378 ExamFormulaSheet

378 ExamFormulaSheet - fame...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
This is the end of the preview. Sign up to access the rest of the document.

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.(. 43.69 43.: . 3.92 3.9 . 5.96 5.9 8.84 8.7 ' 14.55 14.3 20.97 20.7 3.30 3.2‘ 4.74 . 4.6 6.62 6.5 10.05 9.8 - 13.62 13.3. 2.94 2.91 4.06 4.01 5.46 ' 5.3' 7.87 7.7: 10.25 10.0: 2.70 2.6: 3.64 3.5'. 4.76 ' 4.67 6.62 » 6.47 8.38 8.18 8 9 5944 .5986 2389 2405 9567 ‘ 9633 5982 _ 6022 23925 -24091 937 938 1937 1938 3937 3939 '9937 9939 1994 1994‘ ‘ 1 3 524 885 881 I 1454 1447 . 2749, . 2735 - 4413 - 4388 - 395 394 . .604 600 _ 898 890 1430 1466 2135 2114 334.- 332 _432 477 676 668 1029 .1016 1396 1377 :298 5296 . 415 410 ., 560 552 - 810 798 .1057 1039 ~ 275' 272 373 _ 368 490 , 482 684 672 851 868 IK\./4 Tablé _7. (Continued) 6019 .' 2419 ’ 9686 6056 * 24224 9.39 11940. 3940 _9940' . 1994 523' 879 1442- 2723 43.691 392 5.96 ‘ 834 1455_. 2097 '330 ‘474 I 662 1005 1362 V294 406 '546 _’737 1025 270 364 476 662 838 6971 2439 , 9767 6106 yum, 941 1941 3941‘ 9942 1994 522'- “874 r '1434 - 2705 4339 390 591 875 1437‘ '2070 327 4:68 652 V939 .1338 290 400 537. r 772 1003 267 357' 467 647 818 6L22 2459 ‘9849 6157 .24630 . 942 1943 39434 9943 1994 520 870 1425' 2637 4308 '337 536 866 1420 2044 324‘ . 462 643 972 1315 237 394 527 256 '931 ‘263' 351 457 631 797 6L74 2480 ' 9931 6209 24836 944 ‘1945 3945 9945 1994 » 518 866 1417. 2669 4278 334 "530 -856 1402 2017 321‘ . 456 633‘ 955 1290 ‘234 337 517 740 959 259 I 344 447 616 775 6200 2491 9922 6235’ ‘24940 '945 1945 3946 9946 1995 518 864 1412 2660 4262 333 577' 851 1393 2003 319 453 628 947 >1278 _' 232 334 512 .731 947 ’ 258 341 442 607 765 6226 2501 1001‘ 6261 25044 946 1945 3946 9947 1995 » 517 862' 1408 2650 4247 332 '575 M 846 1334 1989* 317 450 0-623 938 1266 280_ 331 507 723 936 256 338- 436' 599 753 6253 25L1 1006 6287 25148 947 1947 3947 9947 1995 516 859 1404 2641 4231 380 572 841 1375 1975 V316 446 618 929 1253 278 377 501 714 924 254 334 431 591 ‘742 6279 2522 1010 6313 25253 I ‘947 1948 3948 . 9948 .1995 515 857 1399 2632 4215 - 379 ’ 569 836. . 1365 1961. 314 443 612 920 1240 276 374 496 706 -912 251 330 425 532 231 6306 2533 1014 6339 . 25359’ 948 1949 3949 9949 1995- 514 855 1395 2622 4L99 378 566 831 1356 1947 312 440 607 _ 911 1227 274 370 '490 697 900 249 327 420 574 719 Tébks 797 6333 '2543 1018 6366 25465 949 1950 3950 9950 1995 513 853 1390 2613 4133 376 563 “.826 1346 ,1932 » 310 436 602 902 1214 272 367 435 638 838 247 323 .414 565 708 100 050 025 .010 005 100 050 025 010 005 100 .050 025 010 005 100 050 025 010 005 100 050 025 010 005 100 050 025 010 005 .100 050 025 010 005_ ...
View Full Document

This note was uploaded on 04/07/2011 for the course ECON 378 taught by Professor Staff during the Spring '08 term at BYU.

Page1 / 12

378 ExamFormulaSheet - fame...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online