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 ) j( +) Poto de ocoameto: 4 Méda da Juta: Q + Q 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 - Q Devo médo aboluto: Orgazação de dado -Dado agruado Dado agruado em er em clae: f Medaa ~ Q j 5 ; Q j 5 ; Q 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 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 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 - Q ~ ( ) Coefcete de varação: C. V.. Coefcete de ametra: A Poíve outler; Se,5 < A < temo ametra moderada LI Q -,5 d q LS Q +,5 d q Se A temo ametra forte Coefcete de Curtoe C mede o grau de achatameto de Q Q uma dtrbução em relação a uma dtrbução adrão C (curva Normal) ( P9 P) C <,6 Letocúrtca Ma fechada que a curva Normal C,6 Meocúrtca É a róra curva Normal C >,6 Platcúrtca Ma aberta que a curva Normal TTaabbeel laa ddee EEt taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t
PROBABILIDADE efoque cláco: ( ( Ω) Efoque emírco: 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() E( - µ) E( ) [E()] x é v.a. deta: E( ) x ( x) é v.a cotíua: : E( ) é v.a. deta: E(Y) x y ( x, y) é v.a cotíua: : E(Y) Covarâca COV(,Y) E(Y) E()E(Y) E(Y) - E()E(Y) COV (, Y ) Coefcete de correlação: ρ, Y - ρ, Y Proredade Y Y x f ( x) x y f ( x, y) 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) TTaabbeel laa ddee EEt taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t dx dxdy
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 Se T ~ t - ( ) ~ 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 Méda da oulação com I.C. erro ( e ) Poulação fta Poulação fta (tamaho N) [ z ] ± z cohecdo Tabela da Normal vera:z z -α/ [ ± ˆ ] Méda da oulação com t ˆ decohecdo (Suor que ~ N ou que ). Tabela t de tudet t -; α/ Proorção Varâca oulacoal [ ˆ zˆ ] t ˆ ± ˆ z ˆ ˆ ˆ ˆ Tabela da Normal vera:z z -α/ ( ) ( ) I. C. ; χ ( ) ; α / χ ( ) ; α / ˆ( ˆ) ˆ ˆ ˆ ˆ( ˆ) N N N N N N TTaabbeel laa ddee EEt taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t
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 HIPÓTESE Tete de hótee ara a MÉDIA, com varâca oulacoal cohecda H : µ µ Regão Crítca Valor Crítco H : µ > µ Z > z- α µ + z α Etatítca de tete: H : µ < µ Z < z- α µ z α µ Z z H : µ µ Z < z - α/ ou Z > z - α/ µ α / + z µ α / Poulação fta: oulação fta: N N Tete de hótee ara a MÉDIA, com varâca oulacoal decohecda (Suor ~ N ou ) H : µ µ Regão Crítca Valor Crítco H : µ > µ T > t- ; α µ t ˆ + ; α Etatítca de Poulação fta: tete: H : µ < µ T < t- ; α µ t ˆ ; α ˆ µ µ t ˆ ; α / T oulação fta: H : 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 H : Regão Crítca Valor Crítco H : > Z > z - α + z α Etatítca de Poulação fta: tete: H : < Z < z - α z α ( ) z α / H : Z oulação fta: Z < z - α/ ou Z > z - α/ µ + z α / ( ) N N Tete de hótee ara a VARIÂNCIA: uor ~N H : Regão Crítca Valor ítco H : > χ > χ ; α H : < ;α > ( χ )/( ) ; α χ < χ < ( χ ;α ) / ( ) H : χ χ ;α / < ou χ > χ ( χ ) / ( ) ; α / < ;α / > ( χ ; α / )/ ( ) Etatítca de tete: χ ( ) TTaabbeel laa ddee EEt taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t 44
CEP LSC LSC LSC + A R LIC A R LSC + A LIC A ~ ~ ~ ~ + A R LIC ~ A R LSC + E R LIC E R ~ D R LIC D R e D extr LSC B LIC B e B extr R 4 R ˆ Etmatva do devo adrão Aále da Caacdade: C C R d ( LSE LIE) 6 ˆ Z m Comrmeto médo de corrda: C CUSUM ( x j ) e C µ j MIN ( Z, Z ) N + e N - :cotadore do úmero coecutvo de eríodo em que a oma acumulada C + e C - ão ão zero. + C ˆ µ µ + + e C + H + > N C ˆ µ µ e C H > N ode Z 4 ˆ Etmatva do devo adrão Etatítca LIE e Z ˆ C LSE Etatítca ˆ CMC ode um oto exceda o lmte de cotrole) + + C max [, x - (µ + ) + C - ] Se C + ou C - C - max [, (µ - ) - x + C - - ] C + C - δ µ µ (em geral δ ) > H, o roceo é coderado fora de cotrole. Um valor acoelhável ara H é 5. 4 TABELA DE FATORES PARA AS CARTAS DE CONTROLE A d D D 4 A,88,8 ------,67,659,798 ------,67,88,66,,69 ------,574,954,886 ------,568,87,77 4,79,59 ------,8,68,9 ------,66,796,457 5,577,6 ------,4,47,94 ------,89,69,9 6,48,54 ------,4,87,95,,97,548,84 7,49,74,76,94,8,959,8,88,58,9 8,7,847,6,864,99,965,85,85,4,54 9,7,97,84,86,,969,9,76,4,,8,78,,777,975,97,84,76,6,975,85,7,56,744,97,975,,679,66,58,8,77,886,978,54,646,49,6,7,69,85,979,8,68 4,5,47,8,67,87,98,46,594 5,,47,47,65,789,98,48,57 6,,5,6,67,76,984,448,55 7,,588,78,6,79,985,466,54 8,94,64,9,68,78,985,48,58 9,87,689,4,597,698,986,497,5,8,75,45,585,68,987,5,49,7,778,45,575,66,988,5,477,67,89,44,566,647,988,54,466,6,858,44,557,6,989,545,455 4,57,895,45,548,69,989,555,445 5,5,9,459,54,66,99,565,45 C 4 B TTaabbeel laa ddee EEt taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t 55 B 4 ~ A E
TABELA NORMAL PADRÃO: Z z ) φ(z) tero e ª ª decmal de z decmal de z 4 5 6 7 8 9 -,9,,,,,,,,,, -,8,,,,,,,,,, -,7,,,,,,,,,, -,6,,,,,,,,,, -,5,,,,,,,,,, -,4,,,,,,,,,, -,,5,5,5,4,4,4,4,4,4, -,,7,7,6,6,6,6,6,5,5,5 -,,,9,9,9,8,8,8,8,7,7 -,,,,,,,,,,, -,9,9,8,8,7,6,6,5,5,4,4 -,8,6,5,4,,,,,,,9 -,7,5,4,,,,,9,8,7,6 -,6,47,45,44,4,4,4,9,8,7,6 -,5,6,6,59,57,55,54,5,5,49,48 -,4,8,8,78,75,7,7,69,68,66,64 -,,7,4,,99,96,94,9,89,87,84 -,,9,6,,9,5,,9,6,, -,,79,74,7,66,6,58,54,5,46,4 -,,8,,7,,7,,97,9,88,8 -,9,87,8,74,68,6,56,5,44,9, -,8,59,5,44,6,9,,4,7,,94 -,7,446,46,47,48,49,4,9,84,75,67 -,6,548,57,56,56,55,495,485,475,465,455 -,5,668,655,64,6,68,66,594,58,57,559 -,4,88,79,778,764,749,75,7,78,694,68 -,,968,95,94,98,9,885,869,85,88,8 -,,5,,,9,75,56,8,,,985 -,,57,5,4,9,7,5,,,9,7 -,,587,56,59,55,49,469,446,4,4,79 -,9,84,84,788,76,76,7,685,66,65,6 -,8,9,9,6,,5,977,949,9,894,867 -,7,4,89,58,7,96,66,6,6,77,48 -,6,74,79,676,64,6,578,546,54,48,45 -,5,85,5,5,98,946,9,877,84,8,776 -,4,446,49,7,6,,64,8,9,56, -,,8,78,745,77,669,6,594,557,5,48 -,,47,468,49,49,45,4,974,96,897,859 -,,46,456,45,448,444,444,464,45,486,447 -,,5,496,49,488,484,48,476,47,468,464,,5,54,58,5,56,599,59,579,59,559,,598,548,5478,557,5557,5596,566,5675,574,575,,579,58,587,59,5948,5987,66,664,6,64,,679,67,655,69,6,668,646,644,648,657,4,6554,659,668,6664,67,676,677,688,6844,6879,5,695,695,6985,79,754,788,7,757,79,74,6,757,79,74,757,789,74,7454,7486,757,7549,7,758,76,764,767,774,774,7764,7794,78,785,8,788,79,799,7967,7995,8,85,878,86,8,9,859,886,8,88,864,889,85,84,865,889,,84,848,846,8485,858,85,8554,8577,8599,86,,864,8665,8686,878,879,8749,877,879,88,88,,8849,8869,8888,897,895,8944,896,898,8997,95,,9,949,966,98,999,95,9,947,96,977,4,99,97,9,96,95,965,979,99,96,99,5,9,945,957,97,98,994,946,948,949,944,6,945,946,9474,9484,9495,955,955,955,955,9545,7,9554,9564,957,958,959,9599,968,966,965,96,8,964,9649,9656,9664,967,9678,9686,969,9699,976,9,97,979,976,97,978,9744,975,9756,976,9767,,977,9778,978,9788,979,9798,98,988,98,987,,98,986,98,984,988,984,9846,985,9854,9857,,986,9864,9868,987,9875,9878,988,9884,9887,989,,989,9896,9898,99,994,996,999,99,99,996,4,998,99,99,995,997,999,99,99,994,996,5,998,994,994,994,9945,9946,9948,9949,995,995,6,995,9955,9956,9957,9959,996,996,996,996,9964,7,9965,9966,9967,9968,9969,997,997,997,997,9974,8,9974,9975,9976,9977,9977,9978,9979,9979,998,998,9,998,998,998,998,9984,9984,9985,9985,9986,9986,,9987,9987,9987,9988,9988,9989,9989,9989,999,999,,999,999,999,999,999,999,999,999,999,999,,999,999,9994,9994,9994,9994,9994,9995,9995,9995,,9995,9995,9995,9996,9996,9996,9996,9996,9996,9997,4,9997,9997,9997,9997,9997,9997,9997,9997,9997,9998,5,9998,9998,9998,9998,9998,9998,9998,9998,9998,9998,6,9998,9998,9999,9999,9999,9999,9999,9999,9999,9999,7,9999,9999,9999,9999,9999,9999,9999,9999,9999,9999,8,9999,9999,9999,9999,9999,9999,9999,9999,9999,9999,9,,,,,,,,,, TTaabbeel laa ddee EEt taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t 66
TABELA INVERSA DA NORMAL PADRÃO φ(z) Z z) tero, ª e ª ª decmal de decma de 4 5 6 7 8 9, -,9 -,878 -,7478 -,65 -,5758 -,5 -,457 -,489 -,656, -,6 -,94 -,57 -,6 -,97 -,7 -,444 -, -,969 -,748, -,57 -,5 -,4 -,9954 -,9774 -,96 -,94 -,968 -,9 -,8957, -,888 -,866 -,85 -,884 -,85 -,89 -,799 -,7866 -,7744 -,764,4 -,757 -,79 -,779 -,769 -,76 -,6954 -,6849 -,6747 -,6646 -,6546,5 -,6449 -,65 -,658 -,664 -,67 -,598 -,589 -,585 -,578 -,56,6 -,5548 -,5464 -,58 -,5 -,5 -,54 -,56 -,4985 -,499 -,48,7 -,4758 -,4684 -,46 -,458 -,4466 -,495 -,45 -,455 -,487 -,48,8 -,45 -,984 -,97 -,85 -,787 -,7 -,658 -,595 -,5 -,469,9 -,48 -,46 -,85 -,5 -,65 -,6 -,47 -,988 -,9 -,87, -,86 -,759 -,7 -,646 -,59 -,56 -,48 -,46 -,7 -,9, -,65 -, -,6 -,7 -,55 -,4 -,95 -,9 -,85 -,8, -,75 -,7 -,65 -,6 -,55 -,5 -,455 -,47 -,59 -,, -,64 -,7 -,7 -, -,77 -, -,985 -,99 -,89 -,848,4 -,8 -,758 -,74 -,669 -,65 -,58 -,57 -,494 -,45 -,47,5 -,64 -, -,79 -,7 -,94 -,5 -, -,69 -,7 -,9986,6 -,9945 -,994 -,986 -,98 -,978 -,974 -,97 -,966 -,96 -,958,7 -,954 -,95 -,946 -,944 -,985 -,946 -,97 -,969 -,9 -,99,8 -,954 -,96 -,978 -,94 -,9 -,8965 -,897 -,889 -,885 -,886,9 -,8779 -,874 -,876 -,8669 -,86 -,8596 -,856 -,854 -,8488 -,845, -,846 -,88 -,845 -,8 -,874 -,89 -,84 -,869 -,84 -,899, -,864 -,8 -,7995 -,796 -,796 -,789 -,7858 -,784 -,779 -,7756, -,77 -,7688 -,7655 -,76 -,7588 -,7554 -,75 -,7488 -,7454 -,74, -,788 -,756 -,7 -,79 -,757 -,75 -,79 -,76 -,78 -,795,4 -,76 -,7 -,6999 -,6967 -,695 -,69 -,687 -,684 -,688 -,6776,5 -,6745 -,67 -,668 -,665 -,66 -,6588 -,6557 -,656 -,6495 -,6464,6 -,64 -,64 -,67 -,64 -,6 -,68 -,65 -,69 -,689 -,658,7 -,68 -,698 -,668 -,68 -,68 -,5978 -,5948 -,598 -,5888 -,5858,8 -,588 -,5799 -,5769 -,574 -,57 -,568 -,565 -,56 -,559 -,556,9 -,554 -,555 -,5476 -,5446 -,547 -,588 -,559 -,5 -,5 -,57, -,544 -,55 -,587 -,558 -,59 -,5 -,57 -,544 -,55 -,4987, -,4958 -,49 -,49 -,4874 -,4845 -,487 -,4789 -,476 -,47 -,475, -,4677 -,4649 -,46 -,459 -,4565 -,458 -,45 -,448 -,4454 -,447, -,499 -,47 -,444 -,46 -,489 -,46 -,44 -,47 -,479 -,45,4 -,45 -,497 -,47 -,44 -,46 -,989 -,96 -,94 -,97 -,88,5 -,85 -,86 -,799 -,77 -,745 -,79 -,69 -,665 -,68 -,6,6 -,585 -,558 -,5 -,55 -,478 -,45 -,45 -,98 -,7 -,45,7 -,9 -,9 -,66 -,9 -, -,86 -,6 -,4 -,7 -,8,8 -,55 -,9 -, -,976 -,95 -,94 -,898 -,87 -,845 -,89,9 -,79 -,767 -,74 -,75 -,689 -,66 -,67 -,6 -,585 -,559,4 -,5 -,58 -,48 -,456 -,4 -,44 -,78 -,5 -,7 -,,4 -,75 -,5 -,4 -,98 -,7 -,47 -, -,96 -,7 -,45,4 -,9 -,99 -,968 -,94 -,97 -,89 -,866 -,84 -,85 -,789,4 -,764 -,78 -,7 -,687 -,66 -,67 -,6 -,586 -,56 -,55,44 -,5 -,484 -,459 -,44 -,48 -,8 -,58 -, -,7 -,8,45 -,57 -, -,6 -,8 -,56 -, -,5 -,8 -,55 -,,46 -,4 -,979 -,954 -,99 -,94 -,878 -,85 -,88 -,8 -,778,47 -,75 -,78 -,7 -,677 -,65 -,67 -,6 -,577 -,55 -,57,48 -,5 -,476 -,45 -,46 -,4 -,76 -,5 -,6 -, -,76,49 -,5 -,6 -, -,75 -,5 -,5 -, -,75 -,5 -,5 TTaabbeel laa ddee EEt taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t 77
TABELA INVERSA DA NORMAL PADRÃO φ(z) Z z) (cotuação) tero, ª e ª ª decmal de decma de 4 5 6 7 8 9,5,,5,5,75,,5,5,75,,6,5,5,76,,6,5,76,4,46,45,476,5,5,57,55,577,6,67,65,677,7,78,5,75,778,8,88,85,878,94,99,954,979,54,4,,55,8,5,,56,8,6,,55,57,8,7,,58,8,48,44,459,484,56,5,55,56,586,6,67,66,687,7,78,57,764,789,85,84,866,89,97,94,968,99,58,9,45,7,96,,47,7,98,4,5,59,75,,7,5,78,44,4,456,48,58,6,5,559,585,6,67,66,689,75,74,767,6,79,89,845,87,898,94,95,976,,9,6,55,8,7,4,6,86,,9,66,9,6,9,45,7,98,45,45,478,55,5,558,64,585,6,68,665,69,79,745,77,799,86,65,85,88,97,94,96,989,46,44,47,497,66,45,45,479,47,44,46,489,46,444,47,67,499,447,4454,448,45,458,4565,459,46,4649,68,4677,475,47,476,4789,487,4845,4874,49,49,69,4958,4987,55,544,57,5,59,558,587,55,7,544,57,5,5,559,588,547,5446,5476,555,7,554,556,559,56,565,568,57,574,5769,5799,7,588,5858,5888,598,5948,5978,68,68,668,698,7,68,658,689,69,65,68,6,64,67,64,74,64,6464,6495,656,6557,6588,66,665,668,67,75,6745,6776,688,684,687,69,695,6967,6999,7,76,76,795,78,76,79,75,757,79,7,756,77,788,74,7454,7488,75,7554,7588,76,7655,7688,78,77,7756,779,784,7858,789,796,796,7995,8,79,864,899,84,869,84,89,874,8,845,88,8,846,845,8488,854,856,8596,86,8669,876,874,8,8779,886,885,889,897,8965,9,94,978,96,8,954,99,9,969,97,946,985,944,946,95,8,954,958,96,966,97,974,978,98,986,994,84,9945,9986,7,69,,5,94,7,79,,85,64,47,45,494,57,58,65,669,74,758,86,8,848,89,99,985,,77,,7,7,87,64,,59,47,455,5,55,6,65,7,88,75,8,85,9,95,4,55,7,6,,89,65,9,7,46,48,56,59,646,7,759,9,86,87,9,988,47,6,65,5,85,46,9,48,469,5,595,658,7,787,85,97,984,9,45,48,487,455,45,495,4466,458,46,4684,9,4758,48,499,4985,56,54,5,5,58,5464,94,5548,56,578,585,589,598,67,664,658,65,95,6449,6546,6646,6747,6849,6954,76,769,779,79,96,757,764,7744,7866,799,89,85,884,85,866,97,888,8957,9,968,94,96,9774,9954,4,5,98,57,748,969,,444,7,97,6,57,94,99,6,656,489,457,5,5758,65,7478,878,9 TTaabbeel laa ddee EEt taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t 88
TABELA t de Studet: T t ) α g.l.,4,5,,5,5,,,5,5,,5,5,,78 6,4,76 5,894,8 6,656 7, 8,89 66,578,89,86,886,9 4, 4,849 6,965 9,95 4,89,8,6,77,765,68,5,8,48 4,54 5,84 7,45,4,94 4,7,74,5,,776,999,747 4,64 5,598 7,7 8,6 5,67,77,476,5,57,757,65 4, 4,77 5,894 6,869 6,65,78,44,94,447,6,4,77 4,7 5,8 5,959 7,6,7,45,895,65,57,998,499 4,9 4,785 5,48 8,6,76,97,86,6,449,896,55,8 4,5 5,4 9,6,7,8,8,6,98,8,5,69 4,97 4,78,6,7,7,8,8,59,764,69,58 4,44 4,587,6,697,6,796,,8,78,6,497 4,5 4,47,59,695,56,78,79,,68,55,48,9 4,8,59,694,5,77,6,8,65,,7,85 4, 4,58,69,45,76,45,64,64,977,6,787 4,4 5,58,69,4,75,,49,6,947,86,7 4,7 6,58,69,7,746,,5,58,9,5,686 4,5 7,57,689,,74,,4,567,898,,646,965 8,57,688,,74,,4,55,878,97,6,9 9,57,688,8,79,9,5,59,86,74,579,88,57,687,5,75,86,97,58,845,5,55,85,57,686,,7,8,89,58,8,5,57,89,56,686,,77,74,8,58,89,9,55,79,56,685,9,74,69,77,5,87,4,485,768 4,56,685,8,7,64,7,49,797,9,467,745 5,56,684,6,78,6,67,485,787,78,45,75 6,56,684,5,76,56,6,479,779,67,45,77 7,56,684,4,7,5,58,47,77,57,4,689 8,56,68,,7,48,54,467,76,47,48,674 9,56,68,,699,45,5,46,756,8,96,66,56,68,,697,4,47,457,75,,85,646,56,68,9,696,4,44,45,744,,75,6,55,68,9,694,7,4,449,78,5,65,6,55,68,8,69,5,8,445,7,8,56,6 4,55,68,7,69,,6,44,78,,48,6 5,55,68,6,69,,,48,74,996,4,59 6,55,68,6,688,8,,44,79,99,,58 7,55,68,5,687,6,9,4,75,985,6,574 8,55,68,4,686,4,7,49,7,98,9,566 9,55,68,4,685,,5,46,78,976,,558 4,55,68,,684,,,4,74,97,7,55 4,55,68,,68,,,4,7,967,,544 4,55,68,,68,8,,48,698,96,96,58 4,55,68,,68,7,8,46,695,959,9,5 44,55,68,,68,5,6,44,69,956,86,56 45,55,68,,679,4,5,4,69,95,8,5 46,55,68,,679,,4,4,687,949,77,55 47,55,68,,678,,,48,685,946,7,5 48,55,68,99,677,,,47,68,94,69,55 49,55,68,99,677,,,45,68,94,65,5 5,55,679,99,676,9,9,4,678,97,6,496 6,54,679,96,67,,99,9,66,95,,46 7,54,678,94,667,994,9,8,648,899,,45 8,54,678,9,664,99,88,74,69,887,95,46 9,54,677,9,66,987,84,68,6,878,8,4,54,677,9,66,984,8,64,66,87,74,9,54,677,89,659,98,78,6,6,865,66,8,54,677,89,658,98,76,58,67,86,6,7,5,674,8,645,96,54,6,576,87,9,9 TTaabbeel laa ddee EEt taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t 99
TABELA QUIQUADRADO: χ valor tabelado) α g.l.,995,99,975,95,9,,5,5,,5,,,,4,6,76,84 5,4 6,65 7,879,,,5,, 4,65 5,99 7,78 9,,597,7,5,6,5,584 6,5 7,85 9,48,45,88 4,7,97,484,7,64 7,779 9,488,4,77 4,86 5,4,554,8,45,6 9,6,7,8 5,86 6,75 6,676,87,7,65,4,645,59 4,449 6,8 8,548 7,989,9,69,67,8,7 4,67 6, 8,475,78 8,44,647,8,7,49,6 5,57 7,55,9,955 9,75,88,7,5 4,68 4,684 6,99 9,,666,589,56,558,47,94 4,865 5,987 8,7,48,9 5,88,6,5,86 4,575 5,578 7,75 9,675,9 4,75 6,757,74,57 4,44 5,6 6,4 8,549,6,7 6,7 8,,565 4,7 5,9 5,89 7,4 9,8,6 4,76 7,688 9,89 4 4,75 4,66 5,69 6,57 7,79,64,685 6,9 9,4,9 5 4,6 5,9 6,6 7,6 8,547,7 4,996 7,488,578,8 6 5,4 5,8 6,98 7,96 9,,54 6,96 8,845, 4,67 7 5,697 6,48 7,564 8,67,85 4,769 7,587,9,49 5,78 8 6,65 7,5 8, 9,9,865 5,989 8,869,56 4,85 7,56 9 6,844 7,6 8,97,7,65 7,4,44,85 6,9 8,58 7,44 8,6 9,59,85,44 8,4,4 4,7 7,566 9,997 8,4 8,897,8,59,4 9,65,67 5,479 8,9 4,4 8,64 9,54,98,8 4,4,8,94 6,78 4,89 4,796 9,6,96,689,9 4,848,7 5,7 8,76 4,68 44,8 4 9,886,856,4,848 5,659,96 6,45 9,64 4,98 45,558 5,5,54, 4,6 6,47 4,8 7,65 4,646 44,4 46,98 6,6,98,844 5,79 7,9 5,56 8,885 4,9 45,64 48,9 7,88,878 4,57 6,5 8,4 6,74 4, 4,95 46,96 49,645 8,46,565 5,8 6,98 8,99 7,96 4,7 44,46 48,78 5,994 9, 4,56 6,47 7,78 9,768 9,87 4,557 45,7 49,588 5,5,787 4,95 6,79 8,49,599 4,56 4,77 46,979 5,89 5,67 4,458 5,655 7,59 9,8,44 4,4 44,985 48, 5,9 55, 5,4 6,6 8,9,7,7 4,585 46,94 49,48 5,486 56,8 5,85 7,7 9,47,867, 4,745 47,4 5,75 54,775 57,648 4 6,5 7,789 9,86,664,95 44,9 48,6 5,966 56,6 58,964 5 7,9 8,59,569,465 4,797 46,59 49,8 5, 57,4 6,75 6 7,887 9,,6,69 5,64 47, 5,998 54,47 58,69 6,58 7 8,586 9,96,6 4,75 6,49 48,6 5,9 55,668 59,89 6,88 8 9,89,69,878 4,884 7,4 49,5 5,84 56,895 6,6 64,8 9 9,996,46,654 5,695 8,96 5,66 54,57 58, 6,48 65,475 4,77,64 4,4 6,59 9,5 5,85 55,758 59,4 6,69 66,766 4,4,96 5,5 7,6 9,97 5,949 56,94 6,56 64,95 68,5 4,8,65 5,999 8,44,765 54,9 58,4 6,777 66,6 69,6 4,86 4,98 6,785 8,965,65 55, 59,4 6,99 67,459 7,66 44,584 5,48 7,575 9,787,487 56,69 6,48 64, 68,7 7,89 45 4, 5,9 8,66,6,5 57,55 6,656 65,4 69,957 7,66 46 5,4 6,657 9,6,49 4,5 58,64 6,8 66,66 7, 74,47 47 5,775 7,46 9,956,68 5,8 59,774 64, 67,8 7,44 75,74 48 6,5 8,77,754,98 5,949 6,97 65,7 69, 7,68 76,969 49 7,49 8,94,555,9 6,88 6,8 66,9 7, 74,99 78, 5 7,99 9,77,57 4,764 7,689 6,67 67,55 7,4 76,54 79,49 6 5,54 7,485 4,48 4,88 46,459 74,97 79,8 8,98 88,79 9,95 7 4,75 45,44 48,758 5,79 55,9 85,57 9,5 95,,45 4,5 8 5,7 5,54 57,5 6,9 64,78 96,578,879 6,69,9 6, 9 59,96 6,754 65,647 69,6 7,9 7,565,45 8,6 4,6 8,99 67,8 7,65 74, 77,99 8,58 8,498 4,4 9,56 5,87 4,7 TTaabbeel laa ddee EEt taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t
TABELA F DE FISHER: α 5%. ν 4 5 6 7 8 9 5 4 4 6 ν 6,446 99,4995 5,767 4,58,64,9875 6,7669 8,884 4,54 4,889 4,947 45,949 48,56 49,54 5,965 5,44 5,956 5,54 8,58 9, 9,64 9,467 9,96 9,95 9,5 9,79 9,847 9,959 9,45 9,49 9,4457 9,454 9,465 9,477 9,479 9,487,8 9,55 9,766 9,7 9,4 8,947 8,8867 8,845 8,8 8,7855 8,7447 8,78 8,66 8,685 8,666 8,5944 8,57 8,5494 4 7,786 6,944 6,594 6,88 6,56 6,6 6,94 6,4 5,9988 5,9644 5,97 5,8578 5,85 5,7744 5,7459 5,77 5,6878 5,658 5 6,679 5,786 5,494 5,9 5,5 4,95 4,8759 4,88 4,775 4,75 4,6777 4,688 4,558 4,57 4,4957 4,468 4,44 4,985 6 5,9874 5,4 4,757 4,57 4,874 4,89 4,67 4,468 4,99 4,6,9999,98,874,844,88,774,798,747 7 5,595 4,774 4,468 4,,975,866,787,757,6767,665,5747,57,4445,45,758,44,4,674 8 5,76 4,459 4,66,879,6875,586,55,48,88,47,89,84,5,5,794,48,5,9669 9 5,74 4,565,865,6,487,78,97,96,789,7,79,6,965,95,867,859,787,7475 4,9646 4,8,78,478,58,7,55,77,4,978,9,845,774,77,6996,669,6,58 4,844,98,5874,567,9,946,,948,896,856,7876,786,6464,69,575,59,49,448 4,747,885,49,59,59,996,94,8486,7964,754,6866,669,546,555,466,459,84,4 4,667,856,45,79,54,95,8,7669,744,67,67,5,4589,4,8,9,966,54 4 4,6,789,49,,958,8477,764,6987,6458,6,54,46,879,487,8,66,9,778 5 4,54,68,874,556,9,795,766,648,5876,547,475,44,75,878,468,4,6,4 6 4,494,67,89,69,854,74,657,59,577,495,447,5,756,54,98,57,58,589 7 4,45,595,968,9647,8,6987,64,548,494,4499,87,77,4,898,477,4,584,7 8 4,49,5546,599,977,779,66,5767,5,456,47,4,686,96,497,7,69,66,968 9 4,88,59,74,895,74,68,545,4768,47,779,8,4,555,4,7,64,9795,9 4,5,498,984,866,79,599,54,447,98,479,776,,4,85,9,998,9464,896 4,48,4668,75,84,6848,577,4876,45,66,,54,757,96,54,,9645,965,8657 4,9,444,49,867,66,549,468,965,49,967,58,58,77,8,984,98,8894,88 4,79,4,8,7955,64,577,44,748,,747,6,8,476,5,965,99,8648,88 4 4,597,48,88,776,67,58,46,55,,547,84,77,67,988,99,89,844,7896 5 4,47,85,99,7587,6,494,447,7,8,65,649,889,75,964,99,878,87,7684 6 4,5,69,975,746,5868,474,88,5,655,97,479,76,9898,9464,9,85,87,7488 7 4,,54,96,778,579,459,7,5,5,4,,558,976,999,884,86,785,77 8 4,96,44,9467,74,558,445,59,9,6,9,79,4,9586,947,8687,8,7689,78 9 4,8,77,94,74,5454,44,46,78,9,768,45,75,9446,95,854,855,757,698 4,79,58,9,6896,56,45,4,66,7,646,9,48,97,8874,849,798,796,685 4 4,847,7,887,66,4495,59,49,8,4,77,5,945,889,799,7444,698,67,5766 6 4,,54,758,55,68,54,665,97,4,996,974,864,748,7,649,594,54,467,9,78,68,447,899,75,868,64,9588,95,87,755,6587,684,554,495,49,59 TTaabbeel laa ddee EEt taat tít tccaa PPr roof feeoor raa Raaqquueel l Cyymr root t