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378 ExamFormulaSheet

378 ExamFormulaSheet - fame...

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Unformatted text preview: fame ‘1‘”Diéefété'biStrihfitioné : "v' - - Moment- Generating Function . 'uoility‘FunEtion' I Mean '~ iv ” 7"Vari'an'ce np ' mph — p)“ [pe,'+(1— m1" A A I expD-(e' — 1)] Moment- Generating - V Probgbi'lity Function ' Mean ' Variance V Function . ~ ' ' ' 17' V - ' ‘ _ 614622 (62—603 . 'e"’=—e"" ' . -- ’ =-—-—~' <' n Un-‘fQF‘F . v f0) ‘ el—ei’e' 5” ‘6‘ 2‘ I 12 ‘ neg—9|) m>= a u-w .. Ix - cr- ' w 2 . 1 , f ‘ f _ Exponentiai‘ -f();') _=-_Ee‘-‘”J; ,6 > 0 [3" 1‘52 (1 —fir) ' j < y < 00 v ~ ‘ 05/3 0"in _ (1 — I30” ' (v/2)—1'-‘—y/2 ‘ - )‘ e v 2v (1—2r)-"/1_ “.Qi'flpKv/Z ; . ‘ .' "i50int I Standard ‘ ’ Estimator ' Error ' m) ' - /,L i I . I‘ n. u V7.1 i Iii/7' ' x H. ‘ ' [3.4.x ‘ l7. 5 . A ' _ n i I II . *T (73 (73 . . __ _ q '_ -;:I1.|21ndl'12 , Y1 — Y3 'li-i — I12 —I "2 ' . .11.]. I'll . . v pic/l paqn f pl — p; 'nfand 11.3 ' [31 — 13;: p] —./72 + - m _ .. V . _' n, 113'- ai undo2 are the variances of populations 1 and 1., respectively. J. ' ' . I ' . _~ _ 'The two samples are'ussumed to be independent. 0 1 2 »_ 4 . L000 5 6 7 8 Table 1. Binomial Probabilities ' ' I - ' I 2 I ' , . Tabulated values are P(Y _<_ a): p( y). (Computations are rounded at third decimal place.) . i p —._———-—-———'-"—‘—— ' '. i i . a 0.01 0.05 0.10 0.20 0.30. 0.40 0.50 0.60 0.70 0.80 0.90 0.95 0.99 » 0 .951 ".774 - v.590 , .328 ’ -168 .078 .031 ' .010 .002 .000 .000 .000 .000 1 .999 I .977 .919 .737 .528 .337 1.188 .087 .031 .007 m .000 .000 .000 ’ 2 * 1.000 .999 .991 .942 .837 .683 .500 .317 .163 .058 .009 .001 .000. 3 ' 1.000 I 1.000 1.000 .993 ’ .969 .913 .812 .663. .472 .263 .081 .023 .001 4 '4 1.000 1.000 'l.000 1.000 .998 -990 0969 .922 .832 .672 .410 .226 .049 (b)n : 10. , . p ' _ 0.05 0.10 ,.O.20 0.30.. 0.40} 0.50' 0.60 0.70 0.80 10.90 0.99- a a 0.01 . . .904 .599 .349 .107 .028 .006 .001 .000 .000 .000 .000 .000 v .000 .996 .914 ' .7136} .376 .149 .046 .011 .002 1000 1000 .000 .000 .000 ‘ 1.000 .988 ' .9301 .678 .383 .167 .055 .012 .002 * .000 .000 .000 .000 1.000 .999 .987 .879 v .650 I .382 .172 ‘ .055 .011 v ' .001 .000 V .000 .000 _ 1.000 998 .967 .850 .633 » .377 .166 .047 - .006 .000 .000 .000 1.000 1.000 , ' 1.000 1.000 1.000 . .999 .989 ' .945 .828 .618 .350 I .121 .013 .001 . .000 ' 1.000 1.000 ' 1.000 1.000 ' .998 .988 .945 .833 .617 I .322 a .070 .012 .000 1.000 ' 1.000 ' 1.000 1.000 I 1.000 ' 998 .989 .954 1851 2.624 ' .264 .086 .004 1.000 .999 .994 .972' .893 .651 . .401 .096 9 ‘1000 1000 _‘1000 1000 L000 Ulla—O Q 0 1 2 3 . 4 1.000 .994 ._ .953 '.8_34 .623 _‘.367 .150 .033 .002 -.000 .000 '5. 6 7 8 9 .I/\ la..-_Table 1. (Continued) Tables 785 \oooqcxmgmmwo ‘3 34 . ____ - . - p ‘ ' a 0.01 0.05 0.10 0.2 0.30 7 0.40 0.50 0.60 0.70 0.80 0.90 0.95 0.99 '0 _778 .277 .072 .004 .000 .000 g .000 .000 .000 ,.000 .000 .000 .000 1 .974 .642 .271 .027 .002 ' I .000 .000 .000 .000 .000 .000 .000 .000 '2" .998 .873 .537 .098 .009 .000 .000 .000 .000 .000 -.000 .000 1.000 - 3 1.000 . .966 .764 .234 .033 .002 .000 .000 .000 .000 .000 .000 _ .000 g 4 1.000 .993 .902 .421 .090 v.009 .000 .000 .000 .000 .000 ' .000 .000 Z 5 1.000 .999 .967 .617 .193 .029 .002 _ .000 .000 .000 .000 .000 .000 6 1.000 1.000 5991 .780 .341 .074 .007 v .000 .000 .000 .000 .000 .000 _. 7 1.000 1.000 .998 . .891 -.512 ..154 .022 .001 . .000 .000 .000 .000 .000 8 _ 1.000 1.000 1.000 .953 .677 .274 V .054 .004 ‘ .000 .000 .000 .000 .000 9 1.000 1.000 1.000 .983 I .811 ..425 .115 » .013 .000 .000 .000 .000 ' .000 10' 1.000 1.000 1.000 5 .994 .902 .586 .212 .034, ' .002 .000 '.000 .000 000 . 10 11 1.000 1000 ' 1.000 .’ .998 .956 .732 @345 .078 . .006 .000 .000 .000 000. 11 12_ 1.000 - '_1.000 1.000 1.000 v .983 ' .846 .500. .154 .017 .000 , .000 ,.000 .000 12 13 1.000 _ 1.0007 1.000 1.000., .994 .922 .655 .268 .044 .002 .000 .000 I 000 13 0‘ 1.000 1.000 1.000 '1.000_ .998 .966 -.788 . .414 _.O98_ .006 .000 j .000 .000 14 15 1.000 1.000 1.000 1.0003 "1.000 .987 ' .885 .575 .189 '_.017 .000" .000 .000 15 16 1.000 1.000 1.000 1.000. 1.000 V .996 .946 ' .726 - '.323 .047 .000 .000 .000; 16 . 17 1.000 1.000 1.000 ' 1.000} 1.000 7 .999 ’ .978 .846 ' .488 .109 .002 .000 .000 17 18 1.000 1.000 1.000 1.000' 1.000 1.000 .993 .926 .659 .220 .009 .000 , .000 18 '19' 1.000 ‘ 1.000. 1.000 1.000 1.000 1.000 .998 .971' ..807 .383 .033 .001 .000 19 20' 1.000 1.000 1.000 1.000 1.0001 1.000 1.000 .991 .910 .579 .098 _.007 ‘ 000- 20 21 ' 1.000 1.000 1.000 1.000. 1.000 1.000 ' 1.000 .998 .967 .766 .236 .034 000 21 22" -1.000 1.000 1.000 1.000 1.000 1.000. 1.000 1.000 . .991 .902 .463 .127 002 22 23 1.000 ‘ 1.000 1.000 1.000 . 1.000 1.000 1.000 1.000 3 .998 .973 .729 .358 026 23 1.000 . 1.000 1.000 1.000 1.000 1.000 I 1.000 .723 222 24 24', L000 1 .000 .996 .928 .vf‘: 1‘ ‘1 ' _ 1 \_/ ‘\/' 786 Appendix Three Table 2. Table of e‘x 'x e"‘ x I e—x x e_x x e“ I 0.00 > 1.000000 2.60 .074274 . 5.10 .006097 7.60 .000501 . 0.10 .904837 2.70 .067206 5.20 005517- 7.70 .000453 0.20 .818731 2.80 .060810 5.30 .004992 . , 7.80 .000410 ' . 0.30 _ .740818 2.90 055023 5.40 004517. . 7.90' 000371 0.40 - . .670320 3.00 049787 5.50 004087 8.00 - 000336 0.50 .606531 ; 3.10 045049 . 5.60 003698 I 8.10 0003041 0.60 , .548812' 3.20 040762. 5.70 ‘ 003346 8.20 v 000275 0.70 .496585' 3.30 036883 - 5.80 003028 8.30 000249 0.80 _ .449329 3.40 f 033373 5.90 ' ' .002739. 8.40 . 000225 0.90 3406570 3.50 » 030197 6.00 .002479 4 8.50 000204 1.00 .367879 3.60 - 027324 6.10 .002243 8.60 000184 1.10 .332871 3.70 ‘ " 024724 6.20 002029 - 8.70 000167 1.20. .301194 0 3.80 .022371 6.30 001836 _ 8.80» .000151 1.30 v .272532 ‘ 3.90 020242 6.40 001661 .V 8.90 .000136= . 1.40 ' .246597 . 4.00. 018316 6.50 001503 . 9.00 000123 1.50 .223130 , 4.10 ._ 016573 6.60 001360 9.10 ' 000112 16.0 - V .201897 4.20 .014996 6.70 ' 001231 9.20 V 000101 1.70 1.182684. 44.30,. - .013569 6.80 001114 . 9.30 000091 ~ 1.80 .165299 4.40 012277 0 6.90 001008 9.40 000083 - 1.90 ‘ .149569 4.50 ‘ 011109 7.00 000912 9.50 000075 _' » - 2.00 ' ' .135335 ‘ 4.60 - 010052 _ 7.10 .000825 9.60 000068 - 2.10 .122456 4.70. , 009095 7.20 000747 9.70 000061 2.20' _.110803 4.80 008230 1 7.30- 000676 9.80 . 000056 . 2.30 ,.100259 ' 4.90 007447 .740 000611 . 9.90 000050“ 2.40 090718‘ 5.00 ".006738 7.50' 000553 10.00 000045] 2.50, 082085 . ' Table 3. Poisson Probabilities 0.980 0.961 0.942 0.923 _ 0.905 0.861 0.819 0.779 10.741 0.705 0.670 0.638 ‘ _ 0.607 I I 0.577 - 0.549 0.522 -' ‘ 0.497 0.472- ’ 0.449 _ 0.427 . " 0.407 0.387 r 0.368 » 0.333 0.301 0.273 , 0.247 0.223 0.202 0.183 0.165 0.150 0.135 1.000 0.999 0.998 ' 0.997 0.995 0.990 0.982 0.974 0.963 0.951 0.938 0.925 0.910 0.894 ' 0.878 - 0.861 . 0.844 0.827 0.809 0.791 4 0.772 0.754 0.736 0.699 ' 0.663 0.627 0.592 - 0.558 0.525 0.493 0.463 0.434 0.406 1.000 1.000 1.000 1.000 0.999 0.999 0.998 ' 0.996 0.994 0.992 0.989 0.986 0.982 0.977 0.972 0.966 0.959 0.953, " 0.945 0.937 0.929 0.920 . 0.900 0.879 0.857 0.833 0.809 0.783 ' 0.757 0.731 0.704 0.677 1.000 1.000 1.000 1.000 1 .000 0.999 ' 0.999 0.998 , 0.988 0.997 0.996 0.994 0.993 0.991 , 0.989 0.987 0.981 0.981 0.974 0.966 - 0.957 0.946 0.934 ' 0.921 0.907 0.891 0.875 0.857 1.000 1.000 v 1.000 1.000 1.000 0.999 0.999 - I 0.999 - 0.999 - 0.99s ' 0.998 , 0.997. 0.996 0.995 0.992 0.989 0.986 0.981 0.976 0.970 0.964 0.956 0.947' 1.000 f 1.000 1.000 1.000 1.000 ' . 1.000 1.000 0.999 0.999 _ 0.998 0.998 0.997 0.996 0.994 0.992 - 0.990 I 0.987 0.983 .1 .000 1.000 1.000 1.000 0.999 0.999 I 0.999 0.998 0.997 0.997 0.995 Tables 787 1.000 1.000 1.000 1.000 0.999 0.999 0.999 1.000 ' 1.000 1.000 788 Appendix Three ' a ‘ 5.8 Table 3.. (Continued) 3 6 1.000 ‘ -' 0.999 ' > 3.2“ 71 0 ' 1 2 4 5 7 8 9 2.2 0.111 0.355 0.623 0.819 0.928 0.975 0.993 0.998 1.000 2.4 0.091 0.308 0.570 0.779 0.904 0.964 0.988 0.997 0.999 2.6 0.074 0.267 0.518 0.736 0.877 0.951 0.983 0.995 0.999 1000. 2.8' 0.06]_ 0.231 0.469 0.6920848 0.935 0.976 0.992 0.998 3.0 0.050 0.199 0,423 0.647 0.815 0.916 0.966 0.988 0.996 0.999' 3.2 0.041 0.171 0.380 0.603 0.781 0.895 0.955 0.983 0.994 0.998 ' 3.4 0.033 0,147 0.340 0.558 0.744 0.871 0.942 0.977 0.992 0.997. 3.6 0.027 0.126 0.303 0.515 0.706 0.844 0.927 0.969 0.988 0.996 3.8 0.022 0.107 0.269 0.473 0.668 0.816 0.909 0.960 0.984 0.994 4.0 0.018 0.092 0.238 0.433 0.629 0.785 0.889 0.949 0.979' 0.992 4.2 ' 0.015‘ 0.078 0.210 0.395 0.590 0.753 0.867 0.936 0.972 0.989. ' 4.4 0.012 0.066 0.185 0.359 0.5510720 0.844 0.921 0.964 0.985 4.6 0.010 0.056 0.163 0.326 0.513 0.686 0.818 0.905 0.955 0.980 4.8 0.008 0.048 0.143 0.294 0476 0.651 0.791 0.887 0.944 0.975 . 5.0 0.007 0.040 0.125 " 0.265 0.440 0.616 0.762 0.867 0.932 0.968.. 5.2 . 0.006 0.034 0.109 0.238 0.406 0.581 0.732- 0.845 0.918- 0.960 5.4 ' 0.005 0.029 0.095 0.213 0.373 0.546 0.702 0.822 0.903 0.951 . 5.6 0.004 0.024 0.082 0.191 0.342 0.512 0.670. 0.797 0.886 0.941- 0003; 0.0210072 0.170 0.313 0.478 0.638 0.771 0.867 0.929 . 6.0 0.002 0.017 0.062 0.151 0.285 0.446 0.606 0.744 0.847. 0.916.‘ _ 10 11 12 .13 14 15 :- 16 28' 1.000 3.0 1.000 1.000 3.4 - 0.999 .1000. ' 3.6 0.999 1.000 . 3.8 - 0.998; 0.999 1.000 4.0 0.997 0.999 1.000 ' 472' 0.996 0.999 1.000 4.4 0.994 0.998 0.999 1.000 ' 4.6 - 0.992 0.997 0.999 1.000 4.8 0.990 0.996 0.999 1.000 5.0 0.986 0.995 0.998 0.999 1.000 5.2 0.982 "0.993 0.997 0.999 1.000 5.4 . 0.977 0.990 0.996 0.999 1.000 - 5.6 0.972. 0.988. 0.995 0.998. 0.999 1.000 5.8 0.965 0.984 0.993 0.997 0.999 1.000 6.0 0.957 0.980 0.991 0.996 0.999 0.999 1.000 w_______________________________________.,— ‘\ / v Table 4. Normal cu'rve areas 792 Appendix Three Standard normal probability in right-hand tail (for negative values of 2 areas are found by symmetry) , Second decimal place‘of z z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 V 0.0 .5000 .4960 .4920 .4880 .4840. .4801 .4761 .4721 .4681 .4641 0.1 .4602 .4562 .4522 .4483 .4443 .4404 .4364 .4325 .4286 .4247 0.2 .4207 .4168 .4129 .4090 .4052 ..4013 .3974 ' .3936 .3897 .3859 0.3 .3821 .3783 .3745 - .3707 .3669 .3632 .3594 .3557 , .3520 .3483 0.4 .3446 . .3409 .3372 .3336 .3300 .3264 ' .3228 “.3192 .3156 .3121 0.5 .3085 .3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 V .2776 0.6 .2743 .2709 .2676 ‘ .2643 .2611 .2578 .2546 . .2514 .2483 .2451 0.7 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177‘ _ .2148 0.8 .2119 .2090 .2061 .2033. .2005 .1977 .1949 .1922 .1894 .1867‘ 0.9 .1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611 1.0 .1587 1.1562 .1539 .1515 .1492 .1469 .1446 .1423 .1401 .1379. 1.1 .1357 .1335 .1314 .1292 .1271~.1251 .1230 .1210 .1190 .1170’ 1.2 .1151 @1131 .1112 .1093 .1075".1056 .1038 .1020 .1003__.0985 1.3 .0968 ' .0951 .0934' .0918 . .0901 .0885 .0869 _.0853 .0838 _.0823 1.4 .0808 .0793 .0778 20764 .0749 .0735 .0722' .0708 .0694 - .0681- 1.5’ .0668 .0655 .0643 .0630 .0618 .0606 - .0594 10582 “1.0571 .0559' 1.6 .0548 .0537 .0526 .0516, .0505 .0495 .0485 .0475 .0465 .0455. 1.7 .0446 .0436 1.0427 .0418 .0409 .0401 .0392 .0384 '.0375 .0367 1.8 .0359 .0352 .0344' .0336 .0329 .0322 .0314 21.0307 .0301 .0294 " 1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244} .0239 .0233 2.0 .0228. .0222, _.0217 .0212 .0207 .0202” .0197 .0192 .0188‘7 .0183 2.1 .0179 .0174 _.0170 .0166 .0162 .0153 .0154' .0150 .0146 1.0143 .2.2 .0139 .0136 ‘.0132 .0129. .0125 .0122 .0119, .0116 .0113 .0110 2.3 .0107 .0104 '.0102 .0099 0096,0094 .0091 .0089 .0087 .0084 2.4 .0082 v.0080 .0078 .0075 .0073 1.0071 .0069. .0068' .0066 .0064 23 ' .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048 2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 .0037 .0036 2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .0026 2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 I .0019 2.9 ..0019 .0018 .0017 .0017 .0016 .0016 .0015": .0015 ’.0014 .0014 3.0 .00135 .1 3.5 .000233 40. 0000317 4.5 .000 003 40 5.0 .000 000 287 ____________________________—_.__—————————-— From R. E. Walpole. Introduction to Statistics (New York: Macmillan. 1968). ii 2‘; .4' 1' . s f3 1 v2 . k' '1 ., , 1 4! ' Table 5. Percentage points of the tdistributions (a 21 .4681 .4641 8—- N 25 .4286 .4247 MW '36 .3897 .3859 3.078 6.314 12.706 31.821 63.657 1 .:57 .3520 .3483 1.886 2.920 4.303 6.965 9.925 2 ‘92 .3156 .3121 1.638 2.353 3.182 I 4.541 5.841 1 3 1.533 1 2.132 2.776' - 3.747 4.604 4 :43 .2810 .2776 I ‘ 114 .2483 ,2451 1.476 2.015 2.571 3.365 V 4.0323 5 - :06 .2177 .2148 1.440 1.943 2.447 . 3.143 3.707 6 122 .1894 .1867 1.415 . 1.895 2.365" 2.998 3.499 7 160 .1635 .1611 1.397 1.860 2.306 ’ 2.896 3.355 8 . '. 1.383 1.833 2.262 2.821 . 3.250 9 123 .1401 .1379 . 1 110 .1190 .1170 1.372 1.812 2.228 2.764 3.169 10 1 120 .1003 .0985 V 1.363 1.796 2.201 2.718 3.106 11 153(’”“838 .0823, 1.356 1.782 ' 2.179 2.681 3.055 ' ’08 9694- .0681 1.350 1.771 2.160 2.650 3.012 13 _ . 1.345 , 1.761 2.145 ’ 2.624 . 2.977 ' 14 ’82 '0571 9559 1.341 1.753 2.131 - 2.602 r 2.947 15 175 .0465 .0455 . _ 184 .0375 ~.0367 1.337 1.746 2.120 2.583 2.921 16 107 .0301 .0294 .1333 , 1.740 2.110 2.567- .‘ 2.898 17 244 .0239. .0233 1.330 1.734 2.101 2.552 2.878 18 , 1.328 1.729 2.093 ' 2.539 2.861 192 *0188 10183 1.325 . 1.725 2.086 - 2.528 2.845 20 150 .0146 .0143 - , v _ 116. , .0113 .0110 " 1.323 ' 1.721 2.080 . 2.518 _ 2.831 21 «)89 .0087 .0084 .' _. 1.321 1.717, 2.074 .v 2.508. ' 2.819 22. )68 .0066 p.0064 ' 1.319 1.714 2.069 2.500 _ 2.807 .23 . r " - 1.711 - .2.064 ' 2.492 2.797 24 351 0°49 0°48 ’ .316 1.708 2.060 2.485 ' 2.787 25 )38 ' .0037 .0036 . . )28 3.0027 .0026 1.315 . 1.706 ..2.056 2.479 _ 2.779- 26' 321 .0020 .0019 1.314 1.703 2.052 2.473 2.771 ' 27 315 .0014 .0014 1.313 1.701 2.048 2.467 2.763 . 28 “ ’ 1.311 1.699 2.045 2.462 2.756 , 29 1.282 1.645 _ 1.960 2.326 2.576" inf. From “Table of Percentage Points of 1he t-Distribufion." Computed by Max- ine Merrington, Biometrika, Vol. 32 (1941), p. 300. Reproduced by per— mission of Professor E. S.' Pearson.. " . ‘ 7—! \O . L 1 1 \ , \J‘ ‘ J. 794 Appendix Three Table 6. Percentage points of the x2 distributions d-f X3995 X3990 X3975 X3950 X3900 1 0.0000393 0.0001571 0.0009821 0.0039321 0.0157908 ,2 0.0100251 0.0201007 ' 0.0506356 0.102587 0.210720 3 0.0717212 0.114832 0.215795 ' 0.351846 0.584375 '4 0.206990 0.297110 , 0.484419 0.710721 1.063623 5 0.411740 0.554300 .. 0.831211 1.145476 1.61031. 6 0.675727 0.872085 . 1.237347 1.63539 2.20413 7 0.989265 1.239043 1.68987 2.16735 - 2.83311 8 1.344419 1.646482 2.17973 . 2.73264. 3.48954 9 1.734926 2.087912 . 2.70039 ' 3.32511, 4.16816’ 10 2.15585 2.55821 3.24697 - 3.94030» 4.86518 11 2.60321 v 3.05347 ' 3.81575 4.57481 5.57779 12» 3.07382 3.57056 4.40379 5.22603 6.30380 13 3.56503 4.10691 5.00874 5.89186 7.04150 14 4.07468 4.66043 5.62872 6.57063 - 7.78953 15 3 4.60094 . 5.22935 ' 6.26214 7.26094 8.54675 16 5.14224 5.81221 6.90766 7.96164 9.31223 . 17 5.69724 6.40776 7.56418 ‘ 8.67176 10.0852 ' 18 6.26481 7.01491 _ 8.23075 9.39046 10.8649 19 . ‘ 6.84398 7.63273 8.90655 10.1170 g 11.6509 20 - 7.43386 1 8.26040 9.59083 10.8508 _' 12.4426 21 8.03366 ’ 8.89720 10.28293 11.5913 ' 13.2396 22- 8.64272 9.54249 10.9823 12.3380 14.0415 23 9.26042 10.19567 11.6885 13.0905 ' 14.8479 24' “ 9.88623 $108564 12.4011 13.8484 - > 25 10.5197 11.5240 .4 13.1197 14.6114 16.4734 " 26 ' 11.1603 -12.1981 13.8439 15.3791 . 17.2919 27 11.8076 12.8786 14.5733 16.1513 18.1138 28 1 12.4613 13.5648 15.3079. 16.9279 18.9392 29 4 413.1211 ' 14.2565 16.0471 17.7083 19.7677 30 .- 13.7867 14.9535 16.7908 , 18.4926 20.5992 40 . . 20.7065 22.1643 . 24.4331». 26.5093 29.0505 '50 ‘ [27.9907 29.7067 ’ 32.3574 34.7642 37.6886 60 . 35.5346 37.4848 - 40.4817 . 43.1879 46.4589 .70 43.2752 45.4418 48.7576 ' _ 51.7393 55.3290 80 51.1720 53.5400 57.1532 60.3915 64.2778 90 59.1963' 61.7541 65.6466 - 69.1260 73.2912 100 67.3276 70.0648 74.2219 - 77.9295 82.3581 ,‘4;.-.:7«.:.»~1 gum-«M (Liza-1: €148”... 1r: u:/_-.-.4un-m\a'.; JLTM'Ai—M “1.4.16.5. #:ra‘axh'uuflian‘ 4419514441.. 2:: i .13 i .3 ii '3 5.lL'kimlait-xfl‘léikfiiuin 1. 1‘. I . . «1 3 1 ‘3" .1 i i 1 i a 1' i d i 3 5 § 3 :3 i i i 3 1 3 1’ J i E i ( 7 Tables 795 Table 6. (Continued) 2 2 2 2 2 X0100 X0050 X0025 X0010 X0005 “- 2.70554 3.84146 V 5.02389 2 6.63490 7.87944 ' . 1 4.60517 5.99147 7.37776 9.21034 10.5966 2 6.25139 7.81473 9.34840 11.3449 12.8381 3 . 7.77944 9.48773 11.1433 13.2767 14.8602 _4 X3900 9.23635 11.0705 1 12.8325 ‘ 15.0863 v 16.7496 5 _’—1 . I 0"0'1'57“9_'08' 10.6446 12.5916. ’ 14.4494 ' -_16.8119 18.5476 _ '6 . ' - 0.210720 12.0170 14.0671 16.0128 18.4753 20.2777 .7 ; 0584375 13.3616 15.5073 17.5346 ' 20.0902 21.9550 8 _ ' 1.063623 14.6837 16.9190 19.0228 , 21.6660 23.5893. 9 ; 1.61031 15.9871 _ . 18.3070 20.4831 23.2093 25.1882 10 220413 17.2750 19.6751 21.9200 _ 24.7250 26.7569 11 ’ 2.83311 - 18.5494 - _ 21.0261 23.3367 26.2170 28.2995 12 3.48954 19.8119 22.3621 , 24.7356 27.6883 29.8194 13 _ 4.16816 21.0642 ‘ 23.6848 26.1190 1 29.1413 31.3193 14 _ .4 436518 22.3072" 24.9958 "' 27.4884 30.5779 32.8013 ' 15 ' 3 5.57779; 23.5418 26.2962 - 28.8454 . ' 31.9999 ' 34.2672 I 16 630330 24.7690 ~ ' 27.5871 - 30.1910 33.4087 ' 35.7185- . 17 ' 704150 . 25.9894 28.8693 31.5264 34.8053 , 37.1564 18 ' 7.78953 27.2036 ' 30.1435 32.8523 , ‘ 36.1908 38.5822- 149 ' 8.54675 28.4120 - 31.4104 34.1696 37.5662 f ' 39.9968 20 931223 29.6151 32.6705 35.4789 1. - 38.9321 41.4010 . 21 10.0852 30.8133 33.9244 36.7807 40.2894 42.7956 . 22 108649 32969 V 35.1725 - 38.0757 41.6384 44.1813 7 '23 116509 @1963) v 36.4151 39.3641 42.9798 ' 45.5585 .24 12.4426 34.3816 37.6525 40.6465 ' ‘ 44.3141 46.9278 25 ' 132396 . ' 35.5631 38.8852 41.9232 45.6417 ' 48.2899 ' 26 14.0415 36.7412 . ~_ 40.1133 43.1944 46.9630 - _ . 49.6449 27 14.8479. 37.9159. 41.3372 44.4607 48.2782 . 50.9933. 28 15.6587 39.0875 3 42.5569 45.7222 . 49.5879 . 52.3356 ‘ 29 164734; 40.2560 43.7729 46.9792 50.8922 ' 53.6720 30 17.2919 51.8050 55.7585 ' 59.3417 . 63.6907 ‘ 66.7659 40' 18.1138 63.1671 ‘ 67.5048 71.4202 _. 76.1539 79.4900 50 ' . 18.9392 74.3970 ' 79.0819 83.2976 88.3794 91.9517 60 19-7577 85.5271 90.5312 ’ 95.0231 100.425 , 104.215 70 ‘ - 20.5992 96.5782 ' 101.879 106.629 V 112.329 116.321 '80 . 29.0505 107.565 113.145 118.136 124.116 128.299 ' 9o 1 37.6886 118.498 124.342 129.561 _ 135.807 140.169 , 100 46.4589 From “Tables of the Percentage Points of the xz-Distribution.” Biometrika, V01. 32 (1941). pp. 188—189. 55 3290 by Catherine M. Thompson. Reproduced by permission of Professor E. S. Pearson. ( --\ 64.2778 1L; 73.2912 82.3581 796 Appendix Three Tablé 7. Percentage points of the F distributions Denominator d.f. Numerat-or d.f. 6 . '9.16 4 5 7 8 9 55.83 ‘ 57.24 58.20 I 58.91 ' 59.44 59.86 224.6 230.2 234.0 236.8 238.9 240.5 899.6 921.8 937.1 948.2 956.7 . 963.3 .. 5625 5764 5859 5928 5982 6022 22500 23056 23437 23715 23925 24091 9.24 9.29 9.33 . 9.35 9.37 . 9.38" 19.25 ' 19.30 19.33 19.35 19.37 19.38 39.25 39.30 ‘ 39.33 39.36 39.37 39.39 99.25 99.30 99.33 99.36 99.37 99.39 199.2 199.3. 199.3 199.4 199.4 199.4 , 5.34. _ 5.31" 5.28 5.27 5.25 5.24 9.12 9.01 - 8.94 8.89' 8.85 8.81 15.10 14.88 ' 14.73 14.62 114.54 14.47. 28.71. 28.24 27.91 27.67 27.49 . 27.35 _, 46.19 45.39 44.84 44.43 44.13 ' 43.88.. 4.11 4.05 4.01 ’ 3.98 3.95 3.94 6.39 6.26 6.16 6.09 6.04 _ 6.00 9.60 9.36 _ 9.20 9.07. 8.98 8.90 15.98 15.52 15.21 . 14.98 14.80 14166" 23.15 22.46 21.97 21.62 21.35 21.14 . 3.52 3.45 3.40 ' 3.37 3.34 3.32 , 5.19 5.05‘ 4.95 4.88. 4.82 ~ 4.77 7.39 7.15' 6.98 ' 6.85 9 6.76 6.68 11.39 10.97 10.67- 10.46 10.29 10.16 15.56.’ 14.94 14.51 14.20 13.96 13.77 " 3.18 3.11 3.05 - 3.01 2.98 2.96 4.53 . 4.39 . 4.28 » 4.21 4.15 4.10 6.23 5.99 5.82 5.70 5.60 ' 5.52 9.15 8.75 _' 8.47 8.26 8.10 7.98 12.03 11.46 11.07 10.79 10.57 10:39 V 2.96 2.88 2.83 2.78 2.75 2.72 4.12 3.97 3.87 3.79 3.73 3.68 5.52 5.29 . 5.12, 4.99 4.90 4.82 7.85 7.46 7.19 6.99 6.84 6.72 - 10.05 9.52 _ 8.89 8.68 8.51 Table 7. (Continu 10 12 60.19 60. 241.9 243. 968.6 976. 6056 6106 24224 24426 9.39 9, 19.40 19.. 39.40 39.. 99.40 99.1 199.4 199.4. 5.23 5.: 8.79 3,: 14.42 14.: 27.23 ‘ 27....
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