TABLAS

ESTADÍSTICAS.

ESTADÍSTICA II 28.

Tabla 8 Test de Kolmogorov-Smirnov sobre Bondad de Ajuste

Nivel de significación α

n 0.20 0.10 0.05 0.02 0.01 0.005 0.002 0.001

1 0.90000 0.95000 0.97500 0.99000 0.99500 0.99750 0.99900 0.99950 2 0.68337 0.77639 0.84189 0.90000 0.92929 0.95000 0.96838 0.97764 3 0.56481 0.63604 0.70760 0.7 8456 0.82900 0.86428 0.90000 0.92065 4 0.49265 0.56522 0.62394 0.68887 0.73424 0.77639 0.82217 0.85047 5 0.44698 0.50945 0.56328 0.62718 0.66853 0.70543 0.75000 0.78137

6 0.41037 0.46799 0.51926 0.5774 1 0.61661 0.65287 0.69571 0.72479 7 0.38148 0.43607 0.48342 0.53844 0.57581 0.60975 0.65071 0.67930 8 0.35831 0.40962 0.45427 0.50654 0.54179 0.57429 0.61368 0.64098

9 0.33910 0.38746 0.43001 0.47960 0.51332 0.54443 0.58210 0.60846 10 0.32260 0.36866 0.40925 0.45562 0.48893 0.51872 0.55500 0.58042

11 0.30829 0.35242 0.39122 0.43670 0.46770 0.49539 0.53135 0-55588

12 0.29577 0.33815 0.37543 0.41918 0.44905 0.47672 0.51047 0.53422 13 0.28470 0.32549 0.36143 0.40362 0.43247 0.45921 0.49189 0.51490

14 0.27481 0.31417 0.34890 0.38970 0.41762 0.44352 0.47520 0.49753 15 0.26589 0.30397 0.33750 0.37713 0.40420 0.42934 0.45611 0.48182

16 0.25778 0.29472 0.32733 0.36571 0.39201 0.41644 0.44637 0.46750

17 0.25039 0.28627 0.31796 0.35528 0.38086 0.40464 0.43380 0.45540 18 0.24360 0.27851 0.30936 0.34569 0.37062 0.39380 0.42224 0.44234 19 0.23735 0.27136 0..30143 0.33685 0.36117 0.38379 0.41156 0.43119 20 0.23156 0.26473 0.29408 0.32866 0.35241 0.37451 0.40165 0.42085

21 0.22517 0.25858 0.28724 0.32104 0.34426 0.36588 0.39243 0.41122

22 0.221I5 0.25283 0.28087 0.31394 0.33666 0.35782 0.38382 0.40223 23 0.21646 0.24746 0.2749tl 0.30728 0.32954 0.35027 0.37575 0.39380 24 0.21205 0.24242 0.26931 0.30104 0.32286 0.34318 0.36787 0.38588

25 0.20790 0.23768 0.26404 0.29518 0.31657 0.33651 0.36104 0.37743

26 0.20399 0.23320 0.25908 0.28962 0.30963 0.33022 0.35431 0.37139

27 0.20030 0.22898 0.25438 0.28438 0.30502 0.32425 0.34794 0.36473 28 0.19680 0.22497 0.24993 0.27942 0.29971 0.31862 0.34190 0.35842 29 0.19348 0.22117 0.24571 0.27471 0.29466 0.31327 0.33617 0.35242 30 0.19032 0.21756 0.24170 0.27023 0.28986 0.30818 0.33072 0.34672

31 0.18732 0.21412 0.23788 0.26596 0.28529 0.30333 0.32553 0.34129

32 0.18445 0.21085 0.23424 0.26189 0.28094 0.29870 0.32058 0.33611

33 0.18171 0.20771 0.23076 0.25801 0.27577 0.29428 0.31584 0.33115 34 0.17909 0.21472 0.22743 0.25429 0.27271 0.29005 0.31131 0.32641 35 0.17659 0.20185 0.22425 0.25073 0.26897 0.28600 0.30597 0.32187 36 0.17418 0.19910 0.22119 0.24732 0.26532 0.28211 0.30281 0.31751

37 0.17188 0.19646 0.21826 0.24404 0.26180 0.27838 0.29882 0.31333 38 0.16966 0.19392 0.21544 0.24089 0.25843 0.27483 0.29498 0.30931

39 0.16753 0.19148 0.21273 0.23785 0.25518 0.27135 0.29125 0.30544

29 TABLAS ESTADÍSTICAS.

Nivel de significación α n 0.20 0.10 0.05 0.02 0.01 0.005 0.002 0.001

40 0.16547 0.18913 0.21012 0.23494 0.25205 0.26803 0.28772 0.30171 41 0.16349 0.18687 0.20760 0.23213 0.24904 0.26482 0.28429 0.29811

42 0.16158 0.18468 0.20517 0.22941 0.24613 0.26173 0.28097 0.29465 43 0.15974 0.18257 0.20283 0.22679 0.24332 0.25875 0.27778 0.29130 44 0.15795 0.18051 0.20056 0.22426 0.24060 0.25587 0.27468 0.28806 45 0.15623 0.17856 0.19837 0.22181 0.23798 0.25308 0.27169 0.28493

46 0.15457 0.17665 0.19625 0.21944 0.23544 0.25038 0.26880 0.28190

47 0.15295 0.17481 0.19420 0.21715 0.23298 0.24776 0.26600 0.27896 48 0.15139 0.17301 0.19221 0.21493 0.23059 0.24523 0.26328 0.27611 49 0.14987 0.17128 0.19028 0.21281 0.22832 0.24281 0.26069 0.27339 50 0.14840 0.16959 0.18841 0.21068 0.22604 0.24039 0.25809 0.27067

n > 50

n

07.1

n22.1

n36.1

n52.1

n63.1

n73.1

n85.1

n95.1

ESTADÍSTICA II 30.

Tabla 9 Corrección de Lilliefors para Normalidad

Nivel de significación α

n 0.20 0.15 0.10 0.05 0.01

4 0.300 0.319 0.352 0.381 0.417 5 0.285 0.299 0.315 0.337 0.405 6 0.265 0.277 0.294 0.319 0.364

7 0.247 0.258 0.276 0.300 0.348 8 0.233 0.244 0.261 0.285 0.331 9 0.223 0.233 0.249 0.271 0.311

10 0.215 0.224 0.239 0.258 0.294 11 0.206 0.217 0.230 0.249 0.284

12 0.199 0.212 0.223 0.242 0.275 13 0.190 0.202 0.214 0.234 0.268 14 0.183 0.194 0.207 0.227 0.261 15 0.177 0.187 0.201 0.220 0.257

16 0.173 0.182 0.195 0.213 0.250 17 0.169 0.177 0.189 0.206 0.245 18 0.166 0.173 0.184 0.200 0.239

19 0.163 0.169 0.179 0.195 0.235 20 0.160 0.166 0.174 0.190 0.231 21 0.157 0.162 0.170 0.186 0.226 22 0.154 0.158 0.167 0.182 0.220 23 0.150 0.154 0.164 0.179 0.213

24 0.146 0.151 0.161 0.176 0.207 25 0.142 0.147 0.158 0.173 0.200 26 0.139 0.14S 0.155 0.171 0.197 27 0.137 0.143 0.153 0.168 0.194 28 0.135 0.140 0.150 0.166 0.192 29 0.133 0.138 0.147 0.163 0.190

30 0.131 0.136 0.144 0.161 0.187

n > 30

n736.0

n768.0

n805.0

n886.0

n031.1

31 TABLAS ESTADÍSTICAS.

Tabla 10 Prueba de homogeneidad de varianzas de Cochran

α = 0.05

n

k 2 3 4 5 6 7 8 9 10 11 17 37 145 1000

2 0.998 0.975 0.939 0.905 0.877 0.853 0.833 0.815 0.801 0.788 0.734 0.660 0.581 0.500 3 0.966 0.870 0.797 0.745 0.707 0.677 0.653 0.633 0.616 0.602 0.546 0.474 0.403 0.333 4 0.906 0.767 0.684 0.628 0.589 0.559 0.536 0.517 0.501 0.488 0.436 0.372 0.309 0.250 5 0.841 0.683 0.598 0.544 0.506 0.478 0.456 0.438 0.424 0.411 0.364 0.306 0.251 0.200 6 0.780 0.616 0.532 0.480 0.444 0.418 0.398 0.381 0.368 0.336 0.313 0.261 0.211 0.166 7 0.727 0.561 0.480 0.430 0.397 0.372 0.353 0.338 0.352 0.315 0.275 0.227 0.183 0.142

8 0.679 0.515 0.437 0.391 0.350 0.336 0.318 0.304 0.292 0.282 0.246 0.202 0.161 0.125 9 0.638 0.477 0.402 0.358 0.328 0.306 0.290 0.276 0.265 0.256 0.222 0.182 0.144 0.111

10 0.602 0.445 0.373 0.331 0.302 0.282 0.266 0.254 0.243 0.735 0.203 0.165 0.130 0.100

α = 0.01

n

k 2 3 4 5 6 7 8 9 10 11 17 37 145 1000

2 0.999 0.995 0.979 0.958 0.937 0.917 0.898 0.882 0.867 0.853 0.794 0.706 0.606 0.500 3 0.993 0.942 0.883 0.831 0.793 0.760 0.733 0.710 0.691 0.674 0.605 0.515 0.423 0.333 4 0.967 0.864 0.781 0.711 0.676 0.641 0.612 0.589 0.570 0.553 0.488 0.405 0.325 0.250 5 0.927 0.788 0.693 0.632 0.587 0.553 0.525 0.503 0.485 0.469 0.409 0.335 0.264 0.200 6 0.882 0.721 0.625 0.563 0.519 0.486 0.460 0.440 0.422 0.408 0.352 0.285 0.222 0.166 7 0.837 0.664 0.568 0.508 0.465 0.434 0.410 0.391 0.375 0.361 0.310 0.249 0.192 0.142 8 0.794 0.615 0.520 0.462 0.422 0.393 0.370 0.352 0.337 0.324 0.277 0.221 0.170 0.125

9 0.754 0.572 0.481 0.425 0.387 0.359 0.337 0.320 0.306 0.295 0.251 0.199 0.152 0.111 10 0.717 0.535 0.446 0.393 0.357 0.330 0.310 0.294 0.251 0.270 0.281 0.181 0.137 0.100

ESTADÍSTICA II 32.

Tabla 11 Test de Rachas

n-

2 3 4 5 6 7 8 9 10

n+=2 α=0.05 0-4 0-5 0-5 0-5 0-5 0-5 2-3 2-5 2-5

α=0.01 0-4 0-5 0-5 0-5 0-5 0-5 0-5 0-5 0-5

n+=3 α=0.05 0-5 0-6 0-6 2-7 2-7 2-7 2-7 2-7 3-7

α=0.01 0-5 0-6 0-7 0-7 0-7 0-7 0-7 2-7 2-7

n+=4 α=0.05 0-5 0-6 2-7 2-8 3-8 3-8 3-9 3-9 3-9

α=0.01 0-5 0-7 0-8 0-9 2-9 2-9 2-9 2-9 2-9

n+=5 α=0.05 0-5 2-7 2-8 3-8 3-9 3-9 3-10 4-10 4-10

α=0.01 0-5 0-7 0-9 2-9 2-10 2-10 2-11 3-10 3-11

n+=6 α=0.05 0 5 2-7 3-8 3-9 3-10 4-10 4-11 4-11 5-11

α=0.01 0 5 0-7 2-9 2-10 2-11 3-11 3-12 3-12 3-13

n+=7 α=0.05 0-5 2-7 3-8 3-9 4-10 4-11 4-12 5-12 5-12

α=0.01 0-5 0-7 2-9 2-10 3-11 3-12 3-12 4-13 4-14

n+=8 α=0.05 2-5 2-7 3-9 3-10 4-11 4-12 5-12 5-13 6-13

α=0.01 0-5 0-7 2-9 2-11 3-12 3-12 4-13 4-14 4-14

n+=9 α=0.05 2-5 2-7 3-9 4-10 4-11 5-12 5-13 6-13 6-14

α=0.01 0-5 2-7 2-9 3-10 3-12 4-13 4-14 4-15 5-15

n+=10 α=0.05 2-5 3-7 3-9 4-10 5-11 5-12 6-13 6-14 6-15

α=0.01 0-5 2-7 2-9 3-11 3-13 4-14 4-14 5-15 5-16

n+=11 α=0.05 2-5 3-7 3-9 4-11 5-12 5-13 6-14 6-14 7-15

α=0.01 0-5 2-7 2-9 3-11 4-13 4-14 4-15 5-16 5-17

n+=12 α=0.05 2-5 3-7 4-9 4-11 5-12 6-13 6-14 7-15 7-16

α=0.01 0-5 2-7 3-9 3-11 4-13 4-14 5-15 5-16 6-17

n+=13 α=0.05 2-5 3-7 4-9 4-11 5-12 6-13 6-14 7-15 8-16

α=0.01 0-5 2-7 3-9 3-11 4-13 5-15 5-16 6-17 6-18

n+=14 α=0.05 2-5 3-7 4-9 5-11 5-12 6-13 7-15 7-16 8-16

α=0.01 0-5 2-7 3-9 3-11 4-13 5-15 5-16 6-17 6-18

n+=15 α=0.05 2-5 3-7 4-9 5-11 6-13 6-14 7-15 8-16 8-17

α=0.01 0-5 2-7 3-9 4-11 4-13 5-15 5-16 6-17 7-18

33 TABLAS ESTADÍSTICAS.

n-

2 3 4 5 6 7 8 9 10

n+=16 α=0.05 2-5 3-7 4-9 5-11 6-13 6-14 7-15 8-16 8-17

α=0.01 0-5 2-7 3-9 4-11 4-13 5-15 6-16 6-17 7-19

n+=17 α=0.05 2-5 3-7 4-9 5-11 6-13 7-14 7-15 8-16 9-17

α=0.01 0-5 2-7 3-9 4-11 5-13 5-15 6-17 7-17 7-19

n+=18 α=0.05 2-5 3-7 4-9 5-11 6-13 7-14 8-15 8-17 9-18

α=0.01 0-5 2-7 3-9 4-11 5-13 5-15 6-17 7-18 7-19

n+=19 α=0.05 2-5 3-7 4-9 5-11 6-13 7-14 8-15 9-17 9-18

α=0.01 2-5 2-7 3-9 4-11 5-13 6-15 6-17 7-18 8-19

n+=20 α=0.05 2-5 3-7 4-9 5-11 6-13 7-14 8-16 9-17 9-18

α=0.01 2-5 2-7 3-9 4-11 5-13 6-15 6-17 7-18 8-19

n-

11 12 13 14 15 16 17 18 19 20

n+=2 α=0.05 2-5 2-5 2-5 2-5 2-5 2-5 2-5 2-5 2-5 2-5

α=0.01 0-5 0-5 0-5 0-5 0-5 0-5 0-5 0-5 2-5 2-5

n+=3 α=0.05 3-7 3-7 3-7 3-7 3-7 3-7 3-7 3-7 3-7 3-7

α=0.01 2-7 2-7 2-7 2-7 2-7 2-7 2-7 2-7 2-7 2-7

n+=4 α=0.05 3-9 4-9 4-9 4-9 4-9 4-9 4-9 4-9 4-9 4-9

α=0.01 2-9 3-9 3-9 3-9 3-9 3-9 3-9 3-9 3-9 3-9

n+=5 α=0.05 4-11 4-11 4-11 5-11 5-11 5-11 5-11 5-11 5-11 5-11

α=0.01 3-11 3-11 3-11 3-11 4 11 4-11 4-11 4-11 4-11 4-11

n+=6 α=0.05 5-12 5-12 5-12 5-12 6-13 6-13 6-13 6-13 6-13 6-13

α=0.01 4-13 4-13 4-13 4-13 4-13 4-13 5-13 5-13 5-13 5-13

n+=7 α=0.05 5-13 6-13 6-13 6-13 6-14 6-14 7-14 7-14 7-14 7-14

α=0.01 4-14 4-14 5-15 5-15 5-15 5-15 5-15 5-15 6-15 6-15

n+=8 α=0.05 6-14 6-14 6-14 7-15 7-15 7-15 7-15 8-15 8-15 8-16

α=0.01 4-15 5-15 5-16 5-16 5-16 6-16 6-17 6-17 6-17 6-17

n+=9 α=0.05 6-14 7-15 7-15 7-16 8-16 8-16 8-16 8-17 9-17 9-17

α=0.01 5-16 5-16 6-17 6-17 6-17 6-17 7-17 7-18 7-18 7-18

n+=10 α=0.05 7-15 7-16 8-16 8-16 8-17 8-17 9-17 9-18 9-18 9-18

α=0.01 5-17 6-17 6-18 6-18 7-18 7-19 7-19 7-19 8-19 8-19

ESTADÍSTICA II 34.

n-

11 12 13 14 15 16 17 18 19 20

n+=11 α=0.05 8-17 9-17 9-18 9-18 10-19 10-19 10-20 10-20 11-20 7-16

α=0.01 7-18 7-19 7-20 8-20 8-21 8-21 8-21 9-22 9-22 6-17

n+=12 α=0.05 9-17 8-16 8-17 8-17 9-18 9-18 9-18 10-19 10-19 10-19

α=0.01 7-19 6-18 6-18 7-19 7-19 7-20 8-20 8-20 8-21 8-21

n+=13 α=0.05 9-18 8-17 9-18 9-19 10-19 10-20 10-20 11-20 11-21 11-21

α=0.01 7-20 6-18 7-20 8-20 8-21 8-21 9-22 9-22 9-23 10-23

n+=14 α=0.05 9-18 8-17 9-19 10-19 10-20 11-20 11-21 11-21 12-22 12-22

α=0.01 8-20 7-19 8-20 8-21 8-22 9-22 9-23 9-23 10-23 10-24

n+=15 α=0.05 10-19 9-18 10-19 10-20 11-20 11-21 11-21 12-22 12-22 12-23

α=0.01 8-21 7-19 8-21 8-22 9-22 9-23 10-23 10-24 10-24 11-25

n+=16 α=0.05 10-19 9-18 10-20 11-20 11-21 11-22 12-22 12-22 12-23 12-23

α=0.01 8-21 7-20 8-21 9-22 9-23 10-23 10-24 10-24 10-25 10-25

n+=17 α=0.05 10-20 9-18 10-20 11-21 11-21 12-22 12-23 13-23 13-24 13-24

α=0.01 8-21 8-20 9-22 9-23 10-23 10-24 10-25 11-25 11-26 11-26

n+=18 α=0.05 10-20 10-19 11-20 11-21 12-22 12-22 13-23 13-24 14-25 14-25

α=0.01 9-22 8-20 9-22 9-23 10-24 10-24 11-25 11-26 12-26 12-27

n+=19 α=0.05 11-20 10-19 11-21 10-19 12-22 12-23 13-24 14-25 14-25 14-26

α=0.01 9-22 8-21 9-23 10-23 10-24 10-25 11-26 12-26 12-27 12-28

n+=20 α=0.05 7-16 10-19 11-21 12-22 12-23 12-23 13-24 14-25 14-26 15-26

α=0.01 6-17 8-21 10-23 10-24 11-25 10-25 11-26 12-27 12-28 13-28

35 TABLAS ESTADÍSTICAS.

Tabla 12 Prueba de Kolmogorov-Smirnov para dos muestras del mismo

tamaño 1 - α

n 0.80 0.90 0.95 0.98 0..99

3 2 2 4 3 3 3 5 3 3 4 4 4 6 3 4 4 5 5 7 4 4 5 5 5 8 4 4 5 5 6 9 4 5 5 6 6

10 4 5 6 6 7 11 5 5 6 7 7 12 5 5 6 7 7

13 5 6 6 7 8 14 5 6 7 7 8 15 5 6 7 8 8 16 6 6 7 8 9

17 6 7 7 8 9 18 6 7 8 9 9 19 6 7 8 9 9 20 6 7 8 9 10 21 6 7 8 9 10

22 7 8 8 10 10 23 7 8 9 10 10

24 7 8 9 10 11 25 7 8 9 10 11 26 7 8 9 10 11 27 7 8 9 11 11 28 8 9 10 11 11 29 8 9 10 11 12 30 8 9 10 11 12 31 8 9 10 11 12 32 8 9 10 12 12 33 8 9 10 12 12 34 8 10 11 12 13

35 8 10 11 12 13 36 9 10 11 12 13 37 9 10 11 Í2 13 38 9 10 11 13 14

39 9 10 12 13 14 40 9 10 12 13 14

ESTADÍSTICA II 36.

1 - α

n 0.80 0.90 0.95 0.98 0..99

n > 40

n52.1

n73.1

n92.1

n15.2

n30.2

37 TABLAS ESTADÍSTICAS.

Tabla 13 Prueba de Kolmogorov-Smirnov para dos muestras de distinto

tamaño

1 - α

n1 n2 0.80 0.90 0.95 0.98 0.99

1 9 17/18 10 9/10

2 3 5/6

4 3/4 5 4/5 4/5 6 5/6 5/6 7 5/7 6/7 8 3/4 7/8 7/8 9 7/9 8/9 8/9 10 7/10 4/5 9/10

3 4 3/4 3/4

5 2/3 4/5 4/5 6 2/3 2/3 5/6 7 2/3 5/7 6/7 6/7 8 5/8 3/4 3/4 7/8 9 2/3 2/3 7/9 8/9 8/9 10 3/5 7/10 4/5 9/10 9/10

12 7/12 2/3 3/4 5/6 11/12

4 5 3/5 1/4 4/5 4/5 6 7/12 2/3 3/4 5/6 5/6

7 17/28 5/7 1/4 6/7 6/7 8 5/8 5/8 3/4 7/8 7/8 9 5/9 2/3 3/4 7/9 8/9

10 11/20 13/20 7/10 4/5 4/5

12 7/12 2/3 2/3 1/4 5/6 16 9/16 5/8 Í1/16 1/4 13/16

5 6 1/5 2/3 2/3 5/6 5/6 7 4/7 23/25 5/7 29/15 6/7

8 11/20 5/8 27/40 4/5 4/5 9 5/9 3/5 31/45 7/9 4/5

10 1/2 3/5 7/10 7/10 4/5 15 8/15 3/5 2/3 11/15 11/15 20 1/2 11/20 3/5 7/10 3/4

6 7 23/42 4/7 29/42 5/7 5/6

8 1/2 7/12 2/3 3/4 3/4 9 1/2 5/9 2/3 13/18 7/9

ESTADÍSTICA II 38. 1 - α

n1 n2 0.80 0.90 0.95 0.98 0.99 6 7 23/42 4/7 29/42 5/7 5/6 8 1/2 7/12 2/3 3/4 3/4 9 1/2 5/9 2/3 13/18 7/9 10 1/2 17/30 19/10 7/10 11/45 12 1/2 7/12 7/12 2/3 3/4 18 4/9 5/9 11/18 2/3 13/18 24 11/24 1/2 7/12 5/8 2/3

7 8 27/56 33/56 5/8 41/56 3/4

9 31/63 5/9 40/63 5/7 47/63

10 13/70 39/70 43/70 7/10 5/7 14 3/7 1/2 4/7 9/14 5/7 28 3/7 13/28 15/28 17/28 9/14

8 8 4/9 13/24 5/8 2/3 3/4

10 19/40 21/40 21/40 27/40 7/10 12 11/24 1/2 7/12 5/8 2/3

16 7/16 1/2 9/16 5/8 5/8 32 13/32 7/16 1/2 9/16 19/32

9 10 7/15 1/2 26/45 2/3 31/45

12 4/9 1/2 5/9 11/18 2/3

15 19/45 22/45 8/15 3/5 29/45

18 7/18 4/9 1/2 5/9 11/18

36 13/36 5/12 17/36 19/36 5/9

10 15 2/5 7/15 1/2 17/30 19/30

20 2/5 9/20 1/2 11/20 3/5

40 7/20 2/5 9/20 1/2

12 15 23/60 9/20 1/2 11/20 7/12

16 3/8 7/16 23/48 13/24 7/12

18 13/36 5/12 17/36 19/36 5/9

20 11/30 5/12 7/15 31/60 17/30

15 20 7/20 2/5 13/30 29/60 31/60

16 20 27/80 31/80 17/40 19/40 41/80

21

21

·07.1

nnnn +

21

21

·22.1

nnnn +

21

21

·36.1

nnnn +

21

21

·48.1

nnnn +

21

21

·63.1

nnnn +