0.9820 0.9744 0.9078 0.7946 0.6488 0.4925 0.3467 0.2253 0.1345 0.07304 1.0000 1.0000 1.0000 0.9999 0.9998 0.9996 0.9991 0.9984 0.9973 0.9957 0.9761 0.9274 0.8424 0.7237 0.5833 0.4382 0.3044 0.19385 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9995 0.9954 0.9806 0.9456 0.8822 0.7873 0.6652 0.5269 0.38726 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9993 0.9961 0.9857 0.9614 0.9154 0.8418 0.7393 0.61287 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9994 0.9972 0.9905 0.9745 0.9427 0.8883 0.80628 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.9983 0.9944 0.9847 0.9644 0.92709 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9992 0.9972 0.9921 0.980710 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9989 0.996811 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.999812 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

n= 13 x= 0 0.8775 0.7690 0.6730 0.5882 0.5133 0.4474 0.3893 0.3383 0.2935 0.2542 0.1209 0.0550 0.0238 0.0097 0.0037 0.0013 0.0004 0.00011 0.9928 0.9730 0.9436 0.9068 0.8646 0.8186 0.7702 0.7206 0.6707 0.6213 0.3983 0.2336 0.1267 0.0637 0.0296 0.0126 0.0049 0.00172 0.9997 0.9980 0.9938 0.9865 0.9755 0.9608 0.9422 0.9201 0.8946 0.8661 0.6920 0.5017 0.3326 0.2025 0.1132 0.0579 0.0269 0.01123 1.0000 0.9999 0.9995 0.9986 0.9969 0.9940 0.9897 0.9837 0.9758 0.9658 0.8820 0.7473 0.5843 0.4206 0.2783 0.1686 0.0929 0.04614 1.0000 1.0000 1.0000 0.9999 0.9997 0.9993 0.9987 0.9976 0.9959 0.9935 0.9658 0.9009 0.7940 0.6543 0.5005 0.3530 0.2279 0.13345 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9997 0.9995 0.9991 0.9925 0.9700 0.9198 0.8346 0.7159 0.5744 0.4268 0.29056 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9987 0.9930 0.9757 0.9376 0.8705 0.7712 0.6437 0.50007 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9988 0.9944 0.9818 0.9538 0.9023 0.8212 0.70958 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9990 0.9960 0.9874 0.9679 0.9302 0.86669 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9993 0.9975 0.9922 0.9797 0.953910 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9987 0.9959 0.988811 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9995 0.998312 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.999913 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

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Page 6: Tablas de las Distribuciones Estadisticas Mas Usadas

p= 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5n= 14 x= 0 0.8687 0.7536 0.6528 0.5647 0.4877 0.4205 0.3620 0.3112 0.2670 0.2288 0.1028 0.0440 0.0178 0.0068 0.0024 0.0008 0.0002 0.0001

1 0.9916 0.9690 0.9355 0.8941 0.8470 0.7963 0.7436 0.6900 0.6368 0.5846 0.3567 0.1979 0.1010 0.0475 0.0205 0.0081 0.0029 0.00092 0.9997 0.9975 0.9923 0.9833 0.9699 0.9522 0.9302 0.9042 0.8745 0.8416 0.6479 0.4481 0.2811 0.1608 0.0839 0.0398 0.0170 0.00653 1.0000 0.9999 0.9994 0.9981 0.9958 0.9920 0.9864 0.9786 0.9685 0.9559 0.8535 0.6982 0.5213 0.3552 0.2205 0.1243 0.0632 0.02874 1.0000 1.0000 1.0000 0.9998 0.9996 0.9990 0.9980 0.9965 0.9941 0.9908 0.9533 0.8702 0.7415 0.5842 0.4227 0.2793 0.1672 0.08985 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9996 0.9992 0.9985 0.9885 0.9561 0.8883 0.7805 0.6405 0.4859 0.3373 0.21206 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9978 0.9884 0.9617 0.9067 0.8164 0.6925 0.5461 0.39537 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9976 0.9897 0.9685 0.9247 0.8499 0.7414 0.60478 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9996 0.9978 0.9917 0.9757 0.9417 0.8811 0.78809 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9983 0.9940 0.9825 0.9574 0.910210 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9989 0.9961 0.9886 0.971311 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9994 0.9978 0.993512 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.999113 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.999914 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

n= 15 x= 0 0.8601 0.7386 0.6333 0.5421 0.4633 0.3953 0.3367 0.2863 0.2430 0.2059 0.0874 0.0352 0.0134 0.0047 0.0016 0.0005 0.0001 0.00001 0.9904 0.9647 0.9270 0.8809 0.8290 0.7738 0.7168 0.6597 0.6035 0.5490 0.3186 0.1671 0.0802 0.0353 0.0142 0.0052 0.0017 0.00052 0.9996 0.9970 0.9906 0.9797 0.9638 0.9429 0.9171 0.8870 0.8531 0.8159 0.6042 0.3980 0.2361 0.1268 0.0617 0.0271 0.0107 0.00373 1.0000 0.9998 0.9992 0.9976 0.9945 0.9896 0.9825 0.9727 0.9601 0.9444 0.8227 0.6482 0.4613 0.2969 0.1727 0.0905 0.0424 0.01764 1.0000 1.0000 0.9999 0.9998 0.9994 0.9986 0.9972 0.9950 0.9918 0.9873 0.9383 0.8358 0.6865 0.5155 0.3519 0.2173 0.1204 0.05925 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9997 0.9993 0.9987 0.9978 0.9832 0.9389 0.8516 0.7216 0.5643 0.4032 0.2608 0.15096 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9964 0.9819 0.9434 0.8689 0.7548 0.6098 0.4522 0.30367 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9994 0.9958 0.9827 0.9500 0.8868 0.7869 0.6535 0.50008 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9992 0.9958 0.9848 0.9578 0.9050 0.8182 0.69649 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9992 0.9963 0.9876 0.9662 0.9231 0.849110 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9993 0.9972 0.9907 0.9745 0.940811 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9995 0.9981 0.9937 0.982412 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9989 0.996313 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.999514 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.000015 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

n= 20 x= 0 0.8179 0.6676 0.5438 0.4420 0.3585 0.2901 0.2342 0.1887 0.1516 0.1216 0.0388 0.0115 0.0032 0.0008 0.0002 0.0000 0.0000 0.00001 0.9831 0.9401 0.8802 0.8103 0.7358 0.6605 0.5869 0.5169 0.4516 0.3917 0.1756 0.0692 0.0243 0.0076 0.0021 0.0005 0.0001 0.00002 0.9990 0.9929 0.9790 0.9561 0.9245 0.8850 0.8390 0.7879 0.7334 0.6769 0.4049 0.2061 0.0913 0.0355 0.0121 0.0036 0.0009 0.00023 1.0000 0.9994 0.9973 0.9926 0.9841 0.9710 0.9529 0.9294 0.9007 0.8670 0.6477 0.4114 0.2252 0.1071 0.0444 0.0160 0.0049 0.00134 1.0000 1.0000 0.9997 0.9990 0.9974 0.9944 0.9893 0.9817 0.9710 0.9568 0.8298 0.6296 0.4148 0.2375 0.1182 0.0510 0.0189 0.00595 1.0000 1.0000 1.0000 0.9999 0.9997 0.9991 0.9981 0.9962 0.9932 0.9887 0.9327 0.8042 0.6172 0.4164 0.2454 0.1256 0.0553 0.02076 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9994 0.9987 0.9976 0.9781 0.9133 0.7858 0.6080 0.4166 0.2500 0.1299 0.05777 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9996 0.9941 0.9679 0.8982 0.7723 0.6010 0.4159 0.2520 0.1316

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Page 7: Tablas de las Distribuciones Estadisticas Mas Usadas

p= 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5n= 20 x= 8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9987 0.9900 0.9591 0.8867 0.7624 0.5956 0.4143 0.2517

9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9974 0.9861 0.9520 0.8782 0.7553 0.5914 0.411910 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9994 0.9961 0.9829 0.9468 0.8725 0.7507 0.588111 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9991 0.9949 0.9804 0.9435 0.8692 0.748312 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9987 0.9940 0.9790 0.9420 0.868413 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9985 0.9935 0.9786 0.942314 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9984 0.9936 0.979315 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9985 0.994116 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.998717 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.999818 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

n= 25 x= 0 0.7778 0.6035 0.4670 0.3604 0.2774 0.2129 0.1630 0.1244 0.0946 0.0718 0.0172 0.0038 0.0008 0.0001 0.0000 0.0000 0.0000 0.00001 0.9742 0.9114 0.8280 0.7358 0.6424 0.5527 0.4696 0.3947 0.3286 0.2712 0.0931 0.0274 0.0070 0.0016 0.0003 0.0001 0.0000 0.00002 0.9980 0.9868 0.9620 0.9235 0.8729 0.8129 0.7466 0.6768 0.6063 0.5371 0.2537 0.0982 0.0321 0.0090 0.0021 0.0004 0.0001 0.00003 0.9999 0.9986 0.9938 0.9835 0.9659 0.9402 0.9064 0.8649 0.8169 0.7636 0.4711 0.2340 0.0962 0.0332 0.0097 0.0024 0.0005 0.00014 1.0000 0.9999 0.9992 0.9972 0.9928 0.9850 0.9726 0.9549 0.9314 0.9020 0.6821 0.4207 0.2137 0.0905 0.0320 0.0095 0.0023 0.00055 1.0000 1.0000 0.9999 0.9996 0.9988 0.9969 0.9935 0.9877 0.9790 0.9666 0.8385 0.6167 0.3783 0.1935 0.0826 0.0294 0.0086 0.00206 1.0000 1.0000 1.0000 1.0000 0.9998 0.9995 0.9987 0.9972 0.9946 0.9905 0.9305 0.7800 0.5611 0.3407 0.1734 0.0736 0.0258 0.00737 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9995 0.9989 0.9977 0.9745 0.8909 0.7265 0.5118 0.3061 0.1536 0.0639 0.02168 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9995 0.9920 0.9532 0.8506 0.6769 0.4668 0.2735 0.1340 0.05399 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9979 0.9827 0.9287 0.8106 0.6303 0.4246 0.2424 0.114810 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9944 0.9703 0.9022 0.7712 0.5858 0.3843 0.212211 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9985 0.9893 0.9558 0.8746 0.7323 0.5426 0.345012 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9996 0.9966 0.9825 0.9396 0.8462 0.6937 0.500013 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9991 0.9940 0.9745 0.9222 0.8173 0.655014 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9982 0.9907 0.9656 0.9040 0.787815 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9971 0.9868 0.9560 0.885216 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9992 0.9957 0.9826 0.946117 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9988 0.9942 0.978418 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9984 0.992719 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.998020 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.999521 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.999922 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

n= 30 x= 0 0.7397 0.5455 0.4010 0.2939 0.2146 0.1563 0.1134 0.0820 0.0591 0.0424 0.0076 0.0012 0.0002 0.0000 0.0000 0.0000 0.0000 0.00001 0.9639 0.8795 0.7731 0.6612 0.5535 0.4555 0.3694 0.2958 0.2343 0.1837 0.0480 0.0105 0.0020 0.0003 0.0000 0.0000 0.0000 0.00002 0.9967 0.9783 0.9399 0.8831 0.8122 0.7324 0.6487 0.5654 0.4855 0.4114 0.1514 0.0442 0.0106 0.0021 0.0003 0.0000 0.0000 0.00003 0.9998 0.9971 0.9881 0.9694 0.9392 0.8974 0.8450 0.7842 0.7175 0.6474 0.3217 0.1227 0.0374 0.0093 0.0019 0.0003 0.0000 0.00004 1.0000 0.9997 0.9982 0.9937 0.9844 0.9685 0.9447 0.9126 0.8723 0.8245 0.5245 0.2552 0.0979 0.0302 0.0075 0.0015 0.0002 0.0000

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Page 8: Tablas de las Distribuciones Estadisticas Mas Usadas

p= 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5n= 30 x= 5 1.0000 1.0000 0.9998 0.9989 0.9967 0.9921 0.9838 0.9707 0.9519 0.9268 0.7106 0.4275 0.2026 0.0766 0.0233 0.0057 0.0011 0.0002

6 1.0000 1.0000 1.0000 0.9999 0.9994 0.9983 0.9960 0.9918 0.9848 0.9742 0.8474 0.6070 0.3481 0.1595 0.0586 0.0172 0.0040 0.00077 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9992 0.9980 0.9959 0.9922 0.9302 0.7608 0.5143 0.2814 0.1238 0.0435 0.0121 0.00268 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.9990 0.9980 0.9722 0.8713 0.6736 0.4315 0.2247 0.0940 0.0312 0.00819 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9995 0.9903 0.9389 0.8034 0.5888 0.3575 0.1763 0.0694 0.021410 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9971 0.9744 0.8943 0.7304 0.5078 0.2915 0.1350 0.049411 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9992 0.9905 0.9493 0.8407 0.6548 0.4311 0.2327 0.100212 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9969 0.9784 0.9155 0.7802 0.5785 0.3592 0.180813 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9991 0.9918 0.9599 0.8737 0.7145 0.5025 0.292314 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9973 0.9831 0.9348 0.8246 0.6448 0.427815 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9992 0.9936 0.9699 0.9029 0.7691 0.572216 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9979 0.9876 0.9519 0.8644 0.707717 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9994 0.9955 0.9788 0.9286 0.819218 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9986 0.9917 0.9666 0.899819 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9996 0.9971 0.9862 0.950620 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9991 0.9950 0.978621 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9984 0.991922 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9996 0.997423 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.999324 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.999825 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

n= 40 x= 0 0.6690 0.4457 0.2957 0.1954 0.1285 0.0842 0.0549 0.0356 0.0230 0.0148 0.0015 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.00001 0.9393 0.8095 0.6615 0.5210 0.3991 0.2990 0.2201 0.1594 0.1140 0.0805 0.0121 0.0015 0.0001 0.0000 0.0000 0.0000 0.0000 0.00002 0.9925 0.9543 0.8822 0.7855 0.6767 0.5665 0.4625 0.3694 0.2894 0.2228 0.0486 0.0079 0.0010 0.0001 0.0000 0.0000 0.0000 0.00003 0.9993 0.9918 0.9686 0.9252 0.8619 0.7827 0.6937 0.6007 0.5092 0.4231 0.1302 0.0285 0.0047 0.0006 0.0001 0.0000 0.0000 0.00004 1.0000 0.9988 0.9933 0.9790 0.9520 0.9104 0.8546 0.7868 0.7103 0.6290 0.2633 0.0759 0.0160 0.0026 0.0003 0.0000 0.0000 0.00005 1.0000 0.9999 0.9988 0.9951 0.9861 0.9691 0.9419 0.9033 0.8535 0.7937 0.4325 0.1613 0.0433 0.0086 0.0013 0.0001 0.0000 0.00006 1.0000 1.0000 0.9998 0.9990 0.9966 0.9909 0.9801 0.9624 0.9361 0.9005 0.6067 0.2859 0.0962 0.0238 0.0044 0.0006 0.0001 0.00007 1.0000 1.0000 1.0000 0.9998 0.9993 0.9977 0.9942 0.9873 0.9758 0.9581 0.7559 0.4371 0.1820 0.0553 0.0124 0.0021 0.0002 0.00008 1.0000 1.0000 1.0000 1.0000 0.9999 0.9995 0.9985 0.9963 0.9919 0.9845 0.8646 0.5931 0.2998 0.1110 0.0303 0.0061 0.0009 0.00019 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9990 0.9976 0.9949 0.9328 0.7318 0.4395 0.1959 0.0644 0.0156 0.0027 0.0003

n= 40 x= 10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9994 0.9985 0.9701 0.8392 0.5839 0.3087 0.1215 0.0352 0.0074 0.001111 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.9880 0.9125 0.7151 0.4406 0.2053 0.0709 0.0179 0.003212 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9957 0.9568 0.8209 0.5772 0.3143 0.1285 0.0386 0.008313 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9986 0.9806 0.8968 0.7032 0.4408 0.2112 0.0751 0.019214 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9996 0.9921 0.9456 0.8074 0.5721 0.3174 0.1326 0.040315 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9971 0.9738 0.8849 0.6946 0.4402 0.2142 0.076916 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9990 0.9884 0.9367 0.7978 0.5681 0.3185 0.134117 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9953 0.9680 0.8761 0.6885 0.4391 0.2148

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Page 9: Tablas de las Distribuciones Estadisticas Mas Usadas

p= 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5n= 40 x= 18 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9983 0.9852 0.9301 0.7911 0.5651 0.3179

19 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9994 0.9937 0.9637 0.8702 0.6844 0.437320 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9976 0.9827 0.9256 0.7870 0.562721 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9991 0.9925 0.9608 0.8669 0.682122 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9970 0.9811 0.9233 0.785223 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9989 0.9917 0.9595 0.865924 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9996 0.9966 0.9804 0.923125 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9988 0.9914 0.959726 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9996 0.9966 0.980827 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9988 0.991728 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9996 0.996829 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.998930 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.999731 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.999932 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

n= 50 x= 0 0.6050 0.3642 0.2181 0.1299 0.0769 0.0453 0.0266 0.0155 0.0090 0.0052 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00001 0.9106 0.7358 0.5553 0.4005 0.2794 0.1900 0.1265 0.0827 0.0532 0.0338 0.0029 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.00002 0.9862 0.9216 0.8108 0.6767 0.5405 0.4162 0.3108 0.2260 0.1605 0.1117 0.0142 0.0013 0.0001 0.0000 0.0000 0.0000 0.0000 0.00003 0.9984 0.9822 0.9372 0.8609 0.7604 0.6473 0.5327 0.4253 0.3303 0.2503 0.0460 0.0057 0.0005 0.0000 0.0000 0.0000 0.0000 0.00004 0.9999 0.9968 0.9832 0.9510 0.8964 0.8206 0.7290 0.6290 0.5277 0.4312 0.1121 0.0185 0.0021 0.0002 0.0000 0.0000 0.0000 0.00005 1.0000 0.9995 0.9963 0.9856 0.9622 0.9224 0.8650 0.7919 0.7072 0.6161 0.2194 0.0480 0.0070 0.0007 0.0001 0.0000 0.0000 0.00006 1.0000 0.9999 0.9993 0.9964 0.9882 0.9711 0.9417 0.8981 0.8404 0.7702 0.3613 0.1034 0.0194 0.0025 0.0002 0.0000 0.0000 0.00007 1.0000 1.0000 0.9999 0.9992 0.9968 0.9906 0.9780 0.9562 0.9232 0.8779 0.5188 0.1904 0.0453 0.0073 0.0008 0.0001 0.0000 0.00008 1.0000 1.0000 1.0000 0.9999 0.9992 0.9973 0.9927 0.9833 0.9672 0.9421 0.6681 0.3073 0.0916 0.0183 0.0025 0.0002 0.0000 0.00009 1.0000 1.0000 1.0000 1.0000 0.9998 0.9993 0.9978 0.9944 0.9875 0.9755 0.7911 0.4437 0.1637 0.0402 0.0067 0.0008 0.0001 0.000010 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9994 0.9983 0.9957 0.9906 0.8801 0.5836 0.2622 0.0789 0.0160 0.0022 0.0002 0.000011 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9995 0.9987 0.9968 0.9372 0.7107 0.3816 0.1390 0.0342 0.0057 0.0006 0.000012 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.9990 0.9699 0.8139 0.5110 0.2229 0.0661 0.0133 0.0018 0.000213 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9868 0.8894 0.6370 0.3279 0.1163 0.0280 0.0045 0.000514 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9947 0.9393 0.7481 0.4468 0.1878 0.0540 0.0104 0.001315 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9981 0.9692 0.8369 0.5692 0.2801 0.0955 0.0220 0.003316 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9993 0.9856 0.9017 0.6839 0.3889 0.1561 0.0427 0.0077

n= 50 x= 17 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9937 0.9449 0.7822 0.5060 0.2369 0.0765 0.016418 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9975 0.9713 0.8594 0.6216 0.3356 0.1273 0.032519 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9991 0.9861 0.9152 0.7264 0.4465 0.1974 0.059520 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9937 0.9522 0.8139 0.5610 0.2862 0.101321 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9974 0.9749 0.8813 0.6701 0.3900 0.161122 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9990 0.9877 0.9290 0.7660 0.5019 0.239923 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9996 0.9944 0.9604 0.8438 0.6134 0.3359

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Page 10: Tablas de las Distribuciones Estadisticas Mas Usadas

p= 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5n= 50 x= 24 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9976 0.9793 0.9022 0.7160 0.4439

25 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9991 0.9900 0.9427 0.8034 0.556126 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9955 0.9686 0.8721 0.664127 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9981 0.9840 0.9220 0.760128 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9993 0.9924 0.9556 0.838929 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9966 0.9765 0.898730 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9986 0.9884 0.940531 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9947 0.967532 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9978 0.983633 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9991 0.992334 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.996735 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.998736 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.999537 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.999838 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

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Page 11: Tablas de las Distribuciones Estadisticas Mas Usadas

POISSON

TABLA DE DISTRIBUCION

α=P[P≤k]

(Probabilidad acumulada inferior o a la izquierda)

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Page 12: Tablas de las Distribuciones Estadisticas Mas Usadas

Cumulative Poisson Probability Distribution Table

t

x 0.01 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0 0.9950 0.9900 0.9802 0.9704 0.9608 0.9512 0.9418 0.9324 0.9231 0.9139 1 1.0000 1.0000 0.9998 0.9996 0.9992 0.9988 0.9983 0.9977 0.9970 0.9962 2 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 3 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

t

x 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0 0.9048 0.8187 0.7408 0.6703 0.6065 0.5488 0.4966 0.4493 0.4066 0.3679 1 0.9953 0.9825 0.9631 0.9384 0.9098 0.8781 0.8442 0.8088 0.7725 0.7358 2 0.9998 0.9989 0.9964 0.9921 0.9856 0.9769 0.9659 0.9526 0.9371 0.9197 3 1.0000 0.9999 0.9997 0.9992 0.9982 0.9966 0.9942 0.9909 0.9865 0.9810 4 1.0000 1.0000 1.0000 0.9999 0.9998 0.9996 0.9992 0.9986 0.9977 0.9963 5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9994 6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

t

x 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00

0 0.3329 0.3012 0.2725 0.2466 0.2231 0.2019 0.1827 0.1653 0.1496 0.1353 1 0.6990 0.6626 0.6268 0.5918 0.5578 0.5249 0.4932 0.4628 0.4337 0.4060 2 0.9004 0.8795 0.8571 0.8335 0.8088 0.7834 0.7572 0.7306 0.7037 0.6767 3 0.9743 0.9662 0.9569 0.9463 0.9344 0.9212 0.9068 0.8913 0.8747 0.8571 4 0.9946 0.9923 0.9893 0.9857 0.9814 0.9763 0.9704 0.9636 0.9559 0.9473 5 0.9990 0.9985 0.9978 0.9968 0.9955 0.9940 0.9920 0.9896 0.9868 0.9834 6 0.9999 0.9997 0.9996 0.9994 0.9991 0.9987 0.9981 0.9974 0.9966 0.9955 7 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994 0.9992 0.9989 8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9998 9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

t

x 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00

0 0.1225 0.1108 0.1003 0.0907 0.0821 0.0743 0.0672 0.0608 0.0550 0.0498 1 0.3796 0.3546 0.3309 0.3084 0.2873 0.2674 0.2487 0.2311 0.2146 0.1991 2 0.6496 0.6227 0.5960 0.5697 0.5438 0.5184 0.4936 0.4695 0.4460 0.4232 3 0.8386 0.8194 0.7993 0.7787 0.7576 0.7360 0.7141 0.6919 0.6696 0.6472 4 0.9379 0.9275 0.9162 0.9041 0.8912 0.8774 0.8629 0.8477 0.8318 0.8153 5 0.9796 0.9751 0.9700 0.9643 0.9580 0.9510 0.9433 0.9349 0.9258 0.9161 6 0.9941 0.9925 0.9906 0.9884 0.9858 0.9828 0.9794 0.9756 0.9713 0.9665 7 0.9985 0.9980 0.9974 0.9967 0.9958 0.9947 0.9934 0.9919 0.9901 0.9881 8 0.9997 0.9995 0.9994 0.9991 0.9989 0.9985 0.9981 0.9976 0.9969 0.9962 9 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9995 0.9993 0.9991 0.9989

10 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 11 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 12 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

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Page 13: Tablas de las Distribuciones Estadisticas Mas Usadas

t

x 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00

0 0.0450 0.0408 0.0369 0.0334 0.0302 0.0273 0.0247 0.0224 0.0202 0.0183 1 0.1847 0.1712 0.1586 0.1468 0.1359 0.1257 0.1162 0.1074 0.0992 0.0916 2 0.4012 0.3799 0.3594 0.3397 0.3208 0.3027 0.2854 0.2689 0.2531 0.2381 3 0.6248 0.6025 0.5803 0.5584 0.5366 0.5152 0.4942 0.4735 0.4532 0.4335 4 0.7982 0.7806 0.7626 0.7442 0.7254 0.7064 0.6872 0.6678 0.6484 0.6288 5 0.9057 0.8946 0.8829 0.8705 0.8576 0.8441 0.8301 0.8156 0.8006 0.7851 6 0.9612 0.9554 0.9490 0.9421 0.9347 0.9267 0.9182 0.9091 0.8995 0.8893 7 0.9858 0.9832 0.9802 0.9769 0.9733 0.9692 0.9648 0.9599 0.9546 0.9489 8 0.9953 0.9943 0.9931 0.9917 0.9901 0.9883 0.9863 0.9840 0.9815 0.9786 9 0.9986 0.9982 0.9978 0.9973 0.9967 0.9960 0.9952 0.9942 0.9931 0.9919

10 0.9996 0.9995 0.9994 0.9992 0.9990 0.9987 0.9984 0.9981 0.9977 0.9972 11 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9995 0.9994 0.9993 0.9991 12 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

t

x 4.10 4.20 4.30 4.40 4.50 4.60 4.70 4.80 4.90 5.00

0 0.0166 0.0150 0.0136 0.0123 0.0111 0.0101 0.0091 0.0082 0.0074 0.0067 1 0.0845 0.0780 0.0719 0.0663 0.0611 0.0563 0.0518 0.0477 0.0439 0.0404 2 0.2238 0.2102 0.1974 0.1851 0.1736 0.1626 0.1523 0.1425 0.1333 0.1247 3 0.4142 0.3954 0.3772 0.3594 0.3423 0.3257 0.3097 0.2942 0.2793 0.2650 4 0.6093 0.5898 0.5704 0.5512 0.5321 0.5132 0.4946 0.4763 0.4582 0.4405 5 0.7693 0.7531 0.7367 0.7199 0.7029 0.6858 0.6684 0.6510 0.6335 0.6160 6 0.8786 0.8675 0.8558 0.8436 0.8311 0.8180 0.8046 0.7908 0.7767 0.7622 7 0.9427 0.9361 0.9290 0.9214 0.9134 0.9049 0.8960 0.8867 0.8769 0.8666 8 0.9755 0.9721 0.9683 0.9642 0.9597 0.9549 0.9497 0.9442 0.9382 0.9319 9 0.9905 0.9889 0.9871 0.9851 0.9829 0.9805 0.9778 0.9749 0.9717 0.9682

10 0.9966 0.9959 0.9952 0.9943 0.9933 0.9922 0.9910 0.9896 0.9880 0.9863 11 0.9989 0.9986 0.9983 0.9980 0.9976 0.9971 0.9966 0.9960 0.9953 0.9945 12 0.9997 0.9996 0.9995 0.9993 0.9992 0.9990 0.9988 0.9986 0.9983 0.9980 13 0.9999 0.9999 0.9998 0.9998 0.9997 0.9997 0.9996 0.9995 0.9994 0.9993 14 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 15 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

t

x 5.10 5.20 5.30 5.40 5.50 5.60 5.70 5.80 5.90 6.00

0 0.0061 0.0055 0.0050 0.0045 0.0041 0.0037 0.0033 0.0030 0.0027 0.0025 1 0.0372 0.0342 0.0314 0.0289 0.0266 0.0244 0.0224 0.0206 0.0189 0.0174 2 0.1165 0.1088 0.1016 0.0948 0.0884 0.0824 0.0768 0.0715 0.0666 0.0620 3 0.2513 0.2381 0.2254 0.2133 0.2017 0.1906 0.1800 0.1700 0.1604 0.1512 4 0.4231 0.4061 0.3895 0.3733 0.3575 0.3422 0.3272 0.3127 0.2987 0.2851 5 0.5984 0.5809 0.5635 0.5461 0.5289 0.5119 0.4950 0.4783 0.4619 0.4457 6 0.7474 0.7324 0.7171 0.7017 0.6860 0.6703 0.6544 0.6384 0.6224 0.6063 7 0.8560 0.8449 0.8335 0.8217 0.8095 0.7970 0.7841 0.7710 0.7576 0.7440 8 0.9252 0.9181 0.9106 0.9027 0.8944 0.8857 0.8766 0.8672 0.8574 0.8472 9 0.9644 0.9603 0.9559 0.9512 0.9462 0.9409 0.9352 0.9292 0.9228 0.9161

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Page 14: Tablas de las Distribuciones Estadisticas Mas Usadas

10 0.9844 0.9823 0.9800 0.9775 0.9747 0.9718 0.9686 0.9651 0.9614 0.9574 11 0.9937 0.9927 0.9916 0.9904 0.9890 0.9875 0.9859 0.9841 0.9821 0.9799 12 0.9976 0.9972 0.9967 0.9962 0.9955 0.9949 0.9941 0.9932 0.9922 0.9912 13 0.9992 0.9990 0.9988 0.9986 0.9983 0.9980 0.9977 0.9973 0.9969 0.9964 14 0.9997 0.9997 0.9996 0.9995 0.9994 0.9993 0.9991 0.9990 0.9988 0.9986 15 0.9999 0.9999 0.9999 0.9998 0.9998 0.9998 0.9997 0.9996 0.9996 0.9995 16 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 17 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 18 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

t

x 6.10 6.20 6.30 6.40 6.50 6.60 6.70 6.80 6.90 7.00

0 0.0022 0.0020 0.0018 0.0017 0.0015 0.0014 0.0012 0.0011 0.0010 0.0009 1 0.0159 0.0146 0.0134 0.0123 0.0113 0.0103 0.0095 0.0087 0.0080 0.0073 2 0.0577 0.0536 0.0498 0.0463 0.0430 0.0400 0.0371 0.0344 0.0320 0.0296 3 0.1425 0.1342 0.1264 0.1189 0.1118 0.1052 0.0988 0.0928 0.0871 0.0818 4 0.2719 0.2592 0.2469 0.2351 0.2237 0.2127 0.2022 0.1920 0.1823 0.1730 5 0.4298 0.4141 0.3988 0.3837 0.3690 0.3547 0.3406 0.3270 0.3137 0.3007 6 0.5902 0.5742 0.5582 0.5423 0.5265 0.5108 0.4953 0.4799 0.4647 0.4497 7 0.7301 0.7160 0.7017 0.6873 0.6728 0.6581 0.6433 0.6285 0.6136 0.5987 8 0.8367 0.8259 0.8148 0.8033 0.7916 0.7796 0.7673 0.7548 0.7420 0.7291 9 0.9090 0.9016 0.8939 0.8858 0.8774 0.8686 0.8596 0.8502 0.8405 0.8305

10 0.9531 0.9486 0.9437 0.9386 0.9332 0.9274 0.9214 0.9151 0.9084 0.9015 11 0.9776 0.9750 0.9723 0.9693 0.9661 0.9627 0.9591 0.9552 0.9510 0.9467 12 0.9900 0.9887 0.9873 0.9857 0.9840 0.9821 0.9801 0.9779 0.9755 0.9730 13 0.9958 0.9952 0.9945 0.9937 0.9929 0.9920 0.9909 0.9898 0.9885 0.9872 14 0.9984 0.9981 0.9978 0.9974 0.9970 0.9966 0.9961 0.9956 0.9950 0.9943 15 0.9994 0.9993 0.9992 0.9990 0.9988 0.9986 0.9984 0.9982 0.9979 0.9976 16 0.9998 0.9997 0.9997 0.9996 0.9996 0.9995 0.9994 0.9993 0.9992 0.9990 17 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9998 0.9997 0.9997 0.9996 18 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 19 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 20 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

t

x 7.10 7.20 7.30 7.40 7.50 7.60 7.70 7.80 7.90 8.00

0 0.0008 0.0007 0.0007 0.0006 0.0006 0.0005 0.0005 0.0004 0.0004 0.0003 1 0.0067 0.0061 0.0056 0.0051 0.0047 0.0043 0.0039 0.0036 0.0033 0.0030 2 0.0275 0.0255 0.0236 0.0219 0.0203 0.0188 0.0174 0.0161 0.0149 0.0138 3 0.0767 0.0719 0.0674 0.0632 0.0591 0.0554 0.0518 0.0485 0.0453 0.0424 4 0.1641 0.1555 0.1473 0.1395 0.1321 0.1249 0.1181 0.1117 0.1055 0.0996 5 0.2881 0.2759 0.2640 0.2526 0.2414 0.2307 0.2203 0.2103 0.2006 0.1912 6 0.4349 0.4204 0.4060 0.3920 0.3782 0.3646 0.3514 0.3384 0.3257 0.3134 7 0.5838 0.5689 0.5541 0.5393 0.5246 0.5100 0.4956 0.4812 0.4670 0.4530 8 0.7160 0.7027 0.6892 0.6757 0.6620 0.6482 0.6343 0.6204 0.6065 0.5925 9 0.8202 0.8096 0.7988 0.7877 0.7764 0.7649 0.7531 0.7411 0.7290 0.7166

10 0.8942 0.8867 0.8788 0.8707 0.8622 0.8535 0.8445 0.8352 0.8257 0.8159 11 0.9420 0.9371 0.9319 0.9265 0.9208 0.9148 0.9085 0.9020 0.8952 0.8881 12 0.9703 0.9673 0.9642 0.9609 0.9573 0.9536 0.9496 0.9454 0.9409 0.9362 13 0.9857 0.9841 0.9824 0.9805 0.9784 0.9762 0.9739 0.9714 0.9687 0.9658

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Page 15: Tablas de las Distribuciones Estadisticas Mas Usadas

14 0.9935 0.9927 0.9918 0.9908 0.9897 0.9886 0.9873 0.9859 0.9844 0.9827 15 0.9972 0.9969 0.9964 0.9959 0.9954 0.9948 0.9941 0.9934 0.9926 0.9918 16 0.9989 0.9987 0.9985 0.9983 0.9980 0.9978 0.9974 0.9971 0.9967 0.9963 17 0.9996 0.9995 0.9994 0.9993 0.9992 0.9991 0.9989 0.9988 0.9986 0.9984 18 0.9998 0.9998 0.9998 0.9997 0.9997 0.9996 0.9996 0.9995 0.9994 0.9993 19 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9998 0.9997 20 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 21 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

t

x 8.10 8.20 8.30 8.40 8.50 8.60 8.70 8.80 8.90 9.00

0 0.0003 0.0003 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0001 0.0001 1 0.0028 0.0025 0.0023 0.0021 0.0019 0.0018 0.0016 0.0015 0.0014 0.0012 2 0.0127 0.0118 0.0109 0.0100 0.0093 0.0086 0.0079 0.0073 0.0068 0.0062 3 0.0396 0.0370 0.0346 0.0323 0.0301 0.0281 0.0262 0.0244 0.0228 0.0212 4 0.0940 0.0887 0.0837 0.0789 0.0744 0.0701 0.0660 0.0621 0.0584 0.0550 5 0.1822 0.1736 0.1653 0.1573 0.1496 0.1422 0.1352 0.1284 0.1219 0.1157 6 0.3013 0.2896 0.2781 0.2670 0.2562 0.2457 0.2355 0.2256 0.2160 0.2068 7 0.4391 0.4254 0.4119 0.3987 0.3856 0.3728 0.3602 0.3478 0.3357 0.3239 8 0.5786 0.5647 0.5507 0.5369 0.5231 0.5094 0.4958 0.4823 0.4689 0.4557 9 0.7041 0.6915 0.6788 0.6659 0.6530 0.6400 0.6269 0.6137 0.6006 0.5874

10 0.8058 0.7955 0.7850 0.7743 0.7634 0.7522 0.7409 0.7294 0.7178 0.7060 11 0.8807 0.8731 0.8652 0.8571 0.8487 0.8400 0.8311 0.8220 0.8126 0.8030 12 0.9313 0.9261 0.9207 0.9150 0.9091 0.9029 0.8965 0.8898 0.8829 0.8758 13 0.9628 0.9595 0.9561 0.9524 0.9486 0.9445 0.9403 0.9358 0.9311 0.9261 14 0.9810 0.9791 0.9771 0.9749 0.9726 0.9701 0.9675 0.9647 0.9617 0.9585 15 0.9908 0.9898 0.9887 0.9875 0.9862 0.9848 0.9832 0.9816 0.9798 0.9780 16 0.9958 0.9953 0.9947 0.9941 0.9934 0.9926 0.9918 0.9909 0.9899 0.9889 17 0.9982 0.9979 0.9977 0.9973 0.9970 0.9966 0.9962 0.9957 0.9952 0.9947 18 0.9992 0.9991 0.9990 0.9989 0.9987 0.9985 0.9983 0.9981 0.9978 0.9976 19 0.9997 0.9997 0.9996 0.9995 0.9995 0.9994 0.9993 0.9992 0.9991 0.9989 20 0.9999 0.9999 0.9998 0.9998 0.9998 0.9998 0.9997 0.9997 0.9996 0.9996 21 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 22 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 23 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

t

x 9.10 9.20 9.30 9.40 9.50 9.60 9.70 9.80 9.90 10.00

0 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0000 1 0.0011 0.0010 0.0009 0.0009 0.0008 0.0007 0.0007 0.0006 0.0005 0.0005 2 0.0058 0.0053 0.0049 0.0045 0.0042 0.0038 0.0035 0.0033 0.0030 0.0028 3 0.0198 0.0184 0.0172 0.0160 0.0149 0.0138 0.0129 0.0120 0.0111 0.0103 4 0.0517 0.0486 0.0456 0.0429 0.0403 0.0378 0.0355 0.0333 0.0312 0.0293 5 0.1098 0.1041 0.0986 0.0935 0.0885 0.0838 0.0793 0.0750 0.0710 0.0671 6 0.1978 0.1892 0.1808 0.1727 0.1649 0.1574 0.1502 0.1433 0.1366 0.1301 7 0.3123 0.3010 0.2900 0.2792 0.2687 0.2584 0.2485 0.2388 0.2294 0.2202 8 0.4426 0.4296 0.4168 0.4042 0.3918 0.3796 0.3676 0.3558 0.3442 0.3328 9 0.5742 0.5611 0.5479 0.5349 0.5218 0.5089 0.4960 0.4832 0.4705 0.4579

10 0.6941 0.6820 0.6699 0.6576 0.6453 0.6329 0.6205 0.6080 0.5955 0.5830 11 0.7932 0.7832 0.7730 0.7626 0.7520 0.7412 0.7303 0.7193 0.7081 0.6968

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Page 16: Tablas de las Distribuciones Estadisticas Mas Usadas

12 0.8684 0.8607 0.8529 0.8448 0.8364 0.8279 0.8191 0.8101 0.8009 0.7916 13 0.9210 0.9156 0.9100 0.9042 0.8981 0.8919 0.8853 0.8786 0.8716 0.8645 14 0.9552 0.9517 0.9480 0.9441 0.9400 0.9357 0.9312 0.9265 0.9216 0.9165 15 0.9760 0.9738 0.9715 0.9691 0.9665 0.9638 0.9609 0.9579 0.9546 0.9513 16 0.9878 0.9865 0.9852 0.9838 0.9823 0.9806 0.9789 0.9770 0.9751 0.9730 17 0.9941 0.9934 0.9927 0.9919 0.9911 0.9902 0.9892 0.9881 0.9870 0.9857 18 0.9973 0.9969 0.9966 0.9962 0.9957 0.9952 0.9947 0.9941 0.9935 0.9928 19 0.9988 0.9986 0.9985 0.9983 0.9980 0.9978 0.9975 0.9972 0.9969 0.9965 20 0.9995 0.9994 0.9993 0.9992 0.9991 0.9990 0.9989 0.9987 0.9986 0.9984 21 0.9998 0.9998 0.9997 0.9997 0.9996 0.9996 0.9995 0.9995 0.9994 0.9993 22 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9998 0.9997 0.9997 23 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 24 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

t

x 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00 19.00 20.00

0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 2 0.0012 0.0005 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 3 0.0049 0.0023 0.0011 0.0005 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 4 0.0151 0.0076 0.0037 0.0018 0.0009 0.0004 0.0002 0.0001 0.0000 0.0000 5 0.0375 0.0203 0.0107 0.0055 0.0028 0.0014 0.0007 0.0003 0.0002 0.0001 6 0.0786 0.0458 0.0259 0.0142 0.0076 0.0040 0.0021 0.0010 0.0005 0.0003 7 0.1432 0.0895 0.0540 0.0316 0.0180 0.0100 0.0054 0.0029 0.0015 0.0008 8 0.2320 0.1550 0.0998 0.0621 0.0374 0.0220 0.0126 0.0071 0.0039 0.0021 9 0.3405 0.2424 0.1658 0.1094 0.0699 0.0433 0.0261 0.0154 0.0089 0.0050

10 0.4599 0.3472 0.2517 0.1757 0.1185 0.0774 0.0491 0.0304 0.0183 0.0108 11 0.5793 0.4616 0.3532 0.2600 0.1848 0.1270 0.0847 0.0549 0.0347 0.0214 12 0.6887 0.5760 0.4631 0.3585 0.2676 0.1931 0.1350 0.0917 0.0606 0.0390 13 0.7813 0.6815 0.5730 0.4644 0.3632 0.2745 0.2009 0.1426 0.0984 0.0661 14 0.8540 0.7720 0.6751 0.5704 0.4657 0.3675 0.2808 0.2081 0.1497 0.1049 15 0.9074 0.8444 0.7636 0.6694 0.5681 0.4667 0.3715 0.2867 0.2148 0.1565 16 0.9441 0.8987 0.8355 0.7559 0.6641 0.5660 0.4677 0.3751 0.2920 0.2211 17 0.9678 0.9370 0.8905 0.8272 0.7489 0.6593 0.5640 0.4686 0.3784 0.2970 18 0.9823 0.9626 0.9302 0.8826 0.8195 0.7423 0.6550 0.5622 0.4695 0.3814 19 0.9907 0.9787 0.9573 0.9235 0.8752 0.8122 0.7363 0.6509 0.5606 0.4703 20 0.9953 0.9884 0.9750 0.9521 0.9170 0.8682 0.8055 0.7307 0.6472 0.5591 21 0.9977 0.9939 0.9859 0.9712 0.9469 0.9108 0.8615 0.7991 0.7255 0.6437 22 0.9990 0.9970 0.9924 0.9833 0.9673 0.9418 0.9047 0.8551 0.7931 0.7206 23 0.9995 0.9985 0.9960 0.9907 0.9805 0.9633 0.9367 0.8989 0.8490 0.7875 24 0.9998 0.9993 0.9980 0.9950 0.9888 0.9777 0.9594 0.9317 0.8933 0.8432 25 0.9999 0.9997 0.9990 0.9974 0.9938 0.9869 0.9748 0.9554 0.9269 0.8878 26 1.0000 0.9999 0.9995 0.9987 0.9967 0.9925 0.9848 0.9718 0.9514 0.9221 27 1.0000 0.9999 0.9998 0.9994 0.9983 0.9959 0.9912 0.9827 0.9687 0.9475 28 1.0000 1.0000 0.9999 0.9997 0.9991 0.9978 0.9950 0.9897 0.9805 0.9657 29 1.0000 1.0000 1.0000 0.9999 0.9996 0.9989 0.9973 0.9941 0.9882 0.9782 30 1.0000 1.0000 1.0000 0.9999 0.9998 0.9994 0.9986 0.9967 0.9930 0.9865 31 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9993 0.9982 0.9960 0.9919 32 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9996 0.9990 0.9978 0.9953 33 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9995 0.9988 0.9973

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Page 17: Tablas de las Distribuciones Estadisticas Mas Usadas

34 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9994 0.9985 35 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9997 0.9992 36 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9996 37 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 38 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 39 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 40 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

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Page 18: Tablas de las Distribuciones Estadisticas Mas Usadas

NORMAL ESTÁNDAR N(0, 1)

TABLA DE DISTRIBUCION

α=P[Z≤z]

(Probabilidad acumulada inferior o a la izquierda)

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Page 19: Tablas de las Distribuciones Estadisticas Mas Usadas

STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09

-3.9 .00005 .00005 .00004 .00004 .00004 .00004 .00004 .00004 .00003 .00003 -3.8 .00007 .00007 .00007 .00006 .00006 .00006 .00006 .00005 .00005 .00005 -3.7 .00011 .00010 .00010 .00010 .00009 .00009 .00008 .00008 .00008 .00008 -3.6 .00016 .00015 .00015 .00014 .00014 .00013 .00013 .00012 .00012 .00011 -3.5 .00023 .00022 .00022 .00021 .00020 .00019 .00019 .00018 .00017 .00017 -3.4 .00034 .00032 .00031 .00030 .00029 .00028 .00027 .00026 .00025 .00024 -3.3 .00048 .00047 .00045 .00043 .00042 .00040 .00039 .00038 .00036 .00035 -3.2 .00069 .00066 .00064 .00062 .00060 .00058 .00056 .00054 .00052 .00050 -3.1 .00097 .00094 .00090 .00087 .00084 .00082 .00079 .00076 .00074 .00071 -3.0 .00135 .00131 .00126 .00122 .00118 .00114 .00111 .00107 .00104 .00100 -2.9 .00187 .00181 .00175 .00169 .00164 .00159 .00154 .00149 .00144 .00139 -2.8 .00256 .00248 .00240 .00233 .00226 .00219 .00212 .00205 .00199 .00193 -2.7 .00347 .00336 .00326 .00317 .00307 .00298 .00289 .00280 .00272 .00264 -2.6 .00466 .00453 .00440 .00427 .00415 .00402 .00391 .00379 .00368 .00357 -2.5 .00621 .00604 .00587 .00570 .00554 .00539 .00523 .00508 .00494 .00480 -2.4 .00820 .00798 .00776 .00755 .00734 .00714 .00695 .00676 .00657 .00639 -2.3 .01072 .01044 .01017 .00990 .00964 .00939 .00914 .00889 .00866 .00842 -2.2 .01390 .01355 .01321 .01287 .01255 .01222 .01191 .01160 .01130 .01101 -2.1 .01786 .01743 .01700 .01659 .01618 .01578 .01539 .01500 .01463 .01426 -2.0 .02275 .02222 .02169 .02118 .02068 .02018 .01970 .01923 .01876 .01831 -1.9 .02872 .02807 .02743 .02680 .02619 .02559 .02500 .02442 .02385 .02330 -1.8 .03593 .03515 .03438 .03362 .03288 .03216 .03144 .03074 .03005 .02938 -1.7 .04457 .04363 .04272 .04182 .04093 .04006 .03920 .03836 .03754 .03673 -1.6 .05480 .05370 .05262 .05155 .05050 .04947 .04846 .04746 .04648 .04551 -1.5 .06681 .06552 .06426 .06301 .06178 .06057 .05938 .05821 .05705 .05592 -1.4 .08076 .07927 .07780 .07636 .07493 .07353 .07215 .07078 .06944 .06811 -1.3 .09680 .09510 .09342 .09176 .09012 .08851 .08691 .08534 .08379 .08226 -1.2 .11507 .11314 .11123 .10935 .10749 .10565 .10383 .10204 .10027 .09853 -1.1 .13567 .13350 .13136 .12924 .12714 .12507 .12302 .12100 .11900 .11702 -1.0 .15866 .15625 .15386 .15151 .14917 .14686 .14457 .14231 .14007 .13786 -0.9 .18406 .18141 .17879 .17619 .17361 .17106 .16853 .16602 .16354 .16109 -0.8 .21186 .20897 .20611 .20327 .20045 .19766 .19489 .19215 .18943 .18673 -0.7 .24196 .23885 .23576 .23270 .22965 .22663 .22363 .22065 .21770 .21476 -0.6 .27425 .27093 .26763 .26435 .26109 .25785 .25463 .25143 .24825 .24510 -0.5 .30854 .30503 .30153 .29806 .29460 .29116 .28774 .28434 .28096 .27760 -0.4 .34458 .34090 .33724 .33360 .32997 .32636 .32276 .31918 .31561 .31207 -0.3 .38209 .37828 .37448 .37070 .36693 .36317 .35942 .35569 .35197 .34827 -0.2 .42074 .41683 .41294 .40905 .40517 .40129 .39743 .39358 .38974 .38591 -0.1 .46017 .45620 .45224 .44828 .44433 .44038 .43644 .43251 .42858 .42465 -0.0 .50000 .49601 .49202 .48803 .48405 .48006 .47608 .47210 .46812 .46414

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Page 20: Tablas de las Distribuciones Estadisticas Mas Usadas

STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score. Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09

0.0 .50000 .50399 .50798 .51197 .51595 .51994 .52392 .52790 .53188 .53586 0.1 .53983 .54380 .54776 .55172 .55567 .55962 .56356 .56749 .57142 .57535 0.2 .57926 .58317 .58706 .59095 .59483 .59871 .60257 .60642 .61026 .61409 0.3 .61791 .62172 .62552 .62930 .63307 .63683 .64058 .64431 .64803 .65173 0.4 .65542 .65910 .66276 .66640 .67003 .67364 .67724 .68082 .68439 .68793 0.5 .69146 .69497 .69847 .70194 .70540 .70884 .71226 .71566 .71904 .72240 0.6 .72575 .72907 .73237 .73565 .73891 .74215 .74537 .74857 .75175 .75490 0.7 .75804 .76115 .76424 .76730 .77035 .77337 .77637 .77935 .78230 .78524 0.8 .78814 .79103 .79389 .79673 .79955 .80234 .80511 .80785 .81057 .81327 0.9 .81594 .81859 .82121 .82381 .82639 .82894 .83147 .83398 .83646 .83891 1.0 .84134 .84375 .84614 .84849 .85083 .85314 .85543 .85769 .85993 .86214 1.1 .86433 .86650 .86864 .87076 .87286 .87493 .87698 .87900 .88100 .88298 1.2 .88493 .88686 .88877 .89065 .89251 .89435 .89617 .89796 .89973 .90147 1.3 .90320 .90490 .90658 .90824 .90988 .91149 .91309 .91466 .91621 .91774 1.4 .91924 .92073 .92220 .92364 .92507 .92647 .92785 .92922 .93056 .93189 1.5 .93319 .93448 .93574 .93699 .93822 .93943 .94062 .94179 .94295 .94408 1.6 .94520 .94630 .94738 .94845 .94950 .95053 .95154 .95254 .95352 .95449 1.7 .95543 .95637 .95728 .95818 .95907 .95994 .96080 .96164 .96246 .96327 1.8 .96407 .96485 .96562 .96638 .96712 .96784 .96856 .96926 .96995 .97062 1.9 .97128 .97193 .97257 .97320 .97381 .97441 .97500 .97558 .97615 .97670 2.0 .97725 .97778 .97831 .97882 .97932 .97982 .98030 .98077 .98124 .98169 2.1 .98214 .98257 .98300 .98341 .98382 .98422 .98461 .98500 .98537 .98574 2.2 .98610 .98645 .98679 .98713 .98745 .98778 .98809 .98840 .98870 .98899 2.3 .98928 .98956 .98983 .99010 .99036 .99061 .99086 .99111 .99134 .99158 2.4 .99180 .99202 .99224 .99245 .99266 .99286 .99305 .99324 .99343 .99361 2.5 .99379 .99396 .99413 .99430 .99446 .99461 .99477 .99492 .99506 .99520 2.6 .99534 .99547 .99560 .99573 .99585 .99598 .99609 .99621 .99632 .99643 2.7 .99653 .99664 .99674 .99683 .99693 .99702 .99711 .99720 .99728 .99736 2.8 .99744 .99752 .99760 .99767 .99774 .99781 .99788 .99795 .99801 .99807 2.9 .99813 .99819 .99825 .99831 .99836 .99841 .99846 .99851 .99856 .99861 3.0 .99865 .99869 .99874 .99878 .99882 .99886 .99889 .99893 .99896 .99900 3.1 .99903 .99906 .99910 .99913 .99916 .99918 .99921 .99924 .99926 .99929 3.2 .99931 .99934 .99936 .99938 .99940 .99942 .99944 .99946 .99948 .99950 3.3 .99952 .99953 .99955 .99957 .99958 .99960 .99961 .99962 .99964 .99965 3.4 .99966 .99968 .99969 .99970 .99971 .99972 .99973 .99974 .99975 .99976 3.5 .99977 .99978 .99978 .99979 .99980 .99981 .99981 .99982 .99983 .99983 3.6 .99984 .99985 .99985 .99986 .99986 .99987 .99987 .99988 .99988 .99989 3.7 .99989 .99990 .99990 .99990 .99991 .99991 .99992 .99992 .99992 .99992 3.8 .99993 .99993 .99993 .99994 .99994 .99994 .99994 .99995 .99995 .99995 3.9 .99995 .99995 .99996 .99996 .99996 .99996 .99996 .99996 .99997 .99997

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Page 21: Tablas de las Distribuciones Estadisticas Mas Usadas

NORMAL ESTÁNDAR N(0, 1)

CON DOS COLAS

α=P[│Z│≥z]=P[Z≤-z]+P[Z≥z]

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Page 22: Tablas de las Distribuciones Estadisticas Mas Usadas

TABLAS

31

Tabla 1 Distribución Normal típica (dos colas)

0,00 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09

0,0 2,576 2,326 2,170 2,054 1,960 1,881 1,812 1,751 1,695 0,1 1,645 1,598 1,555 1,514 1,476 1,440 1,405 1,372 1,341 1,311 0,2 1,282 1,254 1,227 1,200 1,175 1,150 1,126 1,103 1,080 1,058 0,3 1,036 1,015 0,994 0,974 0,954 0,935 0,915 0,896 0,878 0,860 0,4 0,842 0,824 0,806 0,789 0,772 0,755 0,739 0,722 0,706 0,690

0,5 0,674 0,659 0,643 0,628 0,613 0,598 0,583 0,568 0,553 0,539 0,6 0,524 0,510 0,496 0,482 0,468 0,454 0,440 0,426 0,412 0,399 0,7 0,385 0,372 0,358 0,345 0,332 0,319 0,305 0,292 0,279 0,266 0,8 0,253 0,240 0,228 0,215 0,202 0,189 0,176 0,164 0,151 0,138 0,9 0,126 0,113 0,100 0,088 0,075 0,063 0,050 0,038 0,025 0,013

Tabla para los pequeños valores de

0,002 0,001 0,000 1 0,000 01 0,000 001 0,000 000 1

z 3,090 3,290 3,891 4,417 4,892 5,327

Nota: Para cada valor de (en el caso de la tabla principal, la suma de la primera columna y de la primera fila) en el interior de la tabla se da el valor z tal que a la izquierda de z y a la derecha de + z hay un área total de .

z 0 z

/2 /2

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Page 23: Tablas de las Distribuciones Estadisticas Mas Usadas

T DE STUDENT

TABLA DE DISTRIBUCION

α=P[T≤t]

(Probabilidad acumulada inferior o a la izquierda)

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Inversa de la funcion de distribucion t de Student:

Tn(x) = P [tn ≤ x], Tn(tn,α) = α, T −1

n(α) = tn,α

tn,α

α

n�α 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 0.975 0.99 0.995

1 0.158384 0.324920 0.509525 0.726543 1.000000 1.376382 1.962610 3.077684 6.313752 12.706205 31.820516 63.656741

2 0.142134 0.288675 0.444750 0.617213 0.816497 1.060660 1.386207 1.885618 2.919986 4.302653 6.964557 9.924843

3 0.136598 0.276671 0.424202 0.584390 0.764892 0.978472 1.249778 1.637744 2.353363 3.182446 4.540703 5.840909

4 0.133830 0.270722 0.414163 0.568649 0.740697 0.940965 1.189567 1.533206 2.131847 2.776445 3.746947 4.604095

5 0.132175 0.267181 0.408229 0.559430 0.726687 0.919544 1.155767 1.475884 2.015048 2.570582 3.364930 4.032143

6 0.131076 0.264835 0.404313 0.553381 0.717558 0.905703 1.134157 1.439756 1.943180 2.446912 3.142668 3.707428

7 0.130293 0.263167 0.401538 0.549110 0.711142 0.896030 1.119159 1.414924 1.894579 2.364624 2.997952 3.499483

8 0.129707 0.261921 0.399469 0.545934 0.706387 0.888890 1.108145 1.396815 1.859548 2.306004 2.896459 3.355387

9 0.129253 0.260955 0.397868 0.543480 0.702722 0.883404 1.099716 1.383029 1.833113 2.262157 2.821438 3.249836

10 0.128890 0.260185 0.396591 0.541528 0.699812 0.879058 1.093058 1.372184 1.812461 2.228139 2.763769 3.169273

11 0.128594 0.259556 0.395551 0.539938 0.697445 0.875530 1.087666 1.363430 1.795885 2.200985 2.718079 3.105807

12 0.128347 0.259033 0.394686 0.538618 0.695483 0.872609 1.083211 1.356217 1.782288 2.178813 2.680998 3.054540

13 0.128139 0.258591 0.393955 0.537504 0.693829 0.870152 1.079469 1.350171 1.770933 2.160369 2.650309 3.012276

14 0.127961 0.258213 0.393331 0.536552 0.692417 0.868055 1.076280 1.345030 1.761310 2.144787 2.624494 2.976843

15 0.127806 0.257885 0.392790 0.535729 0.691197 0.866245 1.073531 1.340606 1.753050 2.131450 2.602480 2.946713

16 0.127671 0.257599 0.392318 0.535010 0.690132 0.864667 1.071137 1.336757 1.745884 2.119905 2.583487 2.920782

17 0.127552 0.257347 0.391902 0.534377 0.689195 0.863279 1.069033 1.333379 1.739607 2.109816 2.566934 2.898231

18 0.127447 0.257123 0.391533 0.533816 0.688364 0.862049 1.067170 1.330391 1.734064 2.100922 2.552380 2.878440

19 0.127352 0.256923 0.391202 0.533314 0.687621 0.860951 1.065507 1.327728 1.729133 2.093024 2.539483 2.860935

20 0.127267 0.256743 0.390906 0.532863 0.686954 0.859964 1.064016 1.325341 1.724718 2.085963 2.527977 2.845340

21 0.127190 0.256580 0.390637 0.532455 0.686352 0.859074 1.062670 1.323188 1.720743 2.079614 2.517648 2.831360

22 0.127120 0.256432 0.390394 0.532085 0.685805 0.858266 1.061449 1.321237 1.717144 2.073873 2.508325 2.818756

23 0.127056 0.256297 0.390171 0.531747 0.685306 0.857530 1.060337 1.319460 1.713872 2.068658 2.499867 2.807336

24 0.126998 0.256173 0.389967 0.531438 0.684850 0.856855 1.059319 1.317836 1.710882 2.063899 2.492159 2.796940

25 0.126944 0.256060 0.389780 0.531154 0.684430 0.856236 1.058384 1.316345 1.708141 2.059539 2.485107 2.787436

26 0.126895 0.255955 0.389607 0.530892 0.684043 0.855665 1.057523 1.314972 1.705618 2.055529 2.478630 2.778715

27 0.126849 0.255858 0.389448 0.530649 0.683685 0.855137 1.056727 1.313703 1.703288 2.051831 2.472660 2.770683

28 0.126806 0.255768 0.389299 0.530424 0.683353 0.854647 1.055989 1.312527 1.701131 2.048407 2.467140 2.763262

29 0.126767 0.255684 0.389161 0.530214 0.683044 0.854192 1.055302 1.311434 1.699127 2.045230 2.462021 2.756386

30 0.126730 0.255605 0.389032 0.530019 0.682756 0.853767 1.054662 1.310415 1.697261 2.042272 2.457262 2.749996

40 0.126462 0.255039 0.388100 0.528606 0.680673 0.850700 1.050046 1.303077 1.683851 2.021075 2.423257 2.704459

60 0.126194 0.254473 0.387170 0.527198 0.678601 0.847653 1.045469 1.295821 1.670649 2.000298 2.390119 2.660283

120 0.125928 0.253910 0.386244 0.525796 0.676540 0.844627 1.040932 1.288646 1.657651 1.979930 2.357825 2.617421

∞ 0.125661 0.253347 0.385320 0.524401 0.674490 0.841621 1.036433 1.281552 1.644854 1.959964 2.326348 2.575829

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Tablas de Pedro González Ruiz
Page 25: Tablas de las Distribuciones Estadisticas Mas Usadas

T DE STUDENT

TABLA DE DISTRIBUCION

α=P[T≥t]

(Probabilidad acumulada superior o a la derecha)

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Page 26: Tablas de las Distribuciones Estadisticas Mas Usadas

Table of the Student's t-distribution

;tα ν

α

The table gives the values of t ;α ν where Pr(Tν > t α; ν ) = α , with ν degrees of freedom

α ν

0.1 0.05 0.025 0.01 0.005 0.001 0.0005

1 3.078 6.314 12.076 31.821 63.657 318.310 636.620 2 1.886 2.920 4.303 6.965 9.925 22.326 31.598 3 1.638 2.353 3.182 4.541 5.841 10.213 12.924 4 1.533 2.132 2.776 3.747 4.604 7.173 8.610 5 1.476 2.015 2.571 3.365 4.032 5.893 6.869 6 1.440 1.943 2.447 3.143 3.707 5.208 5.959 7 1.415 1.895 2.365 2.998 3.499 4.785 5.408 8 1.397 1.860 2.306 2.896 3.355 4.501 5.041 9 1.383 1.833 2.262 2.821 3.250 4.297 4.781 10 1.372 1.812 2.228 2.764 3.169 4.144 4.587

11 1.363 1.796 2.201 2.718 3.106 4.025 4.437 12 1.356 1.782 2.179 2.681 3.055 3.930 4.318 13 1.350 1.771 2.160 2.650 3.012 3.852 4.221 14 1.345 1.761 2.145 2.624 2.977 3.787 4.140 15 1.341 1.753 2.131 2.602 2.947 3.733 4.073

16 1.337 1.746 2.120 2.583 2.921 3.686 4.015 17 1.333 1.740 2.110 2.567 2.898 3.646 3.965 18 1.330 1.734 2.101 2.552 2.878 3.610 3.922 19 1.328 1.729 2.093 2.539 2.861 3.579 3.883 20 1.325 1.725 2.086 2.528 2.845 3.552 3.850

21 1.323 1.721 2.080 2.518 2.831 3.527 3.819 22 1.321 1.717 2.074 2.508 2.819 3.505 3.792 23 1.319 1.714 2.069 2.500 2.807 3.485 3.767 24 1.318 1.711 2.064 2.492 2.797 3.467 3.745 25 1.316 1.708 2.060 2.485 2.787 3.450 3.725

26 1.315 1.706 2.056 2.479 2.779 3.435 3.707 27 1.314 1.703 2.052 2.473 2.771 3.421 3.690 28 1.313 1.701 2.048 2.467 2.763 3.408 3.674 29 1.311 1.699 2.045 2.462 2.756 3.396 3.659 30 1.310 1.697 2.042 2.457 2.750 3.385 3.646

40 1.303 1.684 2.021 2.423 2.704 3.307 3.551 60 1.296 1.671 2.000 2.390 2.660 3.232 3.460 120 1.289 1.658 1.980 2.358 2.617 3.160 3.373 ∞ 1.282 1.645 1.960 2.326 2.576 3.090 3.291

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Page 27: Tablas de las Distribuciones Estadisticas Mas Usadas

T DE STUDENT

CON DOS COLAS

α=P[│T│≥t]=P[T≤-t]+P[T≥t]

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Page 28: Tablas de las Distribuciones Estadisticas Mas Usadas

TABLAS

33

Tabla 3 Distribución t de Student

g.l. 0,50 0,40 0,30 0,20 0,10 0,05 0,02 0,01 0,001

1 2 3 4 5 6 7 8 9

10

1,0000,8160,7650,7410,7270,7180,7110,7060,7030,700

1,376 1,061 0,978 0,941 0,920 0,906 0,896 0,889 0,883 0,879

1,9631,3861,2501,1901,1561,1341,1191,1081,1001,093

3,0781,8861,6381,5331,4761,4401,4151,3971,3831,372

6,3142,9202,3532,1322,0151,9431,8951,8601,8331,812

12,7064,3033,1822,7762,5712,4472,3652,3062,2622,228

31,8216,9654,5413,7473,3653,1432,9982,8962,8212,764

63,656 9,925 5,841 4,604 4,032 3,707 3,499 3,355 3,250 3,169

636,578 31,600 12,924

8,610 6,869 5,959 5,408 5,041 4,781 4,587

11 12 13 14 15 16 17 18 19 20

0,6970,6950,6940,6920,6910,6900,6890,6880,6880,687

0,876 0,873 0,870 0,868 0,866 0,865 0,863 0,862 0,861 0,860

1,0881,0831,0791,0761,0741,0711,0691,0671,0661,064

1,3631,3561,3501,3451,3411,3371,3331,3301,3281,325

1,7961,7821,7711,7611,7531,7461,7401,7341,7291,725

2,2012,1792,1602,1452,1312,1202,1102,1012,0932,086

2,7182,6812,6502,6242,6022,5832,5672,5522,5392,528

3,106 3,055 3,012 2,977 2,947 2,921 2,898 2,878 2,861 2,845

4,437 4,318 4,221 4,140 4,073 4,015 3,965 3,922 3,883 3,850

21 22 23 24 25 26 27 28 29 30

0,6860,6860,6850,6850,6840,6840,6840,6830,6830,683

0,859 0,858 0,858 0,857 0,856 0,856 0,855 0,855 0,854 0,854

1,0631,0611,0601,0591,0581,0581,0571,0561,0551,055

1,3231,3211,3191,3181,3161,3151,3141,3131,3111,310

1,7211,7171,7141,7111,7081,7061,7031,7011,6991,697

2,0802,0742,0692,0642,0602,0562,0522,0482,0452,042

2,5182,5082,5002,4922,4852,4792,4732,4672,4622,457

2,831 2,819 2,807 2,797 2,787 2,779 2,771 2,763 2,756 2,750

3,819 3,792 3,768 3,745 3,725 3,707 3,689 3,674 3,660 3,646

35 40 45 50 60 80

100

0,6820,6810,6800,6790,6790,6780,6770,674

0,852 0,851 0,850 0,849 0,848 0,846 0,845 0,842

1,0521,0501,0491,0471,0451,0431,0421,036

1,3061,3031,3011,2991,2961,2921,2901,282

1,6901,6841,6791,6761,6711,6641,6601,645

2,0302,0212,0142,0092,0001,9901,9841,960

2,4382,4232,4122,4032,3902,3742,3642,326

2,724 2,704 2,690 2,678 2,660 2,639 2,626 2,576

3,591 3,551 3,520 3,496 3,460 3,416 3,390 3,290

Nota: Para cada valor de los g.l. (primera columna) y de (primera fila), en el interior de la tabla

se da el valor t tal que a la izquierda de t y a la derecha de +t queda un área total de .

t 0 t

/2/2

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Page 29: Tablas de las Distribuciones Estadisticas Mas Usadas

CHI CUADRADO Χ2

TABLA DE DISTRIBUCION

α=P[Χ2≤x]

(Probabilidad acumulada inferior o a la izquierda)

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Page 30: Tablas de las Distribuciones Estadisticas Mas Usadas

Statistical Tables for Students Chi-square

Table 8 Chi-square distribution — inverse cdf

Pdf 0.005 0.010 0.025 0.050 0.100 0.250 0.500 0.750 0.900 0.950 0.975 0.990 0.995 0.999

1 0.000 0.000 0.001 0.004 0.016 0.102 0.455 1.323 2.706 3.841 5.024 6.635 7.879 10.832 0.010 0.020 0.051 0.103 0.211 0.575 1.386 2.773 4.605 5.991 7.378 9.210 10.60 13.823 0.072 0.115 0.216 0.352 0.584 1.213 2.366 4.108 6.251 7.815 9.348 11.34 12.84 16.274 0.207 0.297 0.484 0.711 1.064 1.923 3.357 5.385 7.779 9.488 11.14 13.28 14.86 18.475 0.412 0.554 0.831 1.145 1.610 2.675 4.351 6.626 9.236 11.07 12.83 15.09 16.75 20.516 0.676 0.872 1.237 1.635 2.204 3.455 5.348 7.841 10.64 12.59 14.45 16.81 18.55 22.467 0.989 1.239 1.690 2.167 2.833 4.255 6.346 9.037 12.02 14.07 16.01 18.48 20.28 24.328 1.344 1.647 2.180 2.733 3.490 5.071 7.344 10.22 13.36 15.51 17.53 20.09 21.95 26.129 1.735 2.088 2.700 3.325 4.168 5.899 8.343 11.39 14.68 16.92 19.02 21.67 23.59 27.8810 2.156 2.558 3.247 3.940 4.865 6.737 9.342 12.55 15.99 18.31 20.48 23.21 25.19 29.59

11 2.603 3.053 3.816 4.575 5.578 7.584 10.34 13.70 17.28 19.68 21.92 24.73 26.76 31.2612 3.074 3.571 4.404 5.226 6.304 8.438 11.34 14.85 18.55 21.03 23.34 26.22 28.30 32.9113 3.565 4.107 5.009 5.892 7.041 9.299 12.34 15.98 19.81 22.36 24.74 27.69 29.82 34.5314 4.075 4.660 5.629 6.571 7.790 10.17 13.34 17.12 21.06 23.68 26.12 29.14 31.32 36.1215 4.601 5.229 6.262 7.261 8.547 11.04 14.34 18.25 22.31 25.00 27.49 30.58 32.80 37.7016 5.142 5.812 6.908 7.962 9.312 11.91 15.34 19.37 23.54 26.30 28.85 32.00 34.27 39.2517 5.697 6.408 7.564 8.672 10.09 12.79 16.34 20.49 24.77 27.59 30.19 33.41 35.72 40.7918 6.265 7.015 8.231 9.390 10.86 13.68 17.34 21.60 25.99 28.87 31.53 34.81 37.16 42.3119 6.844 7.633 8.907 10.12 11.65 14.56 18.34 22.72 27.20 30.14 32.85 36.19 38.58 43.8220 7.434 8.260 9.591 10.85 12.44 15.45 19.34 23.83 28.41 31.41 34.17 37.57 40.00 45.31

21 8.034 8.897 10.28 11.59 13.24 16.34 20.34 24.93 29.62 32.67 35.48 38.93 41.40 46.8022 8.643 9.542 10.98 12.34 14.04 17.24 21.34 26.04 30.81 33.92 36.78 40.29 42.80 48.2723 9.260 10.20 11.69 13.09 14.85 18.14 22.34 27.14 32.01 35.17 38.08 41.64 44.18 49.7324 9.886 10.86 12.40 13.85 15.66 19.04 23.34 28.24 33.20 36.42 39.36 42.98 45.56 51.1825 10.52 11.52 13.12 14.61 16.47 19.94 24.34 29.34 34.38 37.65 40.65 44.31 46.93 52.6226 11.16 12.20 13.84 15.38 17.29 20.84 25.34 30.43 35.56 38.89 41.92 45.64 48.29 54.0527 11.81 12.88 14.57 16.15 18.11 21.75 26.34 31.53 36.74 40.11 43.19 46.96 49.65 55.4828 12.46 13.56 15.31 16.93 18.94 22.66 27.34 32.62 37.92 41.34 44.46 48.28 50.99 56.8929 13.12 14.26 16.05 17.71 19.77 23.57 28.34 33.71 39.09 42.56 45.72 49.59 52.34 58.3030 13.79 14.95 16.79 18.49 20.60 24.48 29.34 34.80 40.26 43.77 46.98 50.89 53.67 59.70

31 14.46 15.66 17.54 19.28 21.43 25.39 30.34 35.89 41.42 44.99 48.23 52.19 55.00 61.1032 15.13 16.36 18.29 20.07 22.27 26.30 31.34 36.97 42.58 46.19 49.48 53.49 56.33 62.4933 15.82 17.07 19.05 20.87 23.11 27.22 32.34 38.06 43.75 47.40 50.73 54.78 57.65 63.8734 16.50 17.79 19.81 21.66 23.95 28.14 33.34 39.14 44.90 48.60 51.97 56.06 58.96 65.2535 17.19 18.51 20.57 22.47 24.80 29.05 34.34 40.22 46.06 49.80 53.20 57.34 60.27 66.6236 17.89 19.23 21.34 23.27 25.64 29.97 35.34 41.30 47.21 51.00 54.44 58.62 61.58 67.9837 18.59 19.96 22.11 24.07 26.49 30.89 36.34 42.38 48.36 52.19 55.67 59.89 62.88 69.3538 19.29 20.69 22.88 24.88 27.34 31.81 37.34 43.46 49.51 53.38 56.90 61.16 64.18 70.7039 20.00 21.43 23.65 25.70 28.20 32.74 38.34 44.54 50.66 54.57 58.12 62.43 65.48 72.0640 20.71 22.16 24.43 26.51 29.05 33.66 39.34 45.62 51.81 55.76 59.34 63.69 66.77 73.40

50 27.99 29.71 32.36 34.76 37.69 42.94 49.33 56.33 63.17 67.50 71.42 76.15 79.49 86.6660 35.53 37.48 40.48 43.19 46.46 52.29 59.33 66.98 74.40 79.08 83.30 88.38 91.95 99.6170 43.28 45.44 48.76 51.74 55.33 61.70 69.33 77.58 85.53 90.53 95.02 100.4 104.2 112.380 51.17 53.54 57.15 60.39 64.28 71.14 79.33 88.13 96.58 101.9 106.6 112.3 116.3 124.890 59.20 61.75 65.65 69.13 73.29 80.62 89.33 98.65 107.6 113.1 118.1 124.1 128.3 137.2100 67.33 70.06 74.22 77.93 82.36 90.13 99.33 109.1 118.5 124.3 129.6 135.8 140.2 149.4120 83.85 86.92 91.57 95.70 100.6 109.2 119.3 130.1 140.2 146.6 152.2 159.0 163.6 173.6140 100.7 104.0 109.1 113.7 119.0 128.4 139.3 150.9 161.8 168.6 174.6 181.8 186.8 197.4160 117.7 121.3 126.9 131.8 137.5 147.6 159.3 171.7 183.3 190.5 196.9 204.5 209.8 221.0180 134.9 138.8 144.7 150.0 156.2 166.9 179.3 192.4 204.7 212.3 219.0 227.1 232.6 244.4

200 152.2 156.4 162.7 168.3 174.8 186.2 199.3 213.1 226.0 234.0 241.1 249.4 255.3 267.5240 187.3 192.0 199.0 205.1 212.4 224.9 239.3 254.4 268.5 277.1 284.8 293.9 300.2 313.4300 240.7 246.0 253.9 260.9 269.1 283.1 299.3 316.1 331.8 341.4 349.9 359.9 366.8 381.4400 330.9 337.2 346.5 354.6 364.2 380.6 399.3 418.7 436.6 447.6 457.3 468.7 476.6 493.1

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Page 31: Tablas de las Distribuciones Estadisticas Mas Usadas

CHI CUADRADO Χ2

TABLA DE DISTRIBUCION

α=P[Χ2≥x]

(Probabilidad acumulada superior o a la derecha)

Probability p

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Page 32: Tablas de las Distribuciones Estadisticas Mas Usadas

T-20•

Tables

Table entry for p is thecritical value (χ2)∗ withprobability p lying to itsright.

Probability p

( 2)*χ

TABLE F

χ2 distribution critical values

Tail probability p

df .25 .20 .15 .10 .05 .025 .02 .01 .005 .0025 .001 .0005

1 1.32 1.64 2.07 2.71 3.84 5.02 5.41 6.63 7.88 9.14 10.83 12.122 2.77 3.22 3.79 4.61 5.99 7.38 7.82 9.21 10.60 11.98 13.82 15.203 4.11 4.64 5.32 6.25 7.81 9.35 9.84 11.34 12.84 14.32 16.27 17.734 5.39 5.99 6.74 7.78 9.49 11.14 11.67 13.28 14.86 16.42 18.47 20.005 6.63 7.29 8.12 9.24 11.07 12.83 13.39 15.09 16.75 18.39 20.51 22.116 7.84 8.56 9.45 10.64 12.59 14.45 15.03 16.81 18.55 20.25 22.46 24.107 9.04 9.80 10.75 12.02 14.07 16.01 16.62 18.48 20.28 22.04 24.32 26.028 10.22 11.03 12.03 13.36 15.51 17.53 18.17 20.09 21.95 23.77 26.12 27.879 11.39 12.24 13.29 14.68 16.92 19.02 19.68 21.67 23.59 25.46 27.88 29.67

10 12.55 13.44 14.53 15.99 18.31 20.48 21.16 23.21 25.19 27.11 29.59 31.4211 13.70 14.63 15.77 17.28 19.68 21.92 22.62 24.72 26.76 28.73 31.26 33.1412 14.85 15.81 16.99 18.55 21.03 23.34 24.05 26.22 28.30 30.32 32.91 34.8213 15.98 16.98 18.20 19.81 22.36 24.74 25.47 27.69 29.82 31.88 34.53 36.4814 17.12 18.15 19.41 21.06 23.68 26.12 26.87 29.14 31.32 33.43 36.12 38.1115 18.25 19.31 20.60 22.31 25.00 27.49 28.26 30.58 32.80 34.95 37.70 39.7216 19.37 20.47 21.79 23.54 26.30 28.85 29.63 32.00 34.27 36.46 39.25 41.3117 20.49 21.61 22.98 24.77 27.59 30.19 31.00 33.41 35.72 37.95 40.79 42.8818 21.60 22.76 24.16 25.99 28.87 31.53 32.35 34.81 37.16 39.42 42.31 44.4319 22.72 23.90 25.33 27.20 30.14 32.85 33.69 36.19 38.58 40.88 43.82 45.9720 23.83 25.04 26.50 28.41 31.41 34.17 35.02 37.57 40.00 42.34 45.31 47.5021 24.93 26.17 27.66 29.62 32.67 35.48 36.34 38.93 41.40 43.78 46.80 49.0122 26.04 27.30 28.82 30.81 33.92 36.78 37.66 40.29 42.80 45.20 48.27 50.5123 27.14 28.43 29.98 32.01 35.17 38.08 38.97 41.64 44.18 46.62 49.73 52.0024 28.24 29.55 31.13 33.20 36.42 39.36 40.27 42.98 45.56 48.03 51.18 53.4825 29.34 30.68 32.28 34.38 37.65 40.65 41.57 44.31 46.93 49.44 52.62 54.9526 30.43 31.79 33.43 35.56 38.89 41.92 42.86 45.64 48.29 50.83 54.05 56.4127 31.53 32.91 34.57 36.74 40.11 43.19 44.14 46.96 49.64 52.22 55.48 57.8628 32.62 34.03 35.71 37.92 41.34 44.46 45.42 48.28 50.99 53.59 56.89 59.3029 33.71 35.14 36.85 39.09 42.56 45.72 46.69 49.59 52.34 54.97 58.30 60.7330 34.80 36.25 37.99 40.26 43.77 46.98 47.96 50.89 53.67 56.33 59.70 62.1640 45.62 47.27 49.24 51.81 55.76 59.34 60.44 63.69 66.77 69.70 73.40 76.0950 56.33 58.16 60.35 63.17 67.50 71.42 72.61 76.15 79.49 82.66 86.66 89.5660 66.98 68.97 71.34 74.40 79.08 83.30 84.58 88.38 91.95 95.34 99.61 102.780 88.13 90.41 93.11 96.58 101.9 106.6 108.1 112.3 116.3 120.1 124.8 128.3

100 109.1 111.7 114.7 118.5 124.3 129.6 131.1 135.8 140.2 144.3 149.4 153.2

Integre Technical Publishing Co., Inc. Moore/McCabe November 16, 2007 1:29 p.m. moore page T-20

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Page 33: Tablas de las Distribuciones Estadisticas Mas Usadas

F DE SNEDECOR

TABLA DE DISTRIBUCION

α=P[F≤f]

(Probabilidad acumulada inferior o a la izquierda)

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Page 34: Tablas de las Distribuciones Estadisticas Mas Usadas

Inversa de la funcion de distribucion F de Snedecor:

Fm,n(x) = P [Fm,n ≤ x], Fm,n(Fm,n,α) = α, Fm,n,α = F−1

m,n(α), α = 0,9

n�m 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 50 100 ∞

1 39.8635 49.5000 53.5932 55.8330 57.2401 58.2044 58.9060 59.4390 59.8576 60.1950 60.7052 61.2203 61.7403 62.0020 62.2650 62.6881 63.0073 63.32812 8.5263 9.0000 9.1618 9.2434 9.2926 9.3255 9.3491 9.3668 9.3805 9.3916 9.4081 9.4247 9.4413 9.4496 9.4579 9.4712 9.4812 9.49123 5.5383 5.4624 5.3908 5.3426 5.3092 5.2847 5.2662 5.2517 5.2400 5.2304 5.2156 5.2003 5.1845 5.1764 5.1681 5.1546 5.1443 5.13374 4.5448 4.3246 4.1909 4.1072 4.0506 4.0097 3.9790 3.9549 3.9357 3.9199 3.8955 3.8704 3.8443 3.8310 3.8174 3.7952 3.7782 3.76075 4.0604 3.7797 3.6195 3.5202 3.4530 3.4045 3.3679 3.3393 3.3163 3.2974 3.2682 3.2380 3.2066 3.1905 3.1741 3.1471 3.1263 3.10506 3.7759 3.4633 3.2888 3.1808 3.1075 3.0546 3.0145 2.9830 2.9577 2.9369 2.9047 2.8712 2.8363 2.8183 2.8000 2.7697 2.7463 2.72227 3.5894 3.2574 3.0741 2.9605 2.8833 2.8274 2.7849 2.7516 2.7247 2.7025 2.6681 2.6322 2.5947 2.5753 2.5555 2.5226 2.4971 2.47088 3.4579 3.1131 2.9238 2.8064 2.7264 2.6683 2.6241 2.5893 2.5612 2.5380 2.5020 2.4642 2.4246 2.4041 2.3830 2.3481 2.3208 2.29269 3.3603 3.0065 2.8129 2.6927 2.6106 2.5509 2.5053 2.4694 2.4403 2.4163 2.3789 2.3396 2.2983 2.2768 2.2547 2.2180 2.1892 2.1592

10 3.2850 2.9245 2.7277 2.6053 2.5216 2.4606 2.4140 2.3772 2.3473 2.3226 2.2841 2.2435 2.2007 2.1784 2.1554 2.1171 2.0869 2.055411 3.2252 2.8595 2.6602 2.5362 2.4512 2.3891 2.3416 2.3040 2.2735 2.2482 2.2087 2.1671 2.1230 2.1000 2.0762 2.0364 2.0050 1.972112 3.1765 2.8068 2.6055 2.4801 2.3940 2.3310 2.2828 2.2446 2.2135 2.1878 2.1474 2.1048 2.0597 2.0360 2.0115 1.9704 1.9379 1.903613 3.1362 2.7632 2.5603 2.4337 2.3467 2.2830 2.2341 2.1953 2.1638 2.1376 2.0966 2.0532 2.0070 1.9827 1.9576 1.9153 1.8817 1.846214 3.1022 2.7265 2.5222 2.3947 2.3069 2.2426 2.1931 2.1539 2.1220 2.0954 2.0537 2.0095 1.9625 1.9377 1.9119 1.8686 1.8340 1.797315 3.0732 2.6952 2.4898 2.3614 2.2730 2.2081 2.1582 2.1185 2.0862 2.0593 2.0171 1.9722 1.9243 1.8990 1.8728 1.8284 1.7929 1.755116 3.0481 2.6682 2.4618 2.3327 2.2438 2.1783 2.1280 2.0880 2.0553 2.0281 1.9854 1.9399 1.8913 1.8656 1.8388 1.7934 1.7570 1.718217 3.0262 2.6446 2.4374 2.3077 2.2183 2.1524 2.1017 2.0613 2.0284 2.0009 1.9577 1.9117 1.8624 1.8362 1.8090 1.7628 1.7255 1.685618 3.0070 2.6239 2.4160 2.2858 2.1958 2.1296 2.0785 2.0379 2.0047 1.9770 1.9333 1.8868 1.8368 1.8103 1.7827 1.7356 1.6976 1.656719 2.9899 2.6056 2.3970 2.2663 2.1760 2.1094 2.0580 2.0171 1.9836 1.9557 1.9117 1.8647 1.8142 1.7873 1.7592 1.7114 1.6726 1.630820 2.9747 2.5893 2.3801 2.2489 2.1582 2.0913 2.0397 1.9985 1.9649 1.9367 1.8924 1.8449 1.7938 1.7667 1.7382 1.6896 1.6501 1.607421 2.9610 2.5746 2.3649 2.2333 2.1423 2.0751 2.0233 1.9819 1.9480 1.9197 1.8750 1.8271 1.7756 1.7481 1.7193 1.6700 1.6298 1.586222 2.9486 2.5613 2.3512 2.2193 2.1279 2.0605 2.0084 1.9668 1.9327 1.9043 1.8593 1.8111 1.7590 1.7312 1.7021 1.6521 1.6113 1.566823 2.9374 2.5493 2.3387 2.2065 2.1149 2.0472 1.9949 1.9531 1.9189 1.8903 1.8450 1.7964 1.7439 1.7159 1.6864 1.6358 1.5944 1.549024 2.9271 2.5383 2.3274 2.1949 2.1030 2.0351 1.9826 1.9407 1.9063 1.8775 1.8319 1.7831 1.7302 1.7019 1.6721 1.6209 1.5788 1.532725 2.9177 2.5283 2.3170 2.1842 2.0922 2.0241 1.9714 1.9292 1.8947 1.8658 1.8200 1.7708 1.7175 1.6890 1.6589 1.6072 1.5645 1.517626 2.9091 2.5191 2.3075 2.1745 2.0822 2.0139 1.9610 1.9188 1.8841 1.8550 1.8090 1.7596 1.7059 1.6771 1.6468 1.5945 1.5513 1.503627 2.9012 2.5106 2.2987 2.1655 2.0730 2.0045 1.9515 1.9091 1.8743 1.8451 1.7989 1.7492 1.6951 1.6662 1.6356 1.5827 1.5390 1.490628 2.8938 2.5028 2.2906 2.1571 2.0645 1.9958 1.9427 1.9001 1.8652 1.8359 1.7895 1.7395 1.6852 1.6560 1.6252 1.5718 1.5276 1.478429 2.8870 2.4955 2.2831 2.1494 2.0566 1.9878 1.9345 1.8918 1.8568 1.8274 1.7808 1.7306 1.6759 1.6465 1.6155 1.5616 1.5169 1.467030 2.8807 2.4887 2.2761 2.1422 2.0492 1.9803 1.9269 1.8841 1.8490 1.8195 1.7727 1.7223 1.6673 1.6377 1.6065 1.5522 1.5069 1.456440 2.8354 2.4404 2.2261 2.0909 1.9968 1.9269 1.8725 1.8289 1.7929 1.7627 1.7146 1.6624 1.6052 1.5741 1.5411 1.4830 1.4336 1.376960 2.7911 2.3933 2.1774 2.0410 1.9457 1.8747 1.8194 1.7748 1.7380 1.7070 1.6574 1.6034 1.5435 1.5107 1.4755 1.4126 1.3576 1.2915

100 2.7564 2.3564 2.1394 2.0019 1.9057 1.8339 1.7778 1.7324 1.6949 1.6632 1.6124 1.5566 1.4943 1.4600 1.4227 1.3548 1.2934 1.2142200 2.7308 2.3293 2.1114 1.9732 1.8763 1.8038 1.7470 1.7011 1.6630 1.6308 1.5789 1.5218 1.4575 1.4217 1.3826 1.3100 1.2418 1.1439∞ 2.7055 2.3026 2.0838 1.9449 1.8473 1.7741 1.7167 1.6702 1.6315 1.5987 1.5458 1.4871 1.4206 1.3832 1.3419 1.2633 1.1850 1.0000

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Typewritten Text
Tablas de Pedro González Ruiz
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Page 35: Tablas de las Distribuciones Estadisticas Mas Usadas

Inversa de la funcion de distribucion F de Snedecor:

Fm,n(x) = P [Fm,n ≤ x], Fm,n(Fm,n,α) = α, Fm,n,α = F−1

m,n(α), α = 0,95

n�m 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 50 100 ∞

1 161.4476 199.5000 215.7073 224.5832 230.1619 233.9860 236.7684 238.8827 240.5433 241.8817 243.9060 245.9499 248.0131 249.0518 250.0951 251.7742 253.0411 254.31442 18.5128 19.0000 19.1643 19.2468 19.2964 19.3295 19.3532 19.3710 19.3848 19.3959 19.4125 19.4291 19.4458 19.4541 19.4624 19.4757 19.4857 19.49573 10.1280 9.5521 9.2766 9.1172 9.0135 8.9406 8.8867 8.8452 8.8123 8.7855 8.7446 8.7029 8.6602 8.6385 8.6166 8.5810 8.5539 8.52644 7.7086 6.9443 6.5914 6.3882 6.2561 6.1631 6.0942 6.0410 5.9988 5.9644 5.9117 5.8578 5.8025 5.7744 5.7459 5.6995 5.6641 5.62815 6.6079 5.7861 5.4095 5.1922 5.0503 4.9503 4.8759 4.8183 4.7725 4.7351 4.6777 4.6188 4.5581 4.5272 4.4957 4.4444 4.4051 4.36506 5.9874 5.1433 4.7571 4.5337 4.3874 4.2839 4.2067 4.1468 4.0990 4.0600 3.9999 3.9381 3.8742 3.8415 3.8082 3.7537 3.7117 3.66897 5.5914 4.7374 4.3468 4.1203 3.9715 3.8660 3.7870 3.7257 3.6767 3.6365 3.5747 3.5107 3.4445 3.4105 3.3758 3.3189 3.2749 3.22988 5.3177 4.4590 4.0662 3.8379 3.6875 3.5806 3.5005 3.4381 3.3881 3.3472 3.2839 3.2184 3.1503 3.1152 3.0794 3.0204 2.9747 2.92769 5.1174 4.2565 3.8625 3.6331 3.4817 3.3738 3.2927 3.2296 3.1789 3.1373 3.0729 3.0061 2.9365 2.9005 2.8637 2.8028 2.7556 2.7067

10 4.9646 4.1028 3.7083 3.4780 3.3258 3.2172 3.1355 3.0717 3.0204 2.9782 2.9130 2.8450 2.7740 2.7372 2.6996 2.6371 2.5884 2.537911 4.8443 3.9823 3.5874 3.3567 3.2039 3.0946 3.0123 2.9480 2.8962 2.8536 2.7876 2.7186 2.6464 2.6090 2.5705 2.5066 2.4566 2.404512 4.7472 3.8853 3.4903 3.2592 3.1059 2.9961 2.9134 2.8486 2.7964 2.7534 2.6866 2.6169 2.5436 2.5055 2.4663 2.4010 2.3498 2.296213 4.6672 3.8056 3.4105 3.1791 3.0254 2.9153 2.8321 2.7669 2.7144 2.6710 2.6037 2.5331 2.4589 2.4202 2.3803 2.3138 2.2614 2.206414 4.6001 3.7389 3.3439 3.1122 2.9582 2.8477 2.7642 2.6987 2.6458 2.6022 2.5342 2.4630 2.3879 2.3487 2.3082 2.2405 2.1870 2.130715 4.5431 3.6823 3.2874 3.0556 2.9013 2.7905 2.7066 2.6408 2.5876 2.5437 2.4753 2.4034 2.3275 2.2878 2.2468 2.1780 2.1234 2.065816 4.4940 3.6337 3.2389 3.0069 2.8524 2.7413 2.6572 2.5911 2.5377 2.4935 2.4247 2.3522 2.2756 2.2354 2.1938 2.1240 2.0685 2.009617 4.4513 3.5915 3.1968 2.9647 2.8100 2.6987 2.6143 2.5480 2.4943 2.4499 2.3807 2.3077 2.2304 2.1898 2.1477 2.0769 2.0204 1.960418 4.4139 3.5546 3.1599 2.9277 2.7729 2.6613 2.5767 2.5102 2.4563 2.4117 2.3421 2.2686 2.1906 2.1497 2.1071 2.0354 1.9780 1.916819 4.3807 3.5219 3.1274 2.8951 2.7401 2.6283 2.5435 2.4768 2.4227 2.3779 2.3080 2.2341 2.1555 2.1141 2.0712 1.9986 1.9403 1.878020 4.3512 3.4928 3.0984 2.8661 2.7109 2.5990 2.5140 2.4471 2.3928 2.3479 2.2776 2.2033 2.1242 2.0825 2.0391 1.9656 1.9066 1.843221 4.3248 3.4668 3.0725 2.8401 2.6848 2.5727 2.4876 2.4205 2.3660 2.3210 2.2504 2.1757 2.0960 2.0540 2.0102 1.9360 1.8761 1.811722 4.3009 3.4434 3.0491 2.8167 2.6613 2.5491 2.4638 2.3965 2.3419 2.2967 2.2258 2.1508 2.0707 2.0283 1.9842 1.9092 1.8486 1.783123 4.2793 3.4221 3.0280 2.7955 2.6400 2.5277 2.4422 2.3748 2.3201 2.2747 2.2036 2.1282 2.0476 2.0050 1.9605 1.8848 1.8234 1.757024 4.2597 3.4028 3.0088 2.7763 2.6207 2.5082 2.4226 2.3551 2.3002 2.2547 2.1834 2.1077 2.0267 1.9838 1.9390 1.8625 1.8005 1.733025 4.2417 3.3852 2.9912 2.7587 2.6030 2.4904 2.4047 2.3371 2.2821 2.2365 2.1649 2.0889 2.0075 1.9643 1.9192 1.8421 1.7794 1.711026 4.2252 3.3690 2.9752 2.7426 2.5868 2.4741 2.3883 2.3205 2.2655 2.2197 2.1479 2.0716 1.9898 1.9464 1.9010 1.8233 1.7599 1.690627 4.2100 3.3541 2.9604 2.7278 2.5719 2.4591 2.3732 2.3053 2.2501 2.2043 2.1323 2.0558 1.9736 1.9299 1.8842 1.8059 1.7419 1.671728 4.1960 3.3404 2.9467 2.7141 2.5581 2.4453 2.3593 2.2913 2.2360 2.1900 2.1179 2.0411 1.9586 1.9147 1.8687 1.7898 1.7251 1.654129 4.1830 3.3277 2.9340 2.7014 2.5454 2.4324 2.3463 2.2782 2.2229 2.1768 2.1045 2.0275 1.9446 1.9005 1.8543 1.7748 1.7096 1.637630 4.1709 3.3158 2.9223 2.6896 2.5336 2.4205 2.3343 2.2662 2.2107 2.1646 2.0921 2.0148 1.9317 1.8874 1.8409 1.7609 1.6950 1.622340 4.0847 3.2317 2.8387 2.6060 2.4495 2.3359 2.2490 2.1802 2.1240 2.0772 2.0035 1.9245 1.8389 1.7929 1.7444 1.6600 1.5892 1.508960 4.0012 3.1504 2.7581 2.5252 2.3683 2.2541 2.1665 2.0970 2.0401 1.9926 1.9174 1.8364 1.7480 1.7001 1.6491 1.5590 1.4814 1.3893

100 3.9361 3.0873 2.6955 2.4626 2.3053 2.1906 2.1025 2.0323 1.9748 1.9267 1.8503 1.7675 1.6764 1.6267 1.5733 1.4772 1.3917 1.2832200 3.8884 3.0411 2.6498 2.4168 2.2592 2.1441 2.0556 1.9849 1.9269 1.8783 1.8008 1.7166 1.6233 1.5720 1.5164 1.4146 1.3206 1.1885∞ 3.8415 2.9957 2.6049 2.3719 2.2141 2.0986 2.0096 1.9384 1.8799 1.8307 1.7522 1.6664 1.5705 1.5173 1.4591 1.3501 1.2434 1.0000

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Page 36: Tablas de las Distribuciones Estadisticas Mas Usadas

Inversa de la funcion de distribucion F de Snedecor:

Fm,n(x) = P [Fm,n ≤ x], Fm,n(Fm,n,α) = α, Fm,n,α = F−1

m,n(α), α = 0,975

n�m 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 50 100 ∞

1 647.7890 799.5000 864.1630 899.5833 921.8479 937.1111 948.2169 956.6562 963.2846 968.6274 976.7079 984.8668 993.1028 997.2492 1001.4144 1008.1171 1013.1748 1018.25832 38.5063 39.0000 39.1655 39.2484 39.2982 39.3315 39.3552 39.3730 39.3869 39.3980 39.4146 39.4313 39.4479 39.4562 39.4646 39.4779 39.4879 39.49793 17.4434 16.0441 15.4392 15.1010 14.8848 14.7347 14.6244 14.5399 14.4731 14.4189 14.3366 14.2527 14.1674 14.1241 14.0805 14.0099 13.9563 13.90214 12.2179 10.6491 9.9792 9.6045 9.3645 9.1973 9.0741 8.9796 8.9047 8.8439 8.7512 8.6565 8.5599 8.5109 8.4613 8.3808 8.3195 8.25735 10.0070 8.4336 7.7636 7.3879 7.1464 6.9777 6.8531 6.7572 6.6811 6.6192 6.5245 6.4277 6.3286 6.2780 6.2269 6.1436 6.0800 6.01536 8.8131 7.2599 6.5988 6.2272 5.9876 5.8198 5.6955 5.5996 5.5234 5.4613 5.3662 5.2687 5.1684 5.1172 5.0652 4.9804 4.9154 4.84917 8.0727 6.5415 5.8898 5.5226 5.2852 5.1186 4.9949 4.8993 4.8232 4.7611 4.6658 4.5678 4.4667 4.4150 4.3624 4.2763 4.2101 4.14238 7.5709 6.0595 5.4160 5.0526 4.8173 4.6517 4.5286 4.4333 4.3572 4.2951 4.1997 4.1012 3.9995 3.9472 3.8940 3.8067 3.7393 3.67029 7.2093 5.7147 5.0781 4.7181 4.4844 4.3197 4.1970 4.1020 4.0260 3.9639 3.8682 3.7694 3.6669 3.6142 3.5604 3.4719 3.4034 3.3329

10 6.9367 5.4564 4.8256 4.4683 4.2361 4.0721 3.9498 3.8549 3.7790 3.7168 3.6209 3.5217 3.4185 3.3654 3.3110 3.2214 3.1517 3.079811 6.7241 5.2559 4.6300 4.2751 4.0440 3.8807 3.7586 3.6638 3.5879 3.5257 3.4296 3.3299 3.2261 3.1725 3.1176 3.0268 2.9561 2.882812 6.5538 5.0959 4.4742 4.1212 3.8911 3.7283 3.6065 3.5118 3.4358 3.3736 3.2773 3.1772 3.0728 3.0187 2.9633 2.8714 2.7996 2.724913 6.4143 4.9653 4.3472 3.9959 3.7667 3.6043 3.4827 3.3880 3.3120 3.2497 3.1532 3.0527 2.9477 2.8932 2.8372 2.7443 2.6715 2.595514 6.2979 4.8567 4.2417 3.8919 3.6634 3.5014 3.3799 3.2853 3.2093 3.1469 3.0502 2.9493 2.8437 2.7888 2.7324 2.6384 2.5646 2.487215 6.1995 4.7650 4.1528 3.8043 3.5764 3.4147 3.2934 3.1987 3.1227 3.0602 2.9633 2.8621 2.7559 2.7006 2.6437 2.5488 2.4739 2.395316 6.1151 4.6867 4.0768 3.7294 3.5021 3.3406 3.2194 3.1248 3.0488 2.9862 2.8890 2.7875 2.6808 2.6252 2.5678 2.4719 2.3961 2.316317 6.0420 4.6189 4.0112 3.6648 3.4379 3.2767 3.1556 3.0610 2.9849 2.9222 2.8249 2.7230 2.6158 2.5598 2.5020 2.4053 2.3285 2.247418 5.9781 4.5597 3.9539 3.6083 3.3820 3.2209 3.0999 3.0053 2.9291 2.8664 2.7689 2.6667 2.5590 2.5027 2.4445 2.3468 2.2692 2.186919 5.9216 4.5075 3.9034 3.5587 3.3327 3.1718 3.0509 2.9563 2.8801 2.8172 2.7196 2.6171 2.5089 2.4523 2.3937 2.2952 2.2167 2.133320 5.8715 4.4613 3.8587 3.5147 3.2891 3.1283 3.0074 2.9128 2.8365 2.7737 2.6758 2.5731 2.4645 2.4076 2.3486 2.2493 2.1699 2.085321 5.8266 4.4199 3.8188 3.4754 3.2501 3.0895 2.9686 2.8740 2.7977 2.7348 2.6368 2.5338 2.4247 2.3675 2.3082 2.2081 2.1280 2.042222 5.7863 4.3828 3.7829 3.4401 3.2151 3.0546 2.9338 2.8392 2.7628 2.6998 2.6017 2.4984 2.3890 2.3315 2.2718 2.1710 2.0901 2.003223 5.7498 4.3492 3.7505 3.4083 3.1835 3.0232 2.9023 2.8077 2.7313 2.6682 2.5699 2.4664 2.3567 2.2989 2.2389 2.1374 2.0557 1.967724 5.7166 4.3187 3.7211 3.3794 3.1548 2.9946 2.8738 2.7791 2.7027 2.6396 2.5411 2.4374 2.3273 2.2693 2.2090 2.1067 2.0243 1.935325 5.6864 4.2909 3.6943 3.3530 3.1287 2.9685 2.8478 2.7531 2.6766 2.6135 2.5149 2.4110 2.3005 2.2422 2.1816 2.0787 1.9955 1.905526 5.6586 4.2655 3.6697 3.3289 3.1048 2.9447 2.8240 2.7293 2.6528 2.5896 2.4908 2.3867 2.2759 2.2174 2.1565 2.0530 1.9691 1.878127 5.6331 4.2421 3.6472 3.3067 3.0828 2.9228 2.8021 2.7074 2.6309 2.5676 2.4688 2.3644 2.2533 2.1946 2.1334 2.0293 1.9447 1.852728 5.6096 4.2205 3.6264 3.2863 3.0626 2.9027 2.7820 2.6872 2.6106 2.5473 2.4484 2.3438 2.2324 2.1735 2.1121 2.0073 1.9221 1.829129 5.5878 4.2006 3.6072 3.2674 3.0438 2.8840 2.7633 2.6686 2.5919 2.5286 2.4295 2.3248 2.2131 2.1540 2.0923 1.9870 1.9011 1.807230 5.5675 4.1821 3.5894 3.2499 3.0265 2.8667 2.7460 2.6513 2.5746 2.5112 2.4120 2.3072 2.1952 2.1359 2.0739 1.9681 1.8816 1.786740 5.4239 4.0510 3.4633 3.1261 2.9037 2.7444 2.6238 2.5289 2.4519 2.3882 2.2882 2.1819 2.0677 2.0069 1.9429 1.8324 1.7405 1.637160 5.2856 3.9253 3.3425 3.0077 2.7863 2.6274 2.5068 2.4117 2.3344 2.2702 2.1692 2.0613 1.9445 1.8817 1.8152 1.6985 1.5990 1.4821

100 5.1786 3.8284 3.2496 2.9166 2.6961 2.5374 2.4168 2.3215 2.2439 2.1793 2.0773 1.9679 1.8486 1.7839 1.7148 1.5917 1.4832 1.3473200 5.1004 3.7578 3.1820 2.8503 2.6304 2.4720 2.3513 2.2558 2.1780 2.1130 2.0103 1.8996 1.7780 1.7117 1.6403 1.5108 1.3927 1.2290∞ 5.0239 3.6889 3.1161 2.7858 2.5665 2.4082 2.2875 2.1918 2.1136 2.0483 1.9447 1.8326 1.7085 1.6402 1.5660 1.4284 1.2956 1.0000

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Page 37: Tablas de las Distribuciones Estadisticas Mas Usadas

Inversa de la funcion de distribucion F de Snedecor:

Fm,n(x) = P [Fm,n ≤ x], Fm,n(Fm,n,α) = α, Fm,n,α = F−1

m,n(α), α = 0,99

n�m 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 50 100 ∞

1 4052.181 4999.500 5403.352 5624.583 5763.650 5858.986 5928.356 5981.070 6022.473 6055.847 6106.321 6157.285 6208.730 6234.631 6260.649 6302.517 6334.110 6365.8642 98.503 99.000 99.166 99.249 99.299 99.333 99.356 99.374 99.388 99.399 99.416 99.433 99.449 99.458 99.466 99.479 99.489 99.4993 34.116 30.817 29.457 28.710 28.237 27.911 27.672 27.489 27.345 27.229 27.052 26.872 26.690 26.598 26.505 26.354 26.240 26.1254 21.198 18.000 16.694 15.977 15.522 15.207 14.976 14.799 14.659 14.546 14.374 14.198 14.020 13.929 13.838 13.690 13.577 13.4635 16.258 13.274 12.060 11.392 10.967 10.672 10.456 10.289 10.158 10.051 9.888 9.722 9.553 9.466 9.379 9.238 9.130 9.0206 13.745 10.925 9.780 9.148 8.746 8.466 8.260 8.102 7.976 7.874 7.718 7.559 7.396 7.313 7.229 7.091 6.987 6.8807 12.246 9.547 8.451 7.847 7.460 7.191 6.993 6.840 6.719 6.620 6.469 6.314 6.155 6.074 5.992 5.858 5.755 5.6508 11.259 8.649 7.591 7.006 6.632 6.371 6.178 6.029 5.911 5.814 5.667 5.515 5.359 5.279 5.198 5.065 4.963 4.8599 10.561 8.022 6.992 6.422 6.057 5.802 5.613 5.467 5.351 5.257 5.111 4.962 4.808 4.729 4.649 4.517 4.415 4.311

10 10.044 7.559 6.552 5.994 5.636 5.386 5.200 5.057 4.942 4.849 4.706 4.558 4.405 4.327 4.247 4.115 4.014 3.90911 9.646 7.206 6.217 5.668 5.316 5.069 4.886 4.744 4.632 4.539 4.397 4.251 4.099 4.021 3.941 3.810 3.708 3.60212 9.330 6.927 5.953 5.412 5.064 4.821 4.640 4.499 4.388 4.296 4.155 4.010 3.858 3.780 3.701 3.569 3.467 3.36113 9.074 6.701 5.739 5.205 4.862 4.620 4.441 4.302 4.191 4.100 3.960 3.815 3.665 3.587 3.507 3.375 3.272 3.16514 8.862 6.515 5.564 5.035 4.695 4.456 4.278 4.140 4.030 3.939 3.800 3.656 3.505 3.427 3.348 3.215 3.112 3.00415 8.683 6.359 5.417 4.893 4.556 4.318 4.142 4.004 3.895 3.805 3.666 3.522 3.372 3.294 3.214 3.081 2.977 2.86816 8.531 6.226 5.292 4.773 4.437 4.202 4.026 3.890 3.780 3.691 3.553 3.409 3.259 3.181 3.101 2.967 2.863 2.75317 8.400 6.112 5.185 4.669 4.336 4.102 3.927 3.791 3.682 3.593 3.455 3.312 3.162 3.084 3.003 2.869 2.764 2.65318 8.285 6.013 5.092 4.579 4.248 4.015 3.841 3.705 3.597 3.508 3.371 3.227 3.077 2.999 2.919 2.784 2.678 2.56619 8.185 5.926 5.010 4.500 4.171 3.939 3.765 3.631 3.522 3.434 3.297 3.153 3.003 2.925 2.844 2.709 2.602 2.48920 8.096 5.849 4.938 4.431 4.103 3.871 3.699 3.564 3.457 3.368 3.231 3.088 2.938 2.859 2.778 2.643 2.535 2.42121 8.017 5.780 4.874 4.369 4.042 3.812 3.640 3.506 3.398 3.310 3.173 3.030 2.880 2.801 2.720 2.584 2.475 2.36022 7.945 5.719 4.817 4.313 3.988 3.758 3.587 3.453 3.346 3.258 3.121 2.978 2.827 2.749 2.667 2.531 2.422 2.30523 7.881 5.664 4.765 4.264 3.939 3.710 3.539 3.406 3.299 3.211 3.074 2.931 2.780 2.702 2.620 2.483 2.373 2.25624 7.823 5.614 4.718 4.218 3.895 3.667 3.496 3.363 3.256 3.168 3.032 2.889 2.738 2.659 2.577 2.440 2.329 2.21125 7.770 5.568 4.675 4.177 3.855 3.627 3.457 3.324 3.217 3.129 2.993 2.850 2.699 2.620 2.538 2.400 2.289 2.16926 7.721 5.526 4.637 4.140 3.818 3.591 3.421 3.288 3.182 3.094 2.958 2.815 2.664 2.585 2.503 2.364 2.252 2.13127 7.677 5.488 4.601 4.106 3.785 3.558 3.388 3.256 3.149 3.062 2.926 2.783 2.632 2.552 2.470 2.330 2.218 2.09728 7.636 5.453 4.568 4.074 3.754 3.528 3.358 3.226 3.120 3.032 2.896 2.753 2.602 2.522 2.440 2.300 2.187 2.06429 7.598 5.420 4.538 4.045 3.725 3.499 3.330 3.198 3.092 3.005 2.868 2.726 2.574 2.495 2.412 2.271 2.158 2.03430 7.562 5.390 4.510 4.018 3.699 3.473 3.304 3.173 3.067 2.979 2.843 2.700 2.549 2.469 2.386 2.245 2.131 2.00640 7.314 5.178 4.313 3.828 3.514 3.291 3.124 2.993 2.888 2.801 2.665 2.522 2.369 2.288 2.203 2.058 1.938 1.80560 7.077 4.977 4.126 3.649 3.339 3.119 2.953 2.823 2.718 2.632 2.496 2.352 2.198 2.115 2.028 1.877 1.749 1.601

100 6.895 4.824 3.984 3.513 3.206 2.988 2.823 2.694 2.590 2.503 2.368 2.223 2.067 1.983 1.893 1.735 1.598 1.427200 6.763 4.713 3.881 3.414 3.110 2.893 2.730 2.601 2.497 2.411 2.275 2.129 1.971 1.886 1.794 1.629 1.481 1.279∞ 6.635 4.605 3.782 3.319 3.017 2.802 2.639 2.511 2.407 2.321 2.185 2.039 1.878 1.791 1.696 1.523 1.358 1.000

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Page 38: Tablas de las Distribuciones Estadisticas Mas Usadas

Inversa de la funcion de distribucion F de Snedecor:

Fm,n(x) = P [Fm,n ≤ x], Fm,n(Fm,n,α) = α, Fm,n,α = F−1

m,n(α), α = 0,995

n�m 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 50 100 ∞

1 16210.72 19999.50 21614.74 22499.58 23055.80 23437.11 23714.57 23925.41 24091.00 24224.49 24426.37 24630.21 24835.97 24939.57 25043.63 25211.09 25337.45 25464.462 198.50 199.00 199.17 199.25 199.30 199.33 199.36 199.37 199.39 199.40 199.42 199.43 199.45 199.46 199.47 199.48 199.49 199.503 55.55 49.80 47.47 46.19 45.39 44.84 44.43 44.13 43.88 43.69 43.39 43.08 42.78 42.62 42.47 42.21 42.02 41.834 31.33 26.28 24.26 23.15 22.46 21.97 21.62 21.35 21.14 20.97 20.70 20.44 20.17 20.03 19.89 19.67 19.50 19.325 22.78 18.31 16.53 15.56 14.94 14.51 14.20 13.96 13.77 13.62 13.38 13.15 12.90 12.78 12.66 12.45 12.30 12.146 18.63 14.54 12.92 12.03 11.46 11.07 10.79 10.57 10.39 10.25 10.03 9.81 9.59 9.47 9.36 9.17 9.03 8.887 16.24 12.40 10.88 10.05 9.52 9.16 8.89 8.68 8.51 8.38 8.18 7.97 7.75 7.64 7.53 7.35 7.22 7.088 14.69 11.04 9.60 8.81 8.30 7.95 7.69 7.50 7.34 7.21 7.01 6.81 6.61 6.50 6.40 6.22 6.09 5.959 13.61 10.11 8.72 7.96 7.47 7.13 6.88 6.69 6.54 6.42 6.23 6.03 5.83 5.73 5.62 5.45 5.32 5.19

10 12.83 9.43 8.08 7.34 6.87 6.54 6.30 6.12 5.97 5.85 5.66 5.47 5.27 5.17 5.07 4.90 4.77 4.6411 12.23 8.91 7.60 6.88 6.42 6.10 5.86 5.68 5.54 5.42 5.24 5.05 4.86 4.76 4.65 4.49 4.36 4.2312 11.75 8.51 7.23 6.52 6.07 5.76 5.52 5.34 5.20 5.09 4.91 4.72 4.53 4.43 4.33 4.17 4.04 3.9013 11.37 8.19 6.93 6.23 5.79 5.48 5.25 5.08 4.94 4.82 4.64 4.46 4.27 4.17 4.07 3.91 3.78 3.6514 11.06 7.92 6.68 6.00 5.56 5.26 5.03 4.86 4.72 4.60 4.43 4.25 4.06 3.96 3.86 3.70 3.57 3.4415 10.80 7.70 6.48 5.80 5.37 5.07 4.85 4.67 4.54 4.42 4.25 4.07 3.88 3.79 3.69 3.52 3.39 3.2616 10.58 7.51 6.30 5.64 5.21 4.91 4.69 4.52 4.38 4.27 4.10 3.92 3.73 3.64 3.54 3.37 3.25 3.1117 10.38 7.35 6.16 5.50 5.07 4.78 4.56 4.39 4.25 4.14 3.97 3.79 3.61 3.51 3.41 3.25 3.12 2.9818 10.22 7.21 6.03 5.37 4.96 4.66 4.44 4.28 4.14 4.03 3.86 3.68 3.50 3.40 3.30 3.14 3.01 2.8719 10.07 7.09 5.92 5.27 4.85 4.56 4.34 4.18 4.04 3.93 3.76 3.59 3.40 3.31 3.21 3.04 2.91 2.7820 9.94 6.99 5.82 5.17 4.76 4.47 4.26 4.09 3.96 3.85 3.68 3.50 3.32 3.22 3.12 2.96 2.83 2.6921 9.83 6.89 5.73 5.09 4.68 4.39 4.18 4.01 3.88 3.77 3.60 3.43 3.24 3.15 3.05 2.88 2.75 2.6122 9.73 6.81 5.65 5.02 4.61 4.32 4.11 3.94 3.81 3.70 3.54 3.36 3.18 3.08 2.98 2.82 2.69 2.5523 9.63 6.73 5.58 4.95 4.54 4.26 4.05 3.88 3.75 3.64 3.47 3.30 3.12 3.02 2.92 2.76 2.62 2.4824 9.55 6.66 5.52 4.89 4.49 4.20 3.99 3.83 3.69 3.59 3.42 3.25 3.06 2.97 2.87 2.70 2.57 2.4325 9.48 6.60 5.46 4.84 4.43 4.15 3.94 3.78 3.64 3.54 3.37 3.20 3.01 2.92 2.82 2.65 2.52 2.3826 9.41 6.54 5.41 4.79 4.38 4.10 3.89 3.73 3.60 3.49 3.33 3.15 2.97 2.87 2.77 2.61 2.47 2.3327 9.34 6.49 5.36 4.74 4.34 4.06 3.85 3.69 3.56 3.45 3.28 3.11 2.93 2.83 2.73 2.57 2.43 2.2928 9.28 6.44 5.32 4.70 4.30 4.02 3.81 3.65 3.52 3.41 3.25 3.07 2.89 2.79 2.69 2.53 2.39 2.2529 9.23 6.40 5.28 4.66 4.26 3.98 3.77 3.61 3.48 3.38 3.21 3.04 2.86 2.76 2.66 2.49 2.36 2.2130 9.18 6.35 5.24 4.62 4.23 3.95 3.74 3.58 3.45 3.34 3.18 3.01 2.82 2.73 2.63 2.46 2.32 2.1840 8.83 6.07 4.98 4.37 3.99 3.71 3.51 3.35 3.22 3.12 2.95 2.78 2.60 2.50 2.40 2.23 2.09 1.9360 8.49 5.79 4.73 4.14 3.76 3.49 3.29 3.13 3.01 2.90 2.74 2.57 2.39 2.29 2.19 2.01 1.86 1.69

100 8.24 5.59 4.54 3.96 3.59 3.33 3.13 2.97 2.85 2.74 2.58 2.41 2.23 2.13 2.02 1.84 1.68 1.49200 8.06 5.44 4.41 3.84 3.47 3.21 3.01 2.86 2.73 2.63 2.47 2.30 2.11 2.01 1.90 1.71 1.54 1.31∞ 7.88 5.30 4.28 3.72 3.35 3.09 2.90 2.74 2.62 2.52 2.36 2.19 2.00 1.90 1.79 1.59 1.40 1.00

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Page 39: Tablas de las Distribuciones Estadisticas Mas Usadas

F DE SNEDECOR

TABLA DE DISTRIBUCION

α=P[F≥f]

(Probabilidad acumulada superior o a la derecha)

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Page 40: Tablas de las Distribuciones Estadisticas Mas Usadas

Tabela 4. Limites unilaterais da distribuição F de Fisher-Snedecor ao nível de 10% de probabilidade. GL V1 V2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 20 40 60 120 240 1 39.864 49.500 53.593 55.833 57.240 58.204 58.906 59.439 59.857 60.195 60.473 60.705 60.902 61.073 61.220 61.740 62.529 62.794 63.061 63.194 2 8.526 9.000 9.162 9.243 9.293 9.326 9.349 9.367 9.381 9.392 9.401 9.408 9.415 9.420 9.425 9.441 9.466 9.475 9.483 9.487 3 5.538 5.462 5.391 5.343 5.309 5.285 5.266 5.252 5.240 5.230 5.222 5.216 5.210 5.205 5.200 5.184 5.160 5.151 5.143 5.138

4 4.545 4.325 4.191 4.107 4.051 4.010 3.979 3.955 3.936 3.920 3.907 3.896 3.886 3.878 3.870 3.844 3.804 3.790 3.775 3.768 5 4.060 3.780 3.619 3.520 3.453 3.405 3.368 3.339 3.316 3.297 3.282 3.268 3.257 3.247 3.238 3.207 3.157 3.140 3.123 3.114 6 3.776 3.463 3.289 3.181 3.108 3.055 3.014 2.983 2.958 2.937 2.920 2.905 2.892 2.881 2.871 2.836 2.781 2.762 2.742 2.732 7 3.589 3.257 3.074 2.961 2.883 2.827 2.785 2.752 2.725 2.703 2.684 2.668 2.654 2.643 2.632 2.595 2.535 2.514 2.493 2.482 8 3.458 3.113 2.924 2.806 2.726 2.668 2.624 2.589 2.561 2.538 2.519 2.502 2.488 2.475 2.464 2.425 2.361 2.339 2.316 2.304 9 3.360 3.006 2.813 2.693 2.611 2.551 2.505 2.469 2.440 2.416 2.396 2.379 2.364 2.351 2.340 2.298 2.232 2.208 2.184 2.172 10 3.285 2.924 2.728 2.605 2.522 2.461 2.414 2.377 2.347 2.323 2.302 2.284 2.269 2.255 2.244 2.201 2.132 2.107 2.082 2.069 11 3.225 2.860 2.660 2.536 2.451 2.389 2.342 2.304 2.274 2.248 2.227 2.209 2.193 2.179 2.167 2.123 2.052 2.026 2.000 1.986

12 3.177 2.807 2.606 2.480 2.394 2.331 2.283 2.245 2.214 2.188 2.166 2.147 2.131 2.117 2.105 2.060 1.986 1.960 1.932 1.918 13 3.136 2.763 2.560 2.434 2.347 2.283 2.234 2.195 2.164 2.138 2.116 2.097 2.080 2.066 2.053 2.007 1.931 1.904 1.876 1.861 14 3.102 2.726 2.522 2.395 2.307 2.243 2.193 2.154 2.122 2.095 2.073 2.054 2.037 2.022 2.010 1.962 1.885 1.857 1.828 1.813 15 3.073 2.695 2.490 2.361 2.273 2.208 2.158 2.119 2.086 2.059 2.037 2.017 2.000 1.985 1.972 1.924 1.845 1.817 1.787 1.771 16 3.048 2.668 2.462 2.333 2.244 2.178 2.128 2.088 2.055 2.028 2.005 1.985 1.968 1.953 1.940 1.891 1.811 1.782 1.751 1.735 17 3.026 2.645 2.437 2.308 2.218 2.152 2.102 2.061 2.028 2.001 1.978 1.958 1.940 1.925 1.912 1.862 1.781 1.751 1.719 1.703 18 3.007 2.624 2.416 2.286 2.196 2.130 2.079 2.038 2.005 1.977 1.954 1.933 1.916 1.900 1.887 1.837 1.754 1.723 1.691 1.674

19 2.990 2.606 2.397 2.266 2.176 2.109 2.058 2.017 1.984 1.956 1.932 1.912 1.894 1.878 1.865 1.814 1.730 1.699 1.666 1.649 20 2.975 2.589 2.380 2.249 2.158 2.091 2.040 1.999 1.965 1.937 1.913 1.892 1.875 1.859 1.845 1.794 1.708 1.677 1.643 1.626 21 2.961 2.575 2.365 2.233 2.142 2.075 2.023 1.982 1.948 1.920 1.896 1.875 1.857 1.841 1.827 1.776 1.689 1.657 1.623 1.605 22 2.949 2.561 2.351 2.219 2.128 2.060 2.008 1.967 1.933 1.904 1.880 1.859 1.841 1.825 1.811 1.759 1.671 1.639 1.604 1.586 23 2.937 2.549 2.339 2.207 2.115 2.047 1.995 1.953 1.919 1.890 1.866 1.845 1.827 1.811 1.796 1.744 1.655 1.622 1.587 1.568 24 2.927 2.538 2.327 2.195 2.103 2.035 1.983 1.941 1.906 1.877 1.853 1.832 1.814 1.797 1.783 1.730 1.641 1.607 1.571 1.552 25 2.918 2.528 2.317 2.184 2.092 2.024 1.971 1.929 1.895 1.866 1.841 1.820 1.802 1.785 1.771 1.718 1.627 1.593 1.557 1.538 26 2.909 2.519 2.307 2.174 2.082 2.014 1.961 1.919 1.884 1.855 1.830 1.809 1.790 1.774 1.760 1.706 1.615 1.581 1.544 1.524

27 2.901 2.511 2.299 2.165 2.073 2.005 1.952 1.909 1.874 1.845 1.820 1.799 1.780 1.764 1.749 1.695 1.603 1.569 1.531 1.511 28 2.894 2.503 2.291 2.157 2.064 1.996 1.943 1.900 1.865 1.836 1.811 1.790 1.771 1.754 1.740 1.685 1.592 1.558 1.520 1.500 29 2.887 2.495 2.283 2.149 2.057 1.988 1.935 1.892 1.857 1.827 1.802 1.781 1.762 1.745 1.731 1.676 1.583 1.547 1.509 1.489 30 2.881 2.489 2.276 2.142 2.049 1.980 1.927 1.884 1.849 1.819 1.794 1.773 1.754 1.737 1.722 1.667 1.573 1.538 1.499 1.478 40 2.835 2.440 2.226 2.091 1.997 1.927 1.873 1.829 1.793 1.763 1.737 1.715 1.695 1.678 1.662 1.605 1.506 1.467 1.425 1.402 50 2.809 2.412 2.197 2.061 1.966 1.895 1.840 1.796 1.760 1.729 1.703 1.680 1.660 1.643 1.627 1.568 1.465 1.424 1.379 1.354 60 2.791 2.393 2.177 2.041 1.946 1.875 1.819 1.775 1.738 1.707 1.680 1.657 1.637 1.619 1.603 1.543 1.437 1.395 1.348 1.321

80 2.769 2.370 2.154 2.016 1.921 1.849 1.793 1.748 1.711 1.680 1.653 1.629 1.609 1.590 1.574 1.513 1.403 1.358 1.307 1.278 100 2.756 2.356 2.139 2.002 1.906 1.834 1.778 1.732 1.695 1.663 1.636 1.612 1.592 1.573 1.557 1.494 1.382 1.336 1.282 1.250 120 2.748 2.347 2.130 1.992 1.896 1.824 1.767 1.722 1.684 1.652 1.625 1.601 1.580 1.562 1.545 1.482 1.368 1.320 1.265 1.232 240 2.727 2.325 2.107 1.968 1.871 1.799 1.742 1.696 1.658 1.625 1.598 1.573 1.552 1.533 1.516 1.451 1.332 1.281 1.219 1.180

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Page 41: Tablas de las Distribuciones Estadisticas Mas Usadas

Tabela 5. Limites unilaterais da distribuição F de Fisher-Snedecor ao nível de 5% de probabilidade. GL V1 V2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 20 40 60 120 240 1 161.4 199.5 215.7 224.6 230.2 234.0 236.8 238.9 240.5 241.9 243.0 243.9 244.7 245.4 245.9 248.0 251.1 252.2 253.3 253.8 2 18.513 19.000 19.164 19.247 19.296 19.329 19.353 19.371 19.385 19.396 19.405 19.412 19.419 19.424 19.429 19.446 19.471 19.479 19.487 19.492 3 10.128 9.552 9.277 9.117 9.013 8.941 8.887 8.845 8.812 8.785 8.763 8.745 8.729 8.715 8.703 8.660 8.594 8.572 8.549 8.538

4 7.709 6.944 6.591 6.388 6.256 6.163 6.094 6.041 5.999 5.964 5.936 5.912 5.891 5.873 5.858 5.803 5.717 5.688 5.658 5.643 5 6.608 5.786 5.409 5.192 5.050 4.950 4.876 4.818 4.772 4.735 4.704 4.678 4.655 4.636 4.619 4.558 4.464 4.431 4.398 4.382 6 5.987 5.143 4.757 4.534 4.387 4.284 4.207 4.147 4.099 4.060 4.027 4.000 3.976 3.956 3.938 3.874 3.774 3.740 3.705 3.687 7 5.591 4.737 4.347 4.120 3.972 3.866 3.787 3.726 3.677 3.637 3.603 3.575 3.550 3.529 3.511 3.445 3.340 3.304 3.267 3.249 8 5.318 4.459 4.066 3.838 3.688 3.581 3.500 3.438 3.388 3.347 3.313 3.284 3.259 3.237 3.218 3.150 3.043 3.005 2.967 2.947 9 5.117 4.256 3.863 3.633 3.482 3.374 3.293 3.230 3.179 3.137 3.102 3.073 3.048 3.025 3.006 2.936 2.826 2.787 2.748 2.727 10 4.965 4.103 3.708 3.478 3.326 3.217 3.135 3.072 3.020 2.978 2.943 2.913 2.887 2.865 2.845 2.774 2.661 2.621 2.580 2.559 11 4.844 3.982 3.587 3.357 3.204 3.095 3.012 2.948 2.896 2.854 2.818 2.788 2.761 2.739 2.719 2.646 2.531 2.490 2.448 2.426

12 4.747 3.885 3.490 3.259 3.106 2.996 2.913 2.849 2.796 2.753 2.717 2.687 2.660 2.637 2.617 2.544 2.426 2.384 2.341 2.319 13 4.667 3.806 3.411 3.179 3.025 2.915 2.832 2.767 2.714 2.671 2.635 2.604 2.577 2.554 2.533 2.459 2.339 2.297 2.252 2.230 14 4.600 3.739 3.344 3.112 2.958 2.848 2.764 2.699 2.646 2.602 2.565 2.534 2.507 2.484 2.463 2.388 2.266 2.223 2.178 2.155 15 4.543 3.682 3.287 3.056 2.901 2.790 2.707 2.641 2.588 2.544 2.507 2.475 2.448 2.424 2.403 2.328 2.204 2.160 2.114 2.090 16 4.494 3.634 3.239 3.007 2.852 2.741 2.657 2.591 2.538 2.494 2.456 2.425 2.397 2.373 2.352 2.276 2.151 2.106 2.059 2.035 17 4.451 3.592 3.197 2.965 2.810 2.699 2.614 2.548 2.494 2.450 2.413 2.381 2.353 2.329 2.308 2.230 2.104 2.058 2.011 1.986 18 4.414 3.555 3.160 2.928 2.773 2.661 2.577 2.510 2.456 2.412 2.374 2.342 2.314 2.290 2.269 2.191 2.063 2.017 1.968 1.943

19 4.381 3.522 3.127 2.895 2.740 2.628 2.544 2.477 2.423 2.378 2.340 2.308 2.280 2.256 2.234 2.155 2.026 1.980 1.930 1.905 20 4.351 3.493 3.098 2.866 2.711 2.599 2.514 2.447 2.393 2.348 2.310 2.278 2.250 2.225 2.203 2.124 1.994 1.946 1.896 1.870 21 4.325 3.467 3.072 2.840 2.685 2.573 2.488 2.420 2.366 2.321 2.283 2.250 2.222 2.197 2.176 2.096 1.965 1.916 1.866 1.839 22 4.301 3.443 3.049 2.817 2.661 2.549 2.464 2.397 2.342 2.297 2.259 2.226 2.198 2.173 2.151 2.071 1.938 1.889 1.838 1.811 23 4.279 3.422 3.028 2.796 2.640 2.528 2.442 2.375 2.320 2.275 2.236 2.204 2.175 2.150 2.128 2.048 1.914 1.865 1.813 1.785 24 4.260 3.403 3.009 2.776 2.621 2.508 2.423 2.355 2.300 2.255 2.216 2.183 2.155 2.130 2.108 2.027 1.892 1.842 1.790 1.762 25 4.242 3.385 2.991 2.759 2.603 2.490 2.405 2.337 2.282 2.236 2.198 2.165 2.136 2.111 2.089 2.007 1.872 1.822 1.768 1.740 26 4.225 3.369 2.975 2.743 2.587 2.474 2.388 2.321 2.265 2.220 2.181 2.148 2.119 2.094 2.072 1.990 1.853 1.803 1.749 1.720

27 4.210 3.354 2.960 2.728 2.572 2.459 2.373 2.305 2.250 2.204 2.166 2.132 2.103 2.078 2.056 1.974 1.836 1.785 1.731 1.702 28 4.196 3.340 2.947 2.714 2.558 2.445 2.359 2.291 2.236 2.190 2.151 2.118 2.089 2.064 2.041 1.959 1.820 1.769 1.714 1.685 29 4.183 3.328 2.934 2.701 2.545 2.432 2.346 2.278 2.223 2.177 2.138 2.104 2.075 2.050 2.027 1.945 1.806 1.754 1.698 1.669 30 4.171 3.316 2.922 2.690 2.534 2.421 2.334 2.266 2.211 2.165 2.126 2.092 2.063 2.037 2.015 1.932 1.792 1.740 1.683 1.654 40 4.085 3.232 2.839 2.606 2.449 2.336 2.249 2.180 2.124 2.077 2.038 2.003 1.974 1.948 1.924 1.839 1.693 1.637 1.577 1.544 50 4.034 3.183 2.790 2.557 2.400 2.286 2.199 2.130 2.073 2.026 1.986 1.952 1.921 1.895 1.871 1.784 1.634 1.576 1.511 1.476 60 4.001 3.150 2.758 2.525 2.368 2.254 2.167 2.097 2.040 1.993 1.952 1.917 1.887 1.860 1.836 1.748 1.594 1.534 1.467 1.430

80 3.960 3.111 2.719 2.486 2.329 2.214 2.126 2.056 1.999 1.951 1.910 1.875 1.845 1.817 1.793 1.703 1.545 1.482 1.411 1.370 100 3.936 3.087 2.696 2.463 2.305 2.191 2.103 2.032 1.975 1.927 1.886 1.850 1.819 1.792 1.768 1.676 1.515 1.450 1.376 1.333 120 3.920 3.072 2.680 2.447 2.290 2.175 2.087 2.016 1.959 1.910 1.869 1.834 1.803 1.775 1.750 1.659 1.495 1.429 1.352 1.307 240 3.881 3.033 2.642 2.409 2.252 2.136 2.048 1.977 1.919 1.870 1.829 1.793 1.761 1.733 1.708 1.614 1.445 1.375 1.290 1.237

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Page 42: Tablas de las Distribuciones Estadisticas Mas Usadas

Tabela 6. Limites unilaterais da distribuição F de Fisher-Snedecor ao nível de 2,5% de probabilidade. GL V1 V2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 20 40 60 120 240 1 647.8 799.5 864.2 899.6 921.8 937.1 948.2 956.6 963.3 968.6 973.0 976.7 979.8 982.5 984.9 993.1 1005.6 1009.8 1014.0 1016.1 2 38.506 39.000 39.166 39.248 39.298 39.331 39.356 39.373 39.387 39.398 39.407 39.415 39.421 39.427 39.431 39.448 39.473 39.481 39.489 39.494 3 17.443 16.044 15.439 15.101 14.885 14.735 14.624 14.540 14.473 14.419 14.374 14.337 14.305 14.277 14.253 14.167 14.036 13.992 13.947 13.925

4 12.218 10.649 9.979 9.604 9.364 9.197 9.074 8.980 8.905 8.844 8.794 8.751 8.715 8.684 8.657 8.560 8.411 8.360 8.309 8.283 5 10.007 8.434 7.764 7.388 7.146 6.978 6.853 6.757 6.681 6.619 6.568 6.525 6.488 6.456 6.428 6.329 6.175 6.123 6.069 6.042 6 8.813 7.260 6.599 6.227 5.988 5.820 5.695 5.600 5.523 5.461 5.410 5.366 5.329 5.297 5.269 5.168 5.012 4.959 4.904 4.877 7 8.073 6.542 5.890 5.523 5.285 5.119 4.995 4.899 4.823 4.761 4.709 4.666 4.628 4.596 4.568 4.467 4.309 4.254 4.199 4.171 8 7.571 6.059 5.416 5.053 4.817 4.652 4.529 4.433 4.357 4.295 4.243 4.200 4.162 4.130 4.101 3.999 3.840 3.784 3.728 3.699 9 7.209 5.715 5.078 4.718 4.484 4.320 4.197 4.102 4.026 3.964 3.912 3.868 3.831 3.798 3.769 3.667 3.505 3.449 3.392 3.363 10 6.937 5.456 4.826 4.468 4.236 4.072 3.950 3.855 3.779 3.717 3.665 3.621 3.583 3.550 3.522 3.419 3.255 3.198 3.140 3.110 11 6.724 5.256 4.630 4.275 4.044 3.881 3.759 3.664 3.588 3.526 3.474 3.430 3.392 3.359 3.330 3.226 3.061 3.004 2.944 2.914

12 6.554 5.096 4.474 4.121 3.891 3.728 3.607 3.512 3.436 3.374 3.321 3.277 3.239 3.206 3.177 3.073 2.906 2.848 2.787 2.756 13 6.414 4.965 4.347 3.996 3.767 3.604 3.483 3.388 3.312 3.250 3.197 3.153 3.115 3.082 3.053 2.948 2.780 2.720 2.659 2.628 14 6.298 4.857 4.242 3.892 3.663 3.501 3.380 3.285 3.209 3.147 3.095 3.050 3.012 2.979 2.949 2.844 2.674 2.614 2.552 2.520 15 6.200 4.765 4.153 3.804 3.576 3.415 3.293 3.199 3.123 3.060 3.008 2.963 2.925 2.891 2.862 2.756 2.585 2.524 2.461 2.429 16 6.115 4.687 4.077 3.729 3.502 3.341 3.219 3.125 3.049 2.986 2.934 2.889 2.851 2.817 2.788 2.681 2.509 2.447 2.383 2.350 17 6.042 4.619 4.011 3.665 3.438 3.277 3.156 3.061 2.985 2.922 2.870 2.825 2.786 2.753 2.723 2.616 2.442 2.380 2.315 2.282 18 5.978 4.560 3.954 3.608 3.382 3.221 3.100 3.005 2.929 2.866 2.814 2.769 2.730 2.696 2.667 2.559 2.384 2.321 2.256 2.222

19 5.922 4.508 3.903 3.559 3.333 3.172 3.051 2.956 2.880 2.817 2.765 2.720 2.681 2.647 2.617 2.509 2.333 2.270 2.203 2.169 20 5.871 4.461 3.859 3.515 3.289 3.128 3.007 2.913 2.837 2.774 2.721 2.676 2.637 2.603 2.573 2.464 2.287 2.223 2.156 2.121 21 5.827 4.420 3.819 3.475 3.250 3.090 2.969 2.874 2.798 2.735 2.682 2.637 2.598 2.564 2.534 2.425 2.246 2.182 2.114 2.079 22 5.786 4.383 3.783 3.440 3.215 3.055 2.934 2.839 2.763 2.700 2.647 2.602 2.563 2.528 2.498 2.389 2.210 2.145 2.076 2.040 23 5.750 4.349 3.750 3.408 3.183 3.023 2.902 2.808 2.731 2.668 2.615 2.570 2.531 2.497 2.466 2.357 2.176 2.111 2.041 2.005 24 5.717 4.319 3.721 3.379 3.155 2.995 2.874 2.779 2.703 2.640 2.586 2.541 2.502 2.468 2.437 2.327 2.146 2.080 2.010 1.973 25 5.686 4.291 3.694 3.353 3.129 2.969 2.848 2.753 2.677 2.613 2.560 2.515 2.476 2.441 2.411 2.300 2.118 2.052 1.981 1.944 26 5.659 4.265 3.670 3.329 3.105 2.945 2.824 2.729 2.653 2.590 2.536 2.491 2.452 2.417 2.387 2.276 2.093 2.026 1.954 1.917

27 5.633 4.242 3.647 3.307 3.083 2.923 2.802 2.707 2.631 2.568 2.514 2.469 2.429 2.395 2.364 2.253 2.069 2.002 1.930 1.892 28 5.610 4.221 3.626 3.286 3.063 2.903 2.782 2.687 2.611 2.547 2.494 2.448 2.409 2.374 2.344 2.232 2.048 1.980 1.907 1.869 29 5.588 4.201 3.607 3.267 3.044 2.884 2.763 2.669 2.592 2.529 2.475 2.430 2.390 2.355 2.325 2.213 2.028 1.959 1.886 1.847 30 5.568 4.182 3.589 3.250 3.026 2.867 2.746 2.651 2.575 2.511 2.458 2.412 2.372 2.338 2.307 2.195 2.009 1.940 1.866 1.827 40 5.424 4.051 3.463 3.126 2.904 2.744 2.624 2.529 2.452 2.388 2.334 2.288 2.248 2.213 2.182 2.068 1.875 1.803 1.724 1.682 50 5.340 3.975 3.390 3.054 2.833 2.674 2.553 2.458 2.381 2.317 2.263 2.216 2.176 2.140 2.109 1.993 1.796 1.721 1.639 1.594 60 5.286 3.925 3.343 3.008 2.786 2.627 2.507 2.412 2.334 2.270 2.216 2.169 2.129 2.093 2.061 1.944 1.744 1.667 1.581 1.534

80 5.218 3.864 3.284 2.950 2.730 2.571 2.450 2.355 2.277 2.213 2.158 2.111 2.071 2.035 2.003 1.884 1.679 1.599 1.508 1.457 100 5.179 3.828 3.250 2.917 2.696 2.537 2.417 2.321 2.244 2.179 2.124 2.077 2.036 2.000 1.968 1.849 1.640 1.558 1.463 1.409 120 5.152 3.805 3.227 2.894 2.674 2.515 2.395 2.299 2.222 2.157 2.102 2.055 2.014 1.977 1.945 1.825 1.614 1.530 1.433 1.376 240 5.088 3.746 3.171 2.839 2.620 2.461 2.341 2.245 2.167 2.102 2.047 1.999 1.958 1.921 1.888 1.766 1.549 1.460 1.354 1.289

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Page 43: Tablas de las Distribuciones Estadisticas Mas Usadas

Tabela 7. Limites unilaterais da distribuição F de Fisher-Snedecor ao nível de 1,0% de probabilidade. GL V1 V2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 20 40 60 120 240 1 4052.2 4999.3 5403.5 5624.3 5764.0 5859.0 5928.3 5981.0 6022.4 6055.9 6083.4 6106.7 6125.8 6143.0 6157.0 6208.7 6286.4 6313.0 6339.5 6352.6 2 98.502 99.000 99.164 99.251 99.302 99.331 99.357 99.375 99.390 99.397 99.408 99.419 99.422 99.426 99.433 99.448 99.477 99.484 99.491 99.495 3 34.116 30.816 29.457 28.710 28.237 27.911 27.671 27.489 27.345 27.228 27.132 27.052 26.983 26.924 26.872 26.690 26.411 26.316 26.221 26.173

4 21.198 18.000 16.694 15.977 15.522 15.207 14.976 14.799 14.659 14.546 14.452 14.374 14.306 14.249 14.198 14.019 13.745 13.652 13.558 13.511 5 16.258 13.274 12.060 11.392 10.967 10.672 10.456 10.289 10.158 10.051 9.963 9.888 9.825 9.770 9.722 9.553 9.291 9.202 9.112 9.066 6 13.745 10.925 9.780 9.148 8.746 8.466 8.260 8.102 7.976 7.874 7.790 7.718 7.657 7.605 7.559 7.396 7.143 7.057 6.969 6.925 7 12.246 9.547 8.451 7.847 7.460 7.191 6.993 6.840 6.719 6.620 6.538 6.469 6.410 6.359 6.314 6.155 5.908 5.824 5.737 5.694 8 11.259 8.649 7.591 7.006 6.632 6.371 6.178 6.029 5.911 5.814 5.734 5.667 5.609 5.559 5.515 5.359 5.116 5.032 4.946 4.903 9 10.562 8.022 6.992 6.422 6.057 5.802 5.613 5.467 5.351 5.257 5.178 5.111 5.055 5.005 4.962 4.808 4.567 4.483 4.398 4.354 10 10.044 7.559 6.552 5.994 5.636 5.386 5.200 5.057 4.942 4.849 4.772 4.706 4.650 4.601 4.558 4.405 4.165 4.082 3.996 3.953 11 9.646 7.206 6.217 5.668 5.316 5.069 4.886 4.744 4.632 4.539 4.462 4.397 4.342 4.293 4.251 4.099 3.860 3.776 3.690 3.647

12 9.330 6.927 5.953 5.412 5.064 4.821 4.640 4.499 4.388 4.296 4.220 4.155 4.100 4.052 4.010 3.858 3.619 3.535 3.449 3.405 13 9.074 6.701 5.739 5.205 4.862 4.620 4.441 4.302 4.191 4.100 4.025 3.960 3.905 3.857 3.815 3.665 3.425 3.341 3.255 3.210 14 8.862 6.515 5.564 5.035 4.695 4.456 4.278 4.140 4.030 3.939 3.864 3.800 3.745 3.698 3.656 3.505 3.266 3.181 3.094 3.050 15 8.683 6.359 5.417 4.893 4.556 4.318 4.142 4.004 3.895 3.805 3.730 3.666 3.612 3.564 3.522 3.372 3.132 3.047 2.959 2.914 16 8.531 6.226 5.292 4.773 4.437 4.202 4.026 3.890 3.780 3.691 3.616 3.553 3.498 3.451 3.409 3.259 3.018 2.933 2.845 2.799 17 8.400 6.112 5.185 4.669 4.336 4.101 3.927 3.791 3.682 3.593 3.518 3.455 3.401 3.353 3.312 3.162 2.920 2.835 2.746 2.700 18 8.285 6.013 5.092 4.579 4.248 4.015 3.841 3.705 3.597 3.508 3.434 3.371 3.316 3.269 3.227 3.077 2.835 2.749 2.660 2.613

19 8.185 5.926 5.010 4.500 4.171 3.939 3.765 3.631 3.523 3.434 3.360 3.297 3.242 3.195 3.153 3.003 2.761 2.674 2.584 2.537 20 8.096 5.849 4.938 4.431 4.103 3.871 3.699 3.564 3.457 3.368 3.294 3.231 3.177 3.130 3.088 2.938 2.695 2.608 2.517 2.470 21 8.017 5.780 4.874 4.369 4.042 3.812 3.640 3.506 3.398 3.310 3.236 3.173 3.119 3.072 3.030 2.880 2.636 2.548 2.457 2.409 22 7.945 5.719 4.817 4.313 3.988 3.758 3.587 3.453 3.346 3.258 3.184 3.121 3.067 3.019 2.978 2.827 2.583 2.495 2.403 2.355 23 7.881 5.664 4.765 4.264 3.939 3.710 3.539 3.406 3.299 3.211 3.137 3.074 3.020 2.973 2.931 2.780 2.536 2.447 2.354 2.306 24 7.823 5.614 4.718 4.218 3.895 3.667 3.496 3.363 3.256 3.168 3.094 3.032 2.977 2.930 2.889 2.738 2.492 2.403 2.310 2.261 25 7.770 5.568 4.675 4.177 3.855 3.627 3.457 3.324 3.217 3.129 3.056 2.993 2.939 2.892 2.850 2.699 2.453 2.364 2.270 2.220 26 7.721 5.526 4.637 4.140 3.818 3.591 3.421 3.288 3.182 3.094 3.021 2.958 2.904 2.857 2.815 2.664 2.417 2.327 2.233 2.183

27 7.677 5.488 4.601 4.106 3.785 3.558 3.388 3.256 3.149 3.062 2.988 2.926 2.872 2.824 2.783 2.632 2.384 2.294 2.198 2.148 28 7.636 5.453 4.568 4.074 3.754 3.528 3.358 3.226 3.120 3.032 2.959 2.896 2.842 2.795 2.753 2.602 2.354 2.263 2.167 2.117 29 7.598 5.420 4.538 4.045 3.725 3.499 3.330 3.198 3.092 3.005 2.931 2.868 2.814 2.767 2.726 2.574 2.325 2.234 2.138 2.087 30 7.562 5.390 4.510 4.018 3.699 3.473 3.305 3.173 3.067 2.979 2.906 2.843 2.789 2.742 2.700 2.549 2.299 2.208 2.111 2.060 40 7.314 5.178 4.313 3.828 3.514 3.291 3.124 2.993 2.888 2.801 2.727 2.665 2.611 2.563 2.522 2.369 2.114 2.019 1.917 1.862 50 7.171 5.057 4.199 3.720 3.408 3.186 3.020 2.890 2.785 2.698 2.625 2.563 2.508 2.461 2.419 2.265 2.007 1.909 1.803 1.745 60 7.077 4.977 4.126 3.649 3.339 3.119 2.953 2.823 2.718 2.632 2.559 2.496 2.442 2.394 2.352 2.198 1.936 1.836 1.726 1.666

80 6.963 4.881 4.036 3.563 3.255 3.036 2.871 2.742 2.637 2.551 2.478 2.415 2.361 2.313 2.271 2.115 1.849 1.746 1.630 1.566 100 6.895 4.824 3.984 3.513 3.206 2.988 2.823 2.694 2.590 2.503 2.430 2.368 2.313 2.265 2.223 2.067 1.797 1.692 1.572 1.504 120 6.851 4.787 3.949 3.480 3.174 2.956 2.792 2.663 2.559 2.472 2.399 2.336 2.282 2.234 2.191 2.035 1.763 1.656 1.533 1.462 240 6.742 4.695 3.864 3.398 3.094 2.878 2.714 2.586 2.482 2.395 2.322 2.260 2.205 2.157 2.114 1.956 1.677 1.565 1.432 1.351

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Page 44: Tablas de las Distribuciones Estadisticas Mas Usadas

Tabela 8. Limites unilaterais da distribuição F de Fisher-Snedecor ao nível de 0,5% de probabilidade. GL V1 V2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 20 40 60 120 240 1 16212 19997 21614 22501 23056 23440 23715 23924 24091 24222 24334 24427 24505 24572 24632 24837 25146 25254 25358 25414 2 198.5 199.0 199.2 199.2 199.3 199.3 199.4 199.4 199.4 199.4 199.4 199.4 199.4 199.4 199.4 199.4 199.5 199.5 199.5 199.5 3 55.552 49.800 47.468 46.195 45.391 44.838 44.434 44.125 43.881 43.685 43.525 43.387 43.270 43.172 43.085 42.779 42.310 42.150 41.990 41.910

4 31.332 26.284 24.260 23.154 22.456 21.975 21.622 21.352 21.138 20.967 20.824 20.705 20.603 20.515 20.438 20.167 19.751 19.611 19.469 19.397 5 22.785 18.314 16.530 15.556 14.939 14.513 14.200 13.961 13.772 13.618 13.491 13.385 13.293 13.215 13.146 12.903 12.530 12.402 12.274 12.209 6 18.635 14.544 12.917 12.028 11.464 11.073 10.786 10.566 10.391 10.250 10.133 10.034 9.950 9.878 9.814 9.589 9.241 9.122 9.001 8.941 7 16.235 12.404 10.883 10.050 9.522 9.155 8.885 8.678 8.514 8.380 8.270 8.176 8.097 8.028 7.968 7.754 7.422 7.309 7.193 7.135 8 14.688 11.043 9.597 8.805 8.302 7.952 7.694 7.496 7.339 7.211 7.105 7.015 6.938 6.872 6.814 6.608 6.288 6.177 6.065 6.008 9 13.614 10.107 8.717 7.956 7.471 7.134 6.885 6.693 6.541 6.417 6.314 6.227 6.153 6.089 6.032 5.832 5.519 5.410 5.300 5.244 10 12.827 9.427 8.081 7.343 6.872 6.545 6.303 6.116 5.968 5.847 5.746 5.661 5.589 5.526 5.471 5.274 4.966 4.859 4.750 4.695 11 12.226 8.912 7.600 6.881 6.422 6.102 5.865 5.682 5.537 5.418 5.320 5.236 5.165 5.103 5.049 4.855 4.551 4.445 4.337 4.281

12 11.754 8.510 7.226 6.521 6.071 5.757 5.524 5.345 5.202 5.085 4.988 4.906 4.836 4.775 4.721 4.530 4.228 4.123 4.015 3.960 13 11.374 8.186 6.926 6.233 5.791 5.482 5.253 5.076 4.935 4.820 4.724 4.643 4.573 4.513 4.460 4.270 3.970 3.866 3.758 3.703 14 11.060 7.922 6.680 5.998 5.562 5.257 5.031 4.857 4.717 4.603 4.508 4.428 4.359 4.299 4.247 4.059 3.760 3.655 3.547 3.492 15 10.798 7.701 6.476 5.803 5.372 5.071 4.847 4.674 4.536 4.424 4.329 4.250 4.181 4.122 4.070 3.883 3.585 3.480 3.372 3.317 16 10.576 7.514 6.303 5.638 5.212 4.913 4.692 4.521 4.384 4.272 4.179 4.099 4.031 3.972 3.920 3.734 3.437 3.332 3.224 3.168 17 10.384 7.354 6.156 5.497 5.075 4.779 4.559 4.389 4.254 4.142 4.050 3.971 3.903 3.844 3.793 3.607 3.311 3.206 3.097 3.041 18 10.218 7.215 6.028 5.375 4.956 4.663 4.445 4.276 4.141 4.030 3.938 3.860 3.793 3.734 3.683 3.498 3.201 3.096 2.987 2.931

19 10.073 7.093 5.916 5.268 4.853 4.561 4.345 4.177 4.043 3.933 3.841 3.763 3.696 3.638 3.587 3.402 3.106 3.000 2.891 2.834 20 9.944 6.987 5.818 5.174 4.762 4.472 4.257 4.090 3.956 3.847 3.756 3.678 3.611 3.553 3.502 3.318 3.022 2.916 2.806 2.749 21 9.829 6.891 5.730 5.091 4.681 4.393 4.179 4.013 3.880 3.771 3.680 3.602 3.536 3.478 3.427 3.243 2.947 2.841 2.730 2.673 22 9.727 6.806 5.652 5.017 4.609 4.322 4.109 3.944 3.812 3.703 3.612 3.535 3.469 3.411 3.360 3.176 2.880 2.774 2.663 2.605 23 9.635 6.730 5.582 4.950 4.544 4.259 4.047 3.882 3.750 3.642 3.551 3.474 3.408 3.351 3.300 3.116 2.820 2.713 2.602 2.543 24 9.551 6.661 5.519 4.890 4.486 4.202 3.991 3.826 3.695 3.587 3.497 3.420 3.354 3.296 3.246 3.062 2.765 2.658 2.546 2.488 25 9.475 6.598 5.462 4.835 4.433 4.150 3.939 3.776 3.645 3.537 3.447 3.370 3.304 3.247 3.196 3.013 2.716 2.609 2.496 2.437 26 9.406 6.541 5.409 4.785 4.384 4.103 3.893 3.730 3.599 3.492 3.402 3.325 3.259 3.202 3.151 2.968 2.671 2.563 2.450 2.391

27 9.342 6.489 5.361 4.740 4.340 4.059 3.850 3.687 3.557 3.450 3.360 3.284 3.218 3.161 3.110 2.927 2.630 2.522 2.408 2.348 28 9.284 6.440 5.317 4.698 4.300 4.020 3.811 3.649 3.519 3.412 3.322 3.246 3.180 3.123 3.073 2.890 2.592 2.483 2.369 2.309 29 9.230 6.396 5.276 4.659 4.262 3.983 3.775 3.613 3.483 3.376 3.287 3.211 3.145 3.088 3.038 2.855 2.557 2.448 2.333 2.273 30 9.180 6.355 5.239 4.623 4.228 3.949 3.742 3.580 3.451 3.344 3.255 3.179 3.113 3.056 3.006 2.823 2.524 2.415 2.300 2.239 40 8.828 6.066 4.976 4.374 3.986 3.713 3.509 3.350 3.222 3.117 3.028 2.953 2.888 2.831 2.781 2.598 2.296 2.184 2.064 1.999 50 8.626 5.902 4.826 4.232 3.849 3.579 3.376 3.219 3.092 2.988 2.900 2.825 2.760 2.703 2.653 2.470 2.164 2.050 1.925 1.858 60 8.495 5.795 4.729 4.140 3.760 3.492 3.291 3.134 3.008 2.904 2.817 2.742 2.677 2.620 2.570 2.387 2.079 1.962 1.834 1.764

80 8.335 5.665 4.611 4.028 3.652 3.387 3.188 3.032 2.907 2.803 2.716 2.641 2.577 2.520 2.470 2.286 1.974 1.854 1.720 1.646 100 8.241 5.589 4.542 3.963 3.589 3.325 3.127 2.972 2.847 2.744 2.657 2.583 2.518 2.461 2.411 2.227 1.912 1.790 1.652 1.573 120 8.179 5.539 4.497 3.921 3.548 3.285 3.087 2.933 2.808 2.705 2.618 2.544 2.479 2.423 2.373 2.188 1.871 1.747 1.606 1.524 240 8.027 5.417 4.387 3.816 3.447 3.187 2.991 2.837 2.713 2.610 2.524 2.450 2.385 2.329 2.278 2.093 1.770 1.640 1.488 1.396

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