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a) Distribución acumulada T de Student:F(t) = P[T ≤ t] = (1 - α)
0,25 0,20 0,125 0,10 0,05 0,025 0,01 0,005 0,001 0,0005 Área a la derecha
Grados 0,75 0,80 0,875 0,90 0,95 0,975 0,99 0,995 0,999 0,9995 Área a la izquierda
de
50 60 75 80 90 95 98 99 99,8 99,9 Nivel de confianza (%)
libertad
0,50 0,40 0,25 0,20 0,10 0,05 0,02 0,01 0,002 0,001 α
1 1,000 1,376 2,414 3,078 6,314 12,706 31,821 63,657 318,309 636,619
2 0,816 1,061 1,604 1,886 2,920 4,303 6,965 9,925 22,327 31,599
3 0,765 0,978 1,423 1,638 2,353 3,182 4,541 5,841 10,215 12,924
4 0,741 0,941 1,344 1,533 2,132 2,776 3,747 4,604 7,173 8,610
5 0,727 0,920 1,301 1,476 2,015 2,571 3,365 4,032 5,893 6,869
6 0,718 0,906 1,273 1,440 1,943 2,447 3,143 3,707 5,208 5,959
7 0,711 0,896 1,254 1,415 1,895 2,365 2,998 3,499 4,785 5,408
8 0,706 0,889 1,240 1,397 1,860 2,306 2,896 3,355 4,501 5,041
9 0,703 0,883 1,230 1,383 1,833 2,262 2,821 3,250 4,297 4,781
10 0,700 0,879 1,221 1,372 1,812 2,228 2,764 3,169 4,144 4,587
11 0,697 0,876 1,214 1,363 1,796 2,201 2,718 3,106 4,025 4,437
12 0,695 0,873 1,209 1,356 1,782 2,179 2,681 3,055 3,930 4,318
13 0,694 0,870 1,204 1,350 1,771 2,160 2,650 3,012 3,852 4,221
14 0,692 0,868 1,200 1,345 1,761 2,145 2,624 2,977 3,787 4,140
15 0,691 0,866 1,197 1,341 1,753 2,131 2,602 2,947 3,733 4,073
16 0,690 0,865 1,194 1,337 1,746 2,120 2,583 2,921 3,686 4,015
17 0,689 0,863 1,191 1,333 1,740 2,110 2,567 2,898 3,646 3,965
18 0,688 0,862 1,189 1,330 1,734 2,101 2,552 2,878 3,610 3,922
19 0,688 0,861 1,187 1,328 1,729 2,093 2,539 2,861 3,579 3,883
20 0,687 0,860 1,185 1,325 1,725 2,086 2,528 2,845 3,552 3,850
21 0,686 0,859 1,183 1,323 1,721 2,080 2,518 2,831 3,527 3,819
22 0,686 0,858 1,182 1,321 1,717 2,074 2,508 2,819 3,505 3,792
23 0,685 0,858 1,180 1,319 1,714 2,069 2,500 2,807 3,485 3,768
24 0,685 0,857 1,179 1,318 1,711 2,064 2,492 2,797 3,467 3,745
25 0,684 0,856 1,178 1,316 1,708 2,060 2,485 2,787 3,450 3,725
26 0,684 0,856 1,177 1,315 1,706 2,056 2,479 2,779 3,435 3,707
27 0,684 0,855 1,176 1,314 1,703 2,052 2,473 2,771 3,421 3,690
28 0,683 0,855 1,175 1,313 1,701 2,048 2,467 2,763 3,408 3,674
29 0,683 0,854 1,174 1,311 1,699 2,045 2,462 2,756 3,396 3,659
30 0,683 0,854 1,173 1,310 1,697 2,042 2,457 2,750 3,385 3,646
31 0,682 0,853 1,172 1,309 1,696 2,040 2,453 2,744 3,375 3,633
32 0,682 0,853 1,172 1,309 1,694 2,037 2,449 2,738 3,365 3,622
33 0,682 0,853 1,171 1,308 1,692 2,035 2,445 2,733 3,356 3,611
34 0,682 0,852 1,170 1,307 1,691 2,032 2,441 2,728 3,348 3,601
35 0,682 0,852 1,170 1,306 1,690 2,030 2,438 2,724 3,340 3,591
36 0,681 0,852 1,169 1,306 1,688 2,028 2,434 2,719 3,333 3,582
37 0,681 0,851 1,169 1,305 1,687 2,026 2,431 2,715 3,326 3,574
38 0,681 0,851 1,168 1,304 1,686 2,024 2,429 2,712 3,319 3,566
39 0,681 0,851 1,168 1,304 1,685 2,023 2,426 2,708 3,313 3,558
40 0,681 0,851 1,167 1,303 1,684 2,021 2,423 2,704 3,307 3,551
50 0,679 0,849 1,164 1,299 1,676 2,009 2,403 2,678 3,261 3,496
60 0,679 0,848 1,162 1,296 1,671 2,000 2,390 2,660 3,232 3,460
70 0,678 0,847 1,160 1,294 1,667 1,994 2,381 2,648 3,211 3,435
80 0,678 0,846 1,159 1,292 1,664 1,990 2,374 2,639 3,195 3,416
90 0,677 0,846 1,158 1,291 1,662 1,987 2,368 2,632 3,183 3,402
100 0,677 0,845 1,157 1,290 1,660 1,984 2,364 2,626 3,174 3,390
0,674 0,842 1,150 1,282 1,645 1,960 2,326 2,576 3,090 3,291
,
γ1
γ2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 50 100
1 161,5 199,5 215,7 224,6 230,2 234,0 236,8 238,9 240,5 241,9 243,0 243,9 244,7 245,4 246,0 246,5 246,9 247,3 247,7 248,0 249,3 251,8 253,0 254,3
2 18,51 19,00 19,16 19,25 19,30 19,33 19,35 19,37 19,39 19,40 19,41 19,41 19,42 19,42 19,43 19,43 19,44 19,44 19,44 19,45 19,46 19,48 19,49 19,50
3 10,13 9,552 9,277 9,117 9,013 8,941 8,887 8,845 8,812 8,786 8,763 8,745 8,729 8,715 8,703 8,692 8,683 8,675 8,667 8,660 8,634 8,581 8,554 8,526
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 5,844 5,832 5,821 5,811 5,803 5,769 5,699 5,664 5,628
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 4,604 4,590 4,579 4,568 4,558 4,521 4,444 4,405 4,365
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 3,922 3,908 3,896 3,884 3,874 3,835 3,754 3,712 3,669
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 3,494 3,480 3,467 3,455 3,445 3,404 3,319 3,275 3,230
8 5,318 4,459 4,066 3,838 3,687 3,581 3,500 3,438 3,388 3,347 3,313 3,284 3,259 3,237 3,218 3,202 3,187 3,173 3,161 3,150 3,108 3,020 2,975 2,928
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 2,989 2,974 2,960 2,948 2,936 2,893 2,803 2,756 2,707
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 2,828 2,812 2,798 2,785 2,774 2,730 2,637 2,588 2,538
P[Fγ1,γ2 ≤ f] = (1 - α) = 0,95
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 2,701 2,685 2,671 2,658 2,646 2,601 2,507 2,457 2,405
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 2,599 2,583 2,568 2,555 2,544 2,498 2,401 2,350 2,296
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 2,515 2,499 2,484 2,471 2,459 2,412 2,314 2,261 2,206
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 2,445 2,428 2,413 2,400 2,388 2,341 2,241 2,187 2,131
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 2,385 2,368 2,353 2,340 2,328 2,280 2,178 2,123 2,066
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 2,333 2,317 2,302 2,288 2,276 2,227 2,124 2,068 2,010
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 2,289 2,272 2,257 2,243 2,230 2,181 2,077 2,020 1,960
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 2,250 2,233 2,217 2,203 2,191 2,141 2,035 1,978 1,917
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 2,215 2,198 2,182 2,168 2,155 2,106 1,999 1,940 1,878
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 2,184 2,167 2,151 2,137 2,124 2,074 1,966 1,907 1,843
b) Distribución acumulada F (una cola, α = 0,05):
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 2,069 2,051 2,035 2,021 2,007 1,955 1,842 1,779 1,711
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 1,850 1,831 1,814 1,798 1,784 1,727 1,599 1,525 1,438
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 1,746 1,726 1,708 1,691 1,676 1,616 1,477 1,392 1,283
3,842 2,996 2,605 2,372 2,214 2,099 2,010 1,939 1,880 1,831 1,789 1,752 1,720 1,692 1,666 1,644 1,623 1,604 1,587 1,571 1,506 1,350 1,244 1,010
γ1 = grados de libertad del numerador; γ2 = grados de libertad del denominador
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