Organização de dados -Dados não agrupados n. Mediana:

Transcrição

1 Orgazação de dado -Dado ão agruado Medaa: Poto de ocoameto: Méda: Moda: valor que ocorre com maor freqüêca Méda de Itervalo: + m max + Quartl: (ara j, ou 3) j( +) Poto de ocoameto: 4 Méda da Juta: Q + Q 3 Devo médo aboluto: Coefcete de ( ) varação: Varâca: C. V.. DMA Varâca oulacoal : Na fórmula de, dvdr or ao vé de ( ). Devo adrão: é a raz quadrada otva da varâca Amltude Iterquartl: d q Q 3 - Q Orgazação de dado -Dado agruado Dado agruado em er em clae: f Medaa ~ Q j 5 ; Q j 5 ; Q 3 j 75 j( +) Méda: Percetl: Poto de ocoameto: Poto médo da clae f Freqüêca mle da clae f Dado agruado em clae: Medaa ~ Q 5 ; Q 5 ; Q 3 75 Percetl: Poto de ocoameto: Achar o ercetl utlzado regra de trê. Moda bruta: oto médo da clae que ocorre com maor freqüêca Méda de Itervalo: m + max Méda da Juta: Q + Q 3 m Lmte feror da ª clae e max Lmte ueror da últma clae Devo médo aboluto: f ( ) Varâca: f f f DMA Varâca oulacoal : Na fórmula de, dvdr or ao vé de ( ). Devo adrão: é a raz quadrada otva da varâca Amltude Iterquartl: d q Q 3 - Q ~ 3( ) Coefcete de varação: C. V.. Coefcete de ametra: A Poíve outler; Se,5 < A < temo ametra moderada LI Q -,5 d q LS Q 3 +,5 d q Se A temo ametra forte Coefcete de Curtoe C mede o grau de achatameto de Q3 Q uma dtrbução em relação a uma dtrbução adrão C (curva Normal) ( P9 P) C <,63 Letocúrtca C,63 Meocúrtca C >,63 Platcúrtca Ma fechada que a curva Normal É a róra curva Normal Ma aberta que a curva Normal TTaabbeel laa ddee EEt taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymroot t

2 PROBABILIDADE efoque cláco: ( ( Ω) Efoque emírco: TTaabbeel laa ddee EEt taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t Lm f: freqüêca de ocorrêca do eveto A o exermeto : º de tetatva do exermeto Axoma Ω ) Teorema Se A e B forem mutuamete excludete, etão P ( A + Se A,,..., ão eveto mutuamete excludete P A A... A ) A ) + A ) A ) f ( Se A e B ão forem mutuamete excludete, etão A + A A B C) + + C) A A C) B C) + A B C) Se A φ A é eveto comlemetar ) Se A B A PA A A A A Probabldade codcoal: A A A robabldade do eveto A dado que já ocorreu o eveto B A + A A B ) + P ( A B ) A B A Eveto deedete Se A e B ão eveto deedete etão P ( A Se A,,..., ão eveto mutuamete deedete etre P A A.... A ) A ) A )... A ) Se A e B ão eveto deedete etão A e B ( Teorema de Baye Se F, F,..., F ão eveto mutuamete excludete e F ) A/ F ) exautvo e A for qualquer eveto tal que >, etão F / vale a exreão ao lado. F j ) A/ F j ) FUNÇÃO DE PROBABILIDADE é v.a. deta: (x) e x) Eeraça Matemátca: E() é v.a. deta: E() j + é v.a cotíua: f(x) e f ( x) dx µ x (x) é v.a cotíua: E() µ x f ( x) dx V() x E( - µ) E( ) [E()] é v.a. deta: E( ) x ( x) é v.a cotíua: : E( ) x f ( x) dx ) é v.a. deta: E(Y) x y ( x, y) é v.a cotíua: : E(Y) x y f ( x, y dxdy Covarâca COV(,Y) E(Y) E()E(Y) E(Y) - E()E(Y) COV (, Y ) Coefcete de correlação: ρ, Y - ρ, Y Y Proredade E() V() E() E() V() V() E(+Y) E()+E(Y) V(+Y)V()+V(Y) e e Y ão deedete E( Y) E() E(Y) V( - Y)V()+V(Y) e e Y ão deedete E(a+bY) a E() + b E(Y) V(+Y)V()+V(Y)+ COV(,Y) Se e Y ão deedete, etão COV(,Y) V(a+bY)a V()+b V(Y)+ a b COV(,Y) Y

3 Dtrbuçõe Deta Se ~ B(,), etão: x! x!( x)! x x x x ) ( ) ( ) x E() V() (-) Se ~ hergeométrca etão: Se ~ λ) etão: Dtrbuçõe Cotíua Dtrbução Uforme: Notação: ~ U [a, b] N x x P ( x) N x m(,) E ( ) ode N V ( ) ( λ x e λ x) E() λ V() λ x! N ) N x a a + b x) µ ( b a) b a Dtrbução Exoecal: x) e λx µ Notação: ~EP (λ) > x) e λx λ λ Dtrbução Normal: Dtrbução Normal Padrão: µ Notação: ~ N(µ; Z x) Z z) ) Notação: Z ~ N(;) P (z Z z ) Z z ) Z z ) Z > z) Z z) Seja Y a + b + b. Se ~ N (µ ; ) e ~ N (µ ; ) e e ão v.a. deedete. Etão: Y ~ N( µ ; ) ode µ Y a + b µ + b µ e b b y y y + Seja ~ N(µ ; ) e S com a v. a. deedete Etão: S ~ N ( µ S ; S ) ode µ S µ + µ + µ µ µ e S Iferêca etatítca Z µ Z ~ N(;) T µ T ~ t - Se ( ) ~ N( µ ; ) ~ χ Itervalo de cofaça O tervalo de cofaça é um tervalo cotruído de modo que coteha o verdadero valor do arâmetro etmado com robabldade γ (ível de cofaça γ). etmatva otual erro arâmetro etmatva otual + erro) γ α Méda Varâca Devo adrão roorção arâmetro µ Etmatva otual ˆ I.C. erro ( e ) Poulação fta Poulação fta (tamaho N) [ ± z ] z Méda da oulação com N cohecdo Tabela da Normal vera:z z -α/ N Méda da oulação com [ ± t ˆ ] t ˆ ˆ N ˆ decohecdo N (Suor que ~ N ou que 3). Tabela t de tudet t -; α/ [ ˆ ± zˆ ˆ ] z ˆ Proorção ˆ ˆ( ˆ) ˆ( ˆ) N ˆ ˆ ˆ ˆ Tabela da Normal vera:z z -α/ N Varâca oulacoal ( ) ( ) I. C. ; χ ( ) ; α / χ ( ) ; α / TTaabbeel laa ddee EEt taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t 33

4 Tamaho da amotra Poulação fta Poulação fta (tamaho N) Méda z z N e e ( N ) + z Proorção z ˆ ( ˆ ) z ˆ( ˆ) N e e ( N ) + z ˆ( ˆ) Tabela da Normal vera:z z -α/ e erro máxmo ermtdo ; Tamaho do tervalo e TESTE DE IPÓTESE Tete de hótee ara a MÉDIA, com varâca oulacoal cohecda : µ µ Regão Crítca Valor Crítco : µ > µ Z > z - α µ + zα : µ < µ Z < z - α µ zα : µ µ Z < z- α/ ou Z > z - α/ µ z α / µ + z α / Etatítca de tete: Z µ Poulação fta: oulação fta: N N Tete de hótee ara a MÉDIA, com varâca oulacoal decohecda (Suor ~ N ou 3) : µ µ Regão Crítca Valor Crítco : µ > µ T > t - ; α µ t ˆ + ; α Etatítca de Poulação fta: tete: : µ < µ T < t - ; α µ t ˆ ; α ˆ µ µ t ˆ ; α / T oulação fta: : µ µ T < t- ; α/ ou T > t ˆ - ; α/ N ˆ N µ + α ˆ t ; / Tete de hótee ara a PROPORÇÃO: dtrbuçõe boma ou amotra grade 5 (-) 5 : Regão Crítca Valor Crítco : > Z > z - α + z α Etatítca de Poulação fta: tete: : < Z < z - α z α ( ) z α / : Z oulação fta: Z < z - α/ ou Z > z - α/ µ + z α / ( ) N N Tete de hótee ara a VARIÂNCIA: uor ~N : Regão Crítca Valor ítco : > χ > χ ; α χ : < ;α : χ χ ;α / > ( χ ) / ( ) ; α < χ ( χ ) / ( ) < ou χ ; α / < ;α > χ ( χ ) / ( ) < ;α / > ( χ ; / ) / ( ) α Etatítca de tete: ( ) χ TTaabbeel laa ddee EEt taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t 44

5 Tete de hótee ara a DIFERENÇA DE MÉDIAS, com varâca oulacoa e cohecda : µ µ Regão Crítca Valor Crítco Etatítca de tete: : µ > µ Z > z - α + z α + z : µ < µ Z < z - α : µ µ Z < z - α/ ou Z > z - α/ z + z α α / α / Z d d (em geral ) é a dfereça, ob, etre a méda oulacoa. Tete de hótee ara a DIFERENÇA DE MÉDIA, com varâca oulacoa e decohecda orém gua. (Suor ~ N ou 3 e ~ N ou 3. Amotra deedete ) : µ µ Regão Crítca Etatítca de tete: : µ > µ T > t + ;α ( ) + ( ) c : µ < µ T < t d + + ;α T T < t ˆ ˆ c + + ; α / ou : µ µ d T > t (em geral ) é a dfereça, ob, + ; / etre a méda oulacoa. α Tete de hótee ara a DIFERENÇA DE PROPORÇÕES: dtrbuçõe boma ou amotra grade: 5 (-) 5. (Tete ara dfereça da roorçõe gual a zero) : Regão Crítca : > Z > z - α : < Z < z - α : Z < z - α/ ou Z > z - α/ Etatítca de tete: Z ˆ ˆ ˆ ˆ ˆ ˆ ˆ + + ˆ( ˆ) + Tete de hótee ara a DIFERENÇA DE VARIÂNCIAS: (Suor ~ N e ~ N com mema varâca. Amotra deedete). : Regão Crítca Etatítca de tete: (lembrar que F ; ; α F ; ; α ) : > F > F ; ; α F : < F : < F ; ; α F ou ; ; / < F ; ;α / F > F α Alcaçõe à Teora da Cofabldade Cofabldade: R(t) F(t) N comoete em ére: R (t): cofabldade do -émo comoete R(t) R (t) x R (t) x... x R (t) Se R (t) r(t) etão R(t) [r(t)] Taxa de falha: Z(t) f(t)/r(t) N comoete em aralelo: R (t): cofabldade do -émo comoete R(t) [ R (t)] [ R (t)]... [ R (t)] Se R (t) r(t) etão R(t) [ r(t)] TTaabbeel laa ddee EEt taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t 55

6 TABELA NORMAL PADRÃO: Z z ) φ(z) tero e ª ª decmal de z decmal de z ,9,,,,,,,,,, -3,8,,,,,,,,,, -3,7,,,,,,,,,, -3,6,,,,,,,,,, -3,5,,,,,,,,,, -3,4,3,3,3,3,3,3,3,3,3, -3,3,5,5,5,4,4,4,4,4,4,3-3,,7,7,6,6,6,6,6,5,5,5-3,,,9,9,9,8,8,8,8,7,7-3,,3,3,3,,,,,,, -,9,9,8,8,7,6,6,5,5,4,4 -,8,6,5,4,3,3,,,,,9 -,7,35,34,33,3,3,3,9,8,7,6 -,6,47,45,44,43,4,4,39,38,37,36 -,5,6,6,59,57,55,54,5,5,49,48 -,4,8,8,78,75,73,7,69,68,66,64 -,3,7,4,,99,96,94,9,89,87,84 -,,39,36,3,9,5,,9,6,3, -,,79,74,7,66,6,58,54,5,46,43 -,,8,,7,,7,,97,9,88,83 -,9,87,8,74,68,6,56,5,44,39,33 -,8,359,35,344,336,39,3,34,37,3,94 -,7,446,436,47,48,49,4,39,384,375,367 -,6,548,537,56,56,55,495,485,475,465,455 -,5,668,655,643,63,68,66,594,58,57,559 -,4,88,793,778,764,749,735,7,78,694,68 -,3,968,95,934,98,9,885,869,853,838,83 -,,5,3,,93,75,56,38,,3,985 -,,357,335,34,9,7,5,3,,9,7 -,,587,56,539,55,49,469,446,43,4,379 -,9,84,84,788,76,736,7,685,66,635,6 -,8,9,9,6,33,5,977,949,9,894,867 -,7,4,389,358,37,96,66,36,6,77,48 -,6,743,79,676,643,6,578,546,54,483,45 -,5,385,35,35,98,946,9,877,843,8,776 -,4,3446,349,337,3336,33,364,38,39,356,3 -,3,38,3783,3745,377,3669,363,3594,3557,35,3483 -,,47,468,49,49,45,43,3974,3936,3897,3859 -,,46,456,45,4483,4443,444,4364,435,486,447 -,,5,496,49,488,484,48,476,47,468,464,,5,54,58,5,56,599,539,579,539,5359,,5398,5438,5478,557,5557,5596,5636,5675,574,5753,,5793,583,587,59,5948,5987,66,664,63,64,3,679,67,655,693,633,6368,646,6443,648,657,4,6554,659,668,6664,67,6736,677,688,6844,6879,5,695,695,6985,79,754,788,73,757,79,74,6,757,79,734,7357,7389,74,7454,7486,757,7549,7,758,76,764,7673,774,7734,7764,7794,783,785,8,788,79,7939,7967,7995,83,85,878,86,833,9,859,886,8,838,864,889,835,834,8365,8389,,843,8438,846,8485,858,853,8554,8577,8599,86,,8643,8665,8686,878,879,8749,877,879,88,883,,8849,8869,8888,897,895,8944,896,898,8997,95,3,93,949,966,98,999,95,93,947,96,977,4,99,97,9,936,95,965,979,99,936,939,5,933,9345,9357,937,938,9394,946,948,949,944,6,945,9463,9474,9484,9495,955,955,955,9535,9545,7,9554,9564,9573,958,959,9599,968,966,965,9633,8,964,9649,9656,9664,967,9678,9686,9693,9699,976,9,973,979,976,973,9738,9744,975,9756,976,9767,,977,9778,9783,9788,9793,9798,983,988,98,987,,98,986,983,9834,9838,984,9846,985,9854,9857,,986,9864,9868,987,9875,9878,988,9884,9887,989,3,9893,9896,9898,99,994,996,999,99,993,996,4,998,99,99,995,997,999,993,993,9934,9936,5,9938,994,994,9943,9945,9946,9948,9949,995,995,6,9953,9955,9956,9957,9959,996,996,996,9963,9964,7,9965,9966,9967,9968,9969,997,997,997,9973,9974,8,9974,9975,9976,9977,9977,9978,9979,9979,998,998,9,998,998,998,9983,9984,9984,9985,9985,9986,9986 3,,9987,9987,9987,9988,9988,9989,9989,9989,999,999 3,,999,999,999,999,999,999,999,999,9993,9993 3,,9993,9993,9994,9994,9994,9994,9994,9995,9995,9995 3,3,9995,9995,9995,9996,9996,9996,9996,9996,9996,9997 3,4,9997,9997,9997,9997,9997,9997,9997,9997,9997,9998 3,5,9998,9998,9998,9998,9998,9998,9998,9998,9998,9998 3,6,9998,9998,9999,9999,9999,9999,9999,9999,9999,9999 3,7,9999,9999,9999,9999,9999,9999,9999,9999,9999,9999 3,8,9999,9999,9999,9999,9999,9999,9999,9999,9999,9999 3,9,,,,,,,,,, Taabbeel laa ddee Et taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t 66

7 TABELA INVERSA DA NORMAL PADRÃO φ(z) Z z) tero, ª e ª 3ª decmal de decma de , -3,9 -,878 -,7478 -,65 -,5758 -,5 -,4573 -,489 -,3656, -,363 -,94 -,57 -,6 -,973 -,7 -,444 -, -,969 -,748, -,537 -,335 -,4 -,9954 -,9774 -,96 -,943 -,968 -,9 -,8957,3 -,888 -,8663 -,85 -,8384 -,85 -,89 -,799 -,7866 -,7744 -,764,4 -,757 -,739 -,779 -,769 -,76 -,6954 -,6849 -,6747 -,6646 -,6546,5 -,6449 -,635 -,658 -,664 -,67 -,598 -,5893 -,585 -,578 -,563,6 -,5548 -,5464 -,538 -,53 -,5 -,54 -,563 -,4985 -,499 -,4833,7 -,4758 -,4684 -,46 -,4538 -,4466 -,4395 -,435 -,455 -,487 -,48,8 -,45 -,3984 -,397 -,385 -,3787 -,37 -,3658 -,3595 -,353 -,3469,9 -,348 -,3346 -,385 -,35 -,365 -,36 -,347 -,988 -,93 -,873, -,86 -,759 -,7 -,646 -,59 -,536 -,48 -,46 -,37 -,39, -,65 -, -,6 -,7 -,55 -,4 -,95 -,9 -,85 -,8, -,75 -,7 -,65 -,6 -,55 -,53 -,455 -,47 -,359 -,3,3 -,64 -,7 -,7 -,3 -,77 -,3 -,985 -,939 -,893 -,848,4 -,83 -,758 -,74 -,669 -,65 -,58 -,537 -,494 -,45 -,47,5 -,364 -,3 -,79 -,37 -,94 -,5 -, -,69 -,7 -,9986,6 -,9945 -,994 -,9863 -,98 -,978 -,974 -,97 -,966 -,96 -,958,7 -,954 -,95 -,9463 -,944 -,9385 -,9346 -,937 -,969 -,93 -,99,8 -,954 -,96 -,978 -,94 -,9 -,8965 -,897 -,889 -,8853 -,886,9 -,8779 -,874 -,876 -,8669 -,863 -,8596 -,856 -,854 -,8488 -,845, -,846 -,838 -,8345 -,83 -,874 -,839 -,84 -,869 -,834 -,899, -,864 -,83 -,7995 -,796 -,796 -,789 -,7858 -,784 -,779 -,7756, -,77 -,7688 -,7655 -,76 -,7588 -,7554 -,75 -,7488 -,7454 -,74,3 -,7388 -,7356 -,733 -,79 -,757 -,75 -,79 -,76 -,78 -,795,4 -,763 -,73 -,6999 -,6967 -,6935 -,693 -,687 -,684 -,688 -,6776,5 -,6745 -,673 -,668 -,665 -,66 -,6588 -,6557 -,656 -,6495 -,6464,6 -,6433 -,643 -,637 -,634 -,63 -,68 -,65 -,69 -,689 -,658,7 -,68 -,698 -,668 -,638 -,68 -,5978 -,5948 -,598 -,5888 -,5858,8 -,588 -,5799 -,5769 -,574 -,57 -,568 -,565 -,56 -,559 -,5563,9 -,5534 -,555 -,5476 -,5446 -,547 -,5388 -,5359 -,533 -,53 -,573,3 -,544 -,55 -,587 -,558 -,59 -,5 -,57 -,544 -,55 -,4987,3 -,4958 -,493 -,49 -,4874 -,4845 -,487 -,4789 -,476 -,4733 -,475,3 -,4677 -,4649 -,46 -,4593 -,4565 -,4538 -,45 -,448 -,4454 -,447,33 -,4399 -,437 -,4344 -,436 -,489 -,46 -,434 -,47 -,479 -,45,34 -,45 -,497 -,47 -,443 -,46 -,3989 -,396 -,3934 -,397 -,388,35 -,3853 -,386 -,3799 -,377 -,3745 -,379 -,369 -,3665 -,3638 -,36,36 -,3585 -,3558 -,353 -,355 -,3478 -,345 -,345 -,3398 -,337 -,3345,37 -,339 -,39 -,366 -,339 -,33 -,386 -,36 -,334 -,37 -,38,38 -,355 -,39 -,3 -,976 -,95 -,94 -,898 -,87 -,845 -,89,39 -,793 -,767 -,74 -,75 -,689 -,663 -,637 -,6 -,585 -,559,4 -,533 -,58 -,48 -,456 -,43 -,44 -,378 -,353 -,37 -,3,4 -,75 -,5 -,4 -,98 -,73 -,47 -, -,96 -,7 -,45,4 -,9 -,993 -,968 -,94 -,97 -,89 -,866 -,84 -,85 -,789,43 -,764 -,738 -,73 -,687 -,66 -,637 -,6 -,586 -,56 -,535,44 -,5 -,484 -,459 -,434 -,48 -,383 -,358 -,33 -,37 -,8,45 -,57 -,3 -,6 -,8 -,56 -,3 -,5 -,8 -,55 -,3,46 -,4 -,979 -,954 -,99 -,94 -,878 -,853 -,88 -,83 -,778,47 -,753 -,78 -,7 -,677 -,65 -,67 -,6 -,577 -,55 -,57,48 -,5 -,476 -,45 -,46 -,4 -,376 -,35 -,36 -,3 -,76,49 -,5 -,6 -, -,75 -,5 -,5 -, -,75 -,5 -,5 Taabbeel laa ddee Et taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t 77

8 TABELA INVERSA DA NORMAL PADRÃO φ(z) Z z) (cotuação) tero, ª e ª 3ª decmal de decma de ,5,,5,5,75,,5,5,75,,6,5,5,76,3,36,35,376,4,46,45,476,5,5,57,55,577,6,67,65,677,7,78,53,753,778,83,88,853,878,94,99,954,979,54,4,3,55,8,5,3,56,8,6,3,55,57,8,37,33,358,383,48,434,459,484,56,5,535,56,586,6,637,66,687,73,738,57,764,789,85,84,866,89,97,94,968,993,58,9,45,7,96,,47,73,98,4,5,59,75,3,37,353,378,44,43,456,48,58,6,533,559,585,6,637,663,689,75,74,767,6,793,89,845,87,898,94,95,976,3,39,6,355,38,37,334,36,386,33,339,366,39,63,339,3345,337,3398,345,345,3478,355,353,3558,64,3585,36,3638,3665,369,379,3745,377,3799,386,65,3853,388,397,3934,396,3989,46,443,47,497,66,45,45,479,47,434,46,489,436,4344,437,67,4399,447,4454,448,45,4538,4565,4593,46,4649,68,4677,475,4733,476,4789,487,4845,4874,49,493,69,4958,4987,55,544,57,5,59,558,587,55,7,544,573,53,533,5359,5388,547,5446,5476,555,7,5534,5563,559,56,565,568,57,574,5769,5799,7,588,5858,5888,598,5948,5978,68,638,668,698,73,68,658,689,69,65,68,63,634,637,643,74,6433,6464,6495,656,6557,6588,66,665,668,673,75,6745,6776,688,684,687,693,6935,6967,6999,73,76,763,795,78,76,79,75,757,79,733,7356,77,7388,74,7454,7488,75,7554,7588,76,7655,7688,78,77,7756,779,784,7858,789,796,796,7995,83,79,864,899,834,869,84,839,874,83,8345,838,8,846,845,8488,854,856,8596,863,8669,876,874,8,8779,886,8853,889,897,8965,9,94,978,96,8,954,99,93,969,937,9346,9385,944,9463,95,83,954,958,96,966,97,974,978,98,9863,994,84,9945,9986,7,69,,5,94,37,79,3,85,364,47,45,494,537,58,65,669,74,758,86,83,848,893,939,985,3,77,3,7,7,87,64,3,359,47,455,53,55,6,65,7,88,75,8,85,9,95,4,55,7,6,,89,65,39,37,46,48,536,59,646,7,759,9,86,873,93,988,347,36,365,35,385,3346,9,348,3469,353,3595,3658,37,3787,385,397,3984,9,45,48,487,455,435,4395,4466,4538,46,4684,93,4758,4833,499,4985,563,54,5,53,538,5464,94,5548,563,578,585,5893,598,67,664,658,635,95,6449,6546,6646,6747,6849,6954,76,769,779,739,96,757,764,7744,7866,799,89,85,8384,85,8663,97,888,8957,9,968,943,96,9774,9954,4,335,98,537,748,969,,444,7,973,6,57,94,99,363,3656,489,4573,5,5758,65,7478,878 3,9 Taabbeel laa ddee Et taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t 88

9 TABELA t de Studet: T t ) α g.l.,4,5,,5,5,,,5,5,,5,35, 3,78 6,34,76 5,894 3,8 63,656 7,3 38,89 636,578,89,86,886,9 4,33 4,849 6,965 9,95 4,89,38 3,6 3,77,765,638,353 3,8 3,48 4,54 5,84 7,453,4,94 4,7,74,533,3,776,999 3,747 4,64 5,598 7,73 8,6 5,67,77,476,5,57,757 3,365 4,3 4,773 5,894 6,869 6,65,78,44,943,447,6 3,43 3,77 4,37 5,8 5,959 7,63,7,45,895,365,57,998 3,499 4,9 4,785 5,48 8,6,76,397,86,36,449,896 3,355 3,833 4,5 5,4 9,6,73,383,833,6,398,8 3,5 3,69 4,97 4,78,6,7,37,8,8,359,764 3,69 3,58 4,44 4,587,6,697,363,796,,38,78 3,6 3,497 4,5 4,437,59,695,356,78,79,33,68 3,55 3,48 3,93 4,38 3,59,694,35,77,6,8,65 3, 3,37 3,85 4, 4,58,69,345,76,45,64,64,977 3,36 3,787 4,4 5,58,69,34,753,3,49,6,947 3,86 3,733 4,73 6,58,69,337,746,,35,583,9 3,5 3,686 4,5 7,57,689,333,74,,4,567,898 3, 3,646 3,965 8,57,688,33,734,,4,55,878 3,97 3,6 3,9 9,57,688,38,79,93,5,539,86 3,74 3,579 3,883,57,687,35,75,86,97,58,845 3,53 3,55 3,85,57,686,33,7,8,89,58,83 3,35 3,57 3,89,56,686,3,77,74,83,58,89 3,9 3,55 3,79 3,56,685,39,74,69,77,5,87 3,4 3,485 3,768 4,56,685,38,7,64,7,49,797 3,9 3,467 3,745 5,56,684,36,78,6,67,485,787 3,78 3,45 3,75 6,56,684,35,76,56,6,479,779 3,67 3,435 3,77 7,56,684,34,73,5,58,473,77 3,57 3,4 3,689 8,56,683,33,7,48,54,467,763 3,47 3,48 3,674 9,56,683,3,699,45,5,46,756 3,38 3,396 3,66 3,56,683,3,697,4,47,457,75 3,3 3,385 3,646 3,56,68,39,696,4,44,453,744 3, 3,375 3,633 3,55,68,39,694,37,4,449,738 3,5 3,365 3,6 33,55,68,38,69,35,38,445,733 3,8 3,356 3,6 34,55,68,37,69,3,36,44,78 3, 3,348 3,6 35,55,68,36,69,3,33,438,74,996 3,34 3,59 36,55,68,36,688,8,3,434,79,99 3,333 3,58 37,55,68,35,687,6,9,43,75,985 3,36 3,574 38,55,68,34,686,4,7,49,7,98 3,39 3,566 39,55,68,34,685,3,5,46,78,976 3,33 3,558 4,55,68,33,684,,3,43,74,97 3,37 3,55 4,55,68,33,683,,,4,7,967 3,3 3,544 4,55,68,3,68,8,,48,698,963 3,96 3,538 43,55,68,3,68,7,8,46,695,959 3,9 3,53 44,55,68,3,68,5,6,44,69,956 3,86 3,56 45,55,68,3,679,4,5,4,69,95 3,8 3,5 46,55,68,3,679,3,4,4,687,949 3,77 3,55 47,55,68,3,678,,,48,685,946 3,73 3,5 48,55,68,99,677,,,47,68,943 3,69 3,55 49,55,68,99,677,,,45,68,94 3,65 3,5 5,55,679,99,676,9,9,43,678,937 3,6 3,496 6,54,679,96,67,,99,39,66,95 3,3 3,46 7,54,678,94,667,994,93,38,648,899 3, 3,435 8,54,678,9,664,99,88,374,639,887 3,95 3,46 9,54,677,9,66,987,84,368,63,878 3,83 3,4,54,677,9,66,984,8,364,66,87 3,74 3,39,54,677,89,659,98,78,36,6,865 3,66 3,38,54,677,89,658,98,76,358,67,86 3,6 3,373,53,674,8,645,96,54,36,576,87 3,9 3,9 Taabbeel laa ddee Et taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t 99

10 TABELA QUIQUADRADO: χ valor tabelado) α g.l.,995,99,975,95,9,,5,5,,5,,,,4,6,76 3,84 5,4 6,635 7,879,,,5,3, 4,65 5,99 7,378 9,,597 3,7,5,6,35,584 6,5 7,85 9,348,345,838 4,7,97,484,7,64 7,779 9,488,43 3,77 4,86 5,4,554,83,45,6 9,36,7,83 5,86 6,75 6,676,87,37,635,4,645,59 4,449 6,8 8,548 7,989,39,69,67,833,7 4,67 6,3 8,475,78 8,344,647,8,733 3,49 3,36 5,57 7,535,9,955 9,735,88,7 3,35 4,68 4,684 6,99 9,3,666 3,589,56,558 3,47 3,94 4,865 5,987 8,37,483 3,9 5,88,63 3,53 3,86 4,575 5,578 7,75 9,675,9 4,75 6,757 3,74 3,57 4,44 5,6 6,34 8,549,6 3,337 6,7 8,3 3 3,565 4,7 5,9 5,89 7,4 9,8,36 4,736 7,688 9,89 4 4,75 4,66 5,69 6,57 7,79,64 3,685 6,9 9,4 3,39 5 4,6 5,9 6,6 7,6 8,547,37 4,996 7,488 3,578 3,8 6 5,4 5,8 6,98 7,96 9,3 3,54 6,96 8,845 3, 34,67 7 5,697 6,48 7,564 8,67,85 4,769 7,587 3,9 33,49 35,78 8 6,65 7,5 8,3 9,39,865 5,989 8,869 3,56 34,85 37,56 9 6,844 7,633 8,97,7,65 7,4 3,44 3,85 36,9 38,58 7,434 8,6 9,59,85,443 8,4 3,4 34,7 37,566 39,997 8,34 8,897,83,59 3,4 9,65 3,67 35,479 38,93 4,4 8,643 9,54,98,338 4,4 3,83 33,94 36,78 4,89 4, ,6,96,689 3,9 4,848 3,7 35,7 38,76 4,638 44,8 4 9,886,856,4 3,848 5,659 33,96 36,45 39,364 4,98 45,558 5,5,54 3, 4,6 6,473 34,38 37,65 4,646 44,34 46,98 6,6,98 3,844 5,379 7,9 35,563 38,885 4,93 45,64 48,9 7,88,878 4,573 6,5 8,4 36,74 4,3 43,95 46,963 49,645 8,46 3,565 5,38 6,98 8,939 37,96 4,337 44,46 48,78 5, , 4,56 6,47 7,78 9,768 39,87 4,557 45,7 49,588 5, ,787 4,953 6,79 8,493,599 4,56 43,773 46,979 5,89 53,67 3 4,458 5,655 7,539 9,8,434 4,4 44,985 48,3 5,9 55, 3 5,34 6,36 8,9,7,7 4,585 46,94 49,48 53,486 56, ,85 7,73 9,47,867 3, 43,745 47,4 5,75 54,775 57, ,5 7,789 9,86,664 3,95 44,93 48,6 5,966 56,6 58, ,9 8,59,569,465 4,797 46,59 49,8 53,3 57,34 6, ,887 9,33,336 3,69 5,643 47, 5,998 54,437 58,69 6, ,586 9,96,6 4,75 6,49 48,363 5,9 55,668 59,893 6, ,89,69,878 4,884 7,343 49,53 53,384 56,895 6,6 64,8 39 9,996,46 3,654 5,695 8,96 5,66 54,57 58, 6,48 65,475 4,77,64 4,433 6,59 9,5 5,85 55,758 59,34 63,69 66,766 4,4,96 5,5 7,36 9,97 5,949 56,94 6,56 64,95 68,53 4,38 3,65 5,999 8,44 3,765 54,9 58,4 6,777 66,6 69,336 43,86 4,398 6,785 8,965 3,65 55,3 59,34 6,99 67,459 7, ,584 5,48 7,575 9,787 3,487 56,369 6,48 64, 68,7 7, ,3 5,9 8,366 3,6 33,35 57,55 6,656 65,4 69,957 73, ,4 6,657 9,6 3,439 34,5 58,64 6,83 66,66 7, 74, ,775 7,46 9,956 3,68 35,8 59,774 64, 67,8 7,443 75, ,5 8,77 3,754 33,98 35,949 6,97 65,7 69,3 73,683 76, ,49 8,94 3,555 33,93 36,88 6,38 66,339 7, 74,99 78,3 5 7,99 9,77 3,357 34,764 37,689 63,67 67,55 7,4 76,54 79, ,534 37,485 4,48 43,88 46,459 74,397 79,8 83,98 88,379 9, ,75 45,44 48,758 5,739 55,39 85,57 9,53 95,3,45 4,5 8 5,7 53,54 57,53 6,39 64,78 96,578,879 6,69,39 6,3 9 59,96 6,754 65,647 69,6 73,9 7,565 3,45 8,36 4,6 8,99 67,38 7,65 74, 77,99 8,358 8,498 4,34 9,56 35,87 4,7 Taabbeel laa ddee Et taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t

11 TABELA F DE FISER: α 5%. ν ν 6,446 99,4995 5,767 4,5833 3,64 33, , ,884 4,543 4,889 43,947 45,949 48,56 49,54 5,965 5,44 5,956 53,543 8,58 9, 9,64 9,467 9,963 9,395 9,353 9,379 9,3847 9,3959 9,45 9,49 9,4457 9,454 9,465 9,477 9,479 9,4873 3,8 9,55 9,766 9,7 9,34 8,947 8,8867 8,845 8,83 8,7855 8,7447 8,78 8,66 8,6385 8,666 8,5944 8,57 8, ,786 6,9443 6,594 6,388 6,56 6,63 6,94 6,4 5,9988 5,9644 5,97 5,8578 5,85 5,7744 5,7459 5,77 5,6878 5, ,679 5,786 5,494 5,9 5,53 4,953 4,8759 4,883 4,775 4,735 4,6777 4,688 4,558 4,57 4,4957 4,4638 4,434 4, ,9874 5,43 4,757 4,5337 4,3874 4,839 4,67 4,468 4,99 4,6 3,9999 3,938 3,874 3,844 3,88 3,7743 3,7398 3, ,595 4,7374 4,3468 4,3 3,975 3,866 3,787 3,757 3,6767 3,6365 3,5747 3,57 3,4445 3,45 3,3758 3,344 3,343 3, ,376 4,459 4,66 3,8379 3,6875 3,586 3,55 3,438 3,388 3,347 3,839 3,84 3,53 3,5 3,794 3,48 3,53, ,74 4,565 3,865 3,633 3,487 3,3738 3,97 3,96 3,789 3,373 3,79 3,6,9365,95,8637,859,787,7475 4,9646 4,8 3,783 3,478 3,358 3,7 3,355 3,77 3,4,978,93,845,774,7373,6996,669,6,58 4,8443 3,983 3,5874 3,3567 3,39 3,946 3,3,948,896,8536,7876,786,6464,69,575,539,49,448 4,747 3,8853 3,493 3,59 3,59,996,934,8486,7964,7534,6866,669,5436,555,4663,459,384,34 3 4,667 3,856 3,45 3,79 3,54,953,83,7669,744,67,637,533,4589,4,383,339,966,54 4 4,6 3,7389 3,3439 3,,958,8477,764,6987,6458,6,534,463,3879,3487,38,663,9, ,543 3,683 3,874 3,556,93,795,766,648,5876,5437,4753,434,375,878,468,43,6,4 6 4,494 3,6337 3,389 3,69,854,743,657,59,5377,4935,447,35,756,354,938,57,58, ,453 3,595 3,968,9647,8,6987,643,548,4943,4499,387,377,34,898,477,4,584,7 8 4,439 3,5546 3,599,977,779,663,5767,5,4563,47,34,686,96,497,7,69,66, ,388 3,59 3,74,895,74,683,5435,4768,47,3779,38,34,555,4,7,64,9795,93 4,353 3,498 3,984,866,79,599,54,447,398,3479,776,33,4,85,39,9938,9464,8963 4,348 3,4668 3,75,84,6848,577,4876,45,366,3,54,757,96,54,,9645,965,8657 4,39 3,4434 3,49,867,663,549,4638,3965,349,967,58,58,77,83,984,938,8894, ,793 3,4 3,8,7955,64,577,44,3748,3,747,36,8,476,5,965,939,8648,88 4 4,597 3,48 3,88,7763,67,58,46,355,3,547,834,77,67,9838,939,89,844, ,47 3,385,99,7587,63,494,447,337,8,365,649,889,75,9643,99,878,87, ,5 3,369,975,746,5868,474,3883,35,655,97,479,76,9898,9464,9,8533,87, , 3,354,963,778,579,459,373,353,5,43,33,558,9736,999,884,836,785, ,96 3,344,9467,74,558,4453,3593,93,36,9,79,4,9586,947,8687,83,7689, ,83 3,377,934,74,5454,434,3463,78,9,768,45,75,9446,95,8543,855,7537, ,79 3,358,93,6896,5336,45,3343,66,7,646,9,48,937,8874,849,798,7396, ,847 3,37,8387,66,4495,3359,49,8,4,773,35,945,8389,799,7444,698,6373, , 3,54,758,55,3683,54,665,97,4,996,974,8364,748,7,649,5943,5343,4673 3,9 3,78,68,447,899,75,868,64,9588,95,8337,755,6587,684,5543,495,49,359 TTaabbeel laa ddee EEt taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t