Buaet űzak é Gazaágtuomá Egetem Gazaág- é Táaalomtuomá Ka Üzlet Tuomáok Itézet eezmet é Vállalatgazaágta Tazék Tóth Zuzaa Ezte Jóá Tamá Kéletgűtemé a Gazaágtatztka tág A matematka tatztka alaa című ézhez a Gazálkoá é meezmet (BA, űzak meeze (BSc, emzetköz gazálkoá (BA, valamt az Alkalmazott közgazaágta (BA alazakok ézée Buaet, 7
Leíó tatztka Közééték-mutatók: eá: me me me me h e ',, ' me óuz: mo a a mo h o, mo mo a mo mo Számta átlag:... g Egéb átlagaták: h k g q Kvatlek: k k k k k k k Szóóá mutatók: Teeelem: ma m R, ( k R k k k k
3 Átlago abzolút külöbég: G ( Átlago abzolút eltéé: Vaaca, taaztalat zóá, kogált taaztalat zóá: Relatív zóá: V
4 Rézeke botott okaág vzgálata A őokaág agága: Réz- é őátlagok: S,,...,, S S S S Szóáégzet-elbotá: SST=SSB+SSK K B T,...,,,,,...,, B,...,,,,,...,, K,...,,, K B Tele zóá, ll. tele vaaca: T ( T ( Rézzóá, ll. ézvaaca: B ( ( Belő zóá, ll. belő vaaca: B B ( B Külő zóá, ll. külő vaaca: K K ( K ( Kacolatvzgálat: T K T B SST SSK SST SSB SST H
5 Beclé Itevallumbeclé Váható éték beclée met okaág zóá eeté: Kétolal: P z z P Egolal: z P z P Váható éték beclée meetle okaág zóá eeté: * * t t P (DF=- Sokaág aá beclée: ( ( z P z P Sokaág vaaca beclée: * * P taagág meghatáozáa: z
Hotézvzgálat emaamétee óbák Póba tíua Illezkeévzgálat ták záma egmtá Alkalmazá eltétele agmtá Póbaüggvé é elogaá tatomá F F z kt Póbaügg-vé elozláa DF= Homogetávzgálat Függetleégvzgálat (két mőég mév üggetleége kétmtá agmtá F egmtá A kotgeca táblázat méetétől üggőe ag mta F z kt F F z kt DF = DF=(- (- Kacolat zooága: C ( q q m(, 6
Paamétee óbák Egmtá óbák Tezteleő aaméte Sokaág váható éték Alkalmazá eltételek Sokaág elozlá omál, a okaág zóá met, vag a okaág zóá em met, e >3 Sokaág elozlá omál, a okaág zóá em met Hotézek H : = m H : ( m ( > m (3 < m H : = m H : ( m ( > m (3 < m Póbaüggvé é elogaá tatomá z z ( z z >-z vag z z <z ( z z <z α (3 -z α < z z t z * ( t z >-t vag t z <t ( t z <t α (3 -t α < t z Póbaüggvé elozláa taa omál (z Stuet t- elozlá (DF=- Sokaág vaaca (zóá Sokaág elozlá omál H : σ = σ H : ( σ σ ( σ > σ (3 σ < σ ( ( (3 * z z z z χ -elozlá (DF=- 7
Kétmtá óbák: Tezteleő aaméte Sokaág váható éték Alkalmazá eltételek mkét okaág omál elozláú, é met v. é >3, a mták üggetleek Hotézek H : = H : ( ( > (3 < Póbaüggvé é elogaá tatomá z z ( z z >-z vag z z <z ( z z <z Póbaüggvé elozláa taa omál (z mkét okaág omál elozláú, é em met v. é <3 =, a mták üggetleek H : = H : ( ( > (3 < (3 z z >-z t z, ( ahol * ( * Stuet t- elozlá (DF= + - ( t z >-t vag t z <t ( t z <t (3 t z >-t Sokaág vaaca (zóá a okaág omál elozláú, áo mta két okaág elozlá omál H : = (H : μ =δ H : ( (μ δ ( > (μ > δ (3 < (μ < δ * H : H : * t z ( t z >-t vag t z <t ( t z <t (3 t z >-t * * F z, ahol > F z <F kt Stuet t- elozlá (DF=- F-elozlá (DF = -; DF = - 8
Többmtá óbák Tezteleő aaméte okaág vaacák (zóáok okaág váható étékeke Alkalmazá eltételek alaelozlá omál é a mták m azoo aabzámúak me okaágól eltételezhető a vzgált mév zet omál elozláa, é a okaág zóáok egezőége (Cocha óba Hotézek H... H : em me vaaca egelő H : = = = H : bámel két váható éték em egelő egmáal Póbaüggvé é elogaá tatomá F g z z g ma z g kt SSK ( SSB ( F z F kt... ( ( Szaba-ágok - DF =-, DF = - égzetözeg eve Cootok között Cooto belül égzetözegek Szabaágok Szóá beclée - k - b Tele F éték k b -éték - - - - - - 9
Koelácó- é egezózámítá Leá egezó moell: Kétváltozó leá egezó moell: Paamétebeclé: Rugalmaág: El, ( El, ( Kacolat zooága:, cov( va( va(, cov( SST SSE SST SSR R Regezó egütthatók taa hbá e ŷ e e e e Itevallumbeclé: - átlago étéke e DF t ŷ ŷ t e DF -ege étéke e DF t t e DF
Paaméteek tevallumbeclée: b b b b t b t b t b t b Hotézvzgálat: : : H H o b z b t DF=- Iőook elemzée t t k * * * * ' * * *'
Függelék: táblázatok I. táblázat: Bomál elozlá II. táblázat: Poo-elozlá III. táblázat: Staa omál elozlá IV. táblázat: -elozlá V. táblázat: Stuet-elozlá (t-elozlá VI. táblázat: F-elozlá (=,5 VII. táblázat: F-elozlá (=, VIII. táblázat: Cocha-óba (=,5 I. táblázat: Cocha-óba (=,
I. táblázat: Bomál elozlá k,5,,5,,5,3,35,4,45,5,95,9,85,8,75,7,65,6,55,5,5,,5,,5,3,35,4,45,5,95,8,75,64,565,49,45,36,35,5,95,8,55,3,375,4,455,48,495,5,5,,5,4,65,9,5,6,5,5 3,8574,79,64,5,49,343,746,6,664,5,354,43,35,384,49,44,4436,43,484,375,7,7,574,96,46,89,389,88,334,375 3,,,34,8,56,7,49,64,9,5 4,845,656,5,496,364,4,785,96,95,65,75,96,3685,496,49,46,3845,3456,995,5,35,486,975,536,9,646,35,3456,3675,375 3,5,36,5,56,469,756,5,536,5,5 4,,5,6,39,8,5,56,4,65 5,7738,595,4437,377,373,68,6,778,53,33,36,38,395,496,3955,36,34,59,59,563,4,79,38,48,637,387,3364,3456,3369,35 3,,8,44,5,879,33,8,34,757,35 4,5,,64,46,84,488,768,8,563 5,,3,,4,53,,85,33 6,735,534,377,6,78,76,754,467,77,56,3,3543,3993,393,356,35,437,866,359,938,35,984,76,458,966,34,38,3,78,344 3,,46,45,89,38,85,355,765,33,35 4,,,55,54,33,595,95,38,86,344 5,,4,5,44,,5,369,69,938 6,,,7,8,4,83,56 7,6983,4783,36,97,335,84,49,8,5,78,573,37,396,367,35,47,848,36,87,547,46,4,97,753,35,377,985,63,4,64 3,36,3,67,47,73,69,679,93,98,734 4,,6,9,87,577,97,44,935,388,734 5,,,43,5,5,466,774,7,64 6,,4,3,36,84,7,3,547 7,,,6,6,37,78 8,6634,435,75,678,,576,39,68,84,39,793,386,3847,3355,67,977,373,896,548,33,55,488,376,936,35,965,587,9,569,94 3,54,33,839,468,76,54,786,787,568,88 4,4,46,85,459,865,36,875,3,67,734 5,4,6,9,3,467,88,39,79,88 6,,,38,,7,43,73,94 7,,4,,33,79,64,33 8,,,7,7,39 3
k,5,,5,,5,3,35,4,45,5 9,63,3874,36,34,75,44,7,,46,,985,3874,3679,3,53,556,4,65,339,76,69,7,597,3,33,668,6,6,,73 3,77,446,69,76,336,668,76,58,9,64 4,6,74,83,66,68,75,94,58,6,46 5,8,5,65,389,735,8,67,8,46 6,,6,8,87,,44,743,6,64 7,3,,39,98,,47,73 8,,4,3,35,83,76 9,,3,8,,5987,3487,969,74,563,8,35,6,5,,35,3874,3474,684,877,,75,43,7,98,746,937,759,3,86,335,757,9,763,439 3,5,574,98,3,53,668,5,5,665,7 4,,,4,88,46,,377,58,384,5 5,,5,85,64,584,9,536,7,34,46 6,,,55,6,368,689,5,596,5 7,,8,3,9,,45,746,7 8,,4,4,43,6,9,439 9,,5,6,4,98,,3,,5688,338,673,859,4,98,88,36,4,5,393,3835,348,36,549,93,58,66,5,54,867,3,866,953,58,998,395,887,53,69 3,37,7,57,5,58,568,54,774,59,86 4,4,58,536,7,7,,48,365,6,6 5,,5,3,388,83,3,83,7,36,56 6,3,3,97,68,566,985,47,93,56 7,3,7,64,73,379,7,8,6 8,,,37,,34,46,86 9,,5,8,5,6,69,,7,,54,,5,544,84,4,687,37,38,57,,8,,343,3766,3,6,67,7,368,74,75,9,988,3,94,835,33,678,88,639,339,6 3,73,85,7,36,58,397,954,49,93,537 4,,3,683,39,936,3,367,8,7,8 5,,38,93,53,3,585,39,7,5,934 6,5,4,55,4,79,8,766,4,56 7,6,33,5,9,59,9,489,934 8,,5,4,78,99,4,76,8 9,,4,5,48,5,77,537,,8,5,68,6,,3,,9,, 4
k,5,,5,,5,3,35,4,45,5,5,,5,,5,3,35,4,45,5 3,533,54,9,55,38,97,37,3,4,,35,367,774,787,9,54,59,3,45,6,9,448,937,68,59,388,836,453,,95 3,4,997,9,457,57,8,65,7,66,349 4,8,77,838,535,97,337,,845,35,873 5,3,55,66,69,58,83,54,4,989,57 6,8,63,3,559,3,546,968,69,95 7,,,58,86,44,833,3,775,95 8,,,47,4,336,656,89,57 9,,9,34,,43,495,873,,6,,65,6,349,,3,,36,95,,5,6 3, 4,4877,88,8,44,78,68,4,8,,,3593,3559,539,539,83,47,8,73,7,9,9,57,9,5,8,34,634,37,4,56 3,59,4,56,5,4,943,366,845,46, 4,37,349,998,7,,9,,549,4,6 5,4,78,35,86,468,963,78,66,7, 6,3,93,3,734,6,759,66,88,833 7,,9,9,8,68,8,574,95,95 8,3,,8,3,5,98,398,833 9,3,8,66,83,48,76,,3,4,49,36,3,6,,,33,93,,,5,9,56 3,,,9 4, 5,4633,59,874,35,34,47,6,5,,3658,343,3,39,668,35,6,47,6,5,348,669,856,39,559,96,476,9,9,3 3,37,85,84,5,5,7,,634,38,39 4,49,48,56,876,5,86,79,68,78,47 5,6,5,449,3,65,6,3,859,44,96 6,9,3,43,97,47,96,66,94,57 7,3,3,38,393,8,39,77,3,964 8,5,35,3,348,7,8,647,964 9,,7,34,6,98,6,48,57,,7,3,96,45,55,96,,6,4,74,9,47,,4,6,5,39 3,,3,,3 4,,5 5 5
k,5,,5,,5,3,35,4,45,5 6,44,853,743,8,,33,,3,,376,394,97,6,535,8,87,3,9,,463,745,775,,336,73,353,5,56,8 3,359,43,85,463,79,465,888,468,5,85 4,6,54,3,,5,4,553,4,57,78 5,8,37,555,,8,99,8,63,3,667 6,,8,8,55,,649,98,983,684, 7,4,45,97,54,,54,889,969,746 8,,9,55,97,487,93,47,8,964 9,,,58,85,44,84,38,746,,4,56,67,39,755,,,3,49,4,337,667,,,4,5,78 3,,8,9,85 4,,5,8 5,, 6 7,48,668,63,5,75,3,7,,374,35,893,957,46,69,6,9,5,,575,8,673,94,36,58,6,,35, 3,45,556,359,393,893,45,7,34,44,5 4,76,65,457,93,9,868,3,796,4,8 5,,75,668,36,94,8,849,379,875,47 6,,39,36,68,76,784,99,839,43,944 7,7,65,67,668,,685,97,84,484 8,,4,84,79,644,34,66,883,855 9,3,,93,76,6,7,54,855,4,5,95,63,57,8,484,,5,6,9,4,55,944,,6,4,8,5,47 3,,5,,68,8 4,,4,6,5 5,,3, 6, 7 8,397,5,536,8,56,6,4,,3763,3,74,8,338,6,4,,3,,683,835,556,73,958,458,9,69,,6 3,473,68,46,97,74,46,547,46,95,3 4,93,7,59,53,3,68,4,64,9,7 5,4,8,787,57,988,7,664,46,666,37 6,,5,3,86,436,873,94,655,8,78 7,,9,35,8,376,79,89,657,4 8,,,,376,8,37,734,864,669 9,4,33,39,386,794,84,694,855,,8,4,49,385,77,48,669,,,46,5,374,74,4,,,47,45,354,78 3,,,45,34,37 4,,,39,7 5,,9,3 6,,6 7, 8 6
k,5,,5,,5,3,35,4,45,5 9,3774,35,456,44,4,,3,,3774,85,59,685,68,93,9,8,,787,85,48,54,83,358,38,46,3,3 3,533,796,48,8,57,869,4,75,6,8 4,,798,74,8,3,49,99,467,3,74 5,8,66,97,636,3,96,468,933,497, 6,,69,374,955,574,96,844,45,949,58 7,4,,443,974,55,844,797,443,96 8,,3,66,487,98,489,797,77,44 9,7,5,98,54,98,464,77,76,,3,66,,58,976,449,76,3,8,77,33,53,97,44,4,,83,37,59,96 3,,5,4,85,33,58 4,,6,4,8, 5,,5,,74 6,,5,8 7,,3 8 9,3585,6,388,5,3,8,,3774,7,368,576,,68,,5,,887,85,93,369,669,78,,3,8, 3,596,9,48,54,339,76,33,3,4, 4,33,898,8,8,897,34,738,35,39,46 5,,39,8,746,3,789,7,746,365,48 6,3,89,454,9,686,96,7,44,746,37 7,,6,545,4,643,844,659,,739 8,4,46,,69,44,64,797,63, 9,,,74,7,654,58,597,77,6,,,99,38,686,7,593,76,5,3,,336,7,85,6,,8,39,36,355,77, 3,,,45,46,366,739 4,,,49,5,37 5,3,3,49,48 6,3,3,46 7,, 8, 9 7
II. táblázat. Poo-elozlá k,,,3,4,5,6,7,8,9,,94,88,74,67,66,548,496,449,46,367,9,63,,68,33,39,347,359,365,367,4,6,33,53,75,98,,43,64,83 3,,,3,7,,9,8,38,49,6 4,,,,,,3,5,7,,5 5,,,,,,,,,,3 6,,,,,,,,,, 7,,,,,,,,,, k,,,3,4,5,6,7,8,9,,33,3,7,46,3,,8,65,49,35,366,36,354,345,334,33,3,97,84,7, 3,73 4,6,86 9,3,99 3,4, 7,5,5,58,37 4,64,49,67,6 8,7,7,7,8 7 4, 8,6 7,3 8,39 8,47 5,55 8,63 6,7 7,8,9 4 5,4 3,6,8 4, 5,4,7, 6,6 3,3,36 6, 5,, 4,,3,4 6,66,7,99, 7, 8,, 8, 6, 5, 7,, 8, 8,3 8,,, 3, 5, 8,, 5, 7, 4 9,,,,, 3, 5, 6, 9 k,,,3,4,5,6,7,8,9 3,,,57 5,,43 8,,3 3,9,77,8,5,74,933,67,8,6,7 8,55,59,49,49 8,7,688,65 6,6 7,56,5,455,38 3,3 6,44 3,89,96,3,9 3,3 5,7,, 4,3 4,4 4,99,8 6,6 3,5,33 8,4 6,48 5,555,6 7,68 5,4,47,53 9,6 4,666,73 4,8 8,877,94, 6,4 7,7 6, 8,4,7 8,3 5,36 4,4,45,5 8 7,4 6,5 4,66,8,9 8, 9,3,6 7,8 5, 4 8, 4, 5, 8, 3,3 9,3 8,4 9,5 3,6 8,8 6 9,, 5, 9, 5,, 8, 7, 7, 8,, 3, 4, 5, 7, 9,, 4, 8,, 7,,,,,, 3, 4, 5, 6, 8,,,,, k 3, 3, 3,3 3,4 3,5 3,6 3,7 3,8 3,9 4,,45,39,4,3 8,36, 9,33,3 4,3,5,7,98 3,4,9 7,,85 4,,78,8,733,6 7,8 4, 7,9 5,85 7,77 4,69 5,6,53 9,46 3 3,3 5, 7, 8,8 9,5,,8,4 5, 9,955 4,73 7,78 6,8 9,85 6,888,9 5,93 7,94 6,95,95 4 5,7 3,4, 3,6 8,3 8,37,4,47 4,5,56 4 6,555,6,66 3,7 4,77,8 7,88 9,93 7,98,4 3 7,4 5,7 8,3,34 6,38,4 6,46,5 6,55 9,59 8,9 6 5, 8, 9,4 8 8,6 5 9,9 5, 6 5,4 8,6 9,9 5 8 8
9,3,4,4,5,6,7,8,,,3,,,,,,,3,3,4,5,,,,,,,,,,,,,,,,,,,, 3,,,,,,,,,, 4,,,,,,,,,, k 4, 4, 4,3 4,4 4,5 4,6 4,7 4,8 4,9 5,,6,5,3,,,,9,8,7,6,67,63,58,54,5,46,4,39,36,33,39,3,5,8,,6,,94,89,84 3,9,85,79,74,68,63,57,5,46,4 4,95,94,93,9,89,87,84,8,78,75 5,6,63,66,68,7,7,73,74,75,75 6,9,4,9,3,8,3 5,36 8,39 7,433,46 5 7,64 3,68 3,73,777,8,86 3,9,95 8,,4 8,3,366,39,4 8,46 4,5 9,53 4,57 9,6,65 4 9,5 8,6,8 3, 8,33,5,8 7,3 5,33 4,36 3,6,7 8,88,99,, 5,3,4 7,6 4,8 3,,,3,3,44,4 8,5,6 7,7 4,8, 3, 7,, 7, 3, 9, 6, 4,33,3 3, 8, 9,, 3, 6, 9,, 6,, 4 4,, 3, 4, 5, 6, 7, 8, 9,, 3 5,,,,,,, 3, 3, 4, 5 k 5, 5, 5,3 5,4 5,5 5,6 5,7 5,8 5,9 6,,6,3,5,8 5,5,6,4,4 5,4,,3, 7,3,9 3,3,7,,6 7,,4 5,79,74 7,7 5,65 4,6 5,58 7,54,5 6,47,44 9 3,34 3,9 6,3,8 9,3 8,8,3 4,98 9,93 7,89 6 4,7 8,68 3,64 9,6 5,55 3,5,47 3,4 5,388,33 5,75 9,74,74,7,7 8,69 5,67,65 8,633,6 9 6,49 3,5 8,53,55 8,57 4,58 7,59 8,6 6,6,6 6 7,8, 5,6 7, 5,3,6 4,9 4,3,355,37 6 8,69 6,73 5,77 3,8,844,88 7,9 8,966,99 3,3 7 9,39,4,45,48,5 9,55 7,58 5,6,65 8,68 3,, 3,44,66,8 9,3,33 6,35,38 4,4 8,9,,,,4 5,5 9,7 4,99, 6, 3,33,44,5 6,5 9,6 3,77,8 3,9, 7, 5 3, 9, 5,, 8, 5,33,3,4,4,5 3 4, 5, 8,, 4, 8,, 6,, 6, 5, 6, 7, 8, 9,, 3, 5, 7, 9, 6,,, 3, 3, 4, 5, 6, 7, 8, 9 7,,,,,,,,, 3, 3 k 6, 6, 6,3 6,4 6,5 6,6 6,7 6,8 6,9 7,,,3,,,, 8,, 7,,9 5,,9 4,,8,,7,,7,,6 9,4 7,39 6,366,34 6,3 8,9,7,5 6,4, 4 3,84 7 8,8 6,76 4 5,7 6,688 8,65 6,6 6 7,588 4,55,5 3 9
4,9,4,,6,,7,3,99,95,9 5,57,54,5,48,45,4,38,34,3,7 6,6,6,59,58,57,56,54,5,5,49 7,39,4,43,45,46,47,48,48,48,49 8,6,9,3,6,8,,4,6,8,3 9,7,75,79,8,85,89,9,95,98,,44,46,49,5,55,58,6,64,67,7,4,6,8,3,33,35,37,4,4,45,,3,5,6,7,9,,,4,6 3,5,6,7,8,8,9,,,3,4 4,,,3,3,4,4,5,5,6,7 5,,,,,,,,,,3 6,,,,,,,,,, 7,,,,,,,,,, 4 8,,,,, 3, 3, 4, 4, 5, 6 9,,,,,,,,, k 7, 7, 7,3 7,4 7,5 7,6 7,7 7,8 7,9 8,,,5 8,,5 7,,4 7,,4 6,,4 6,,3 5,,3 5,,3 4,, 4,, 3, 9,9 4,8 9,6 5,5,4 8,3 5,, 9, 7 3,49 8,46 4,43,4 7,38 6,36 5,344,3 5,3 6,8 7 4,87,83 4,79 8,76 3,7 9,69 6,66 5,63 4,6 5,57 6 5,44, 6,6 9,3 4,99,5 6, 3,98,95,9 3 6,46,444,4 7,39,36 4,33 7,3,8 6,5, 6 7,488,48 5,48,47 4,46 7,45 9,44,4,4,39 8,3 9,33 6,35,36 4,37 5,38 4,38,39 8,39 3,39 6 9,4,77,9, 3,4 3,6,88,, 5,4 6,74,77,8 6,8,85 4,88 7,9 7,94 7,96 4,99,47,5,53,55 9,588,6 7,644,66,69 7,7 3,88,3 4,3,34 8,36 5,38 3,4,43 7,455,48 3,5 3,6 3,8 3,9 4, 6, 8,4,6 4,77,9 4,7 4,88,9, 6,, 7,33,4,5 8,66 5,3 8,4 6,4 5,5 4,5 3,6 3,6 4,7 5,8 7,99 6, 7,, 6,, 7,3,3 9,3 5,4 3,4 7, 6, 9,, 4, 6,, 3, 7,, 5 8, 7, 8, 9,, 3, 5, 7, 9, 9, 3, 3, 4, 4, 5, 6, 6, 7, 8, 9,,,,,,, 3, 3, 3, 4,,,,,,,, k 8, 8, 8,3 8,4 8,5 8,6 8,7 8,8 8,9 9,,, 3,, 3,,,,,,,,,,,,,,,,, 5,9 3,8,7 9,77,66,6 4,5 3,5,5 3,6,5,3 6, 9, 4,9 8,8 3,7 8,6 4,5 4,54 9,5,49 7,46,44 8,4 5,39 3,37,35,33 5,88 4,84 7,8,78 6,75 3,7,69 8,66 7,63 7,6 7 6,9,6 9, 6 8,9 4 7,6 6,3 4, 3,97 3,94 5,9 7
7,37,35,33,3,9,7,4,,9,7 8,39,39,38,38,37,36,35,34,33,3 9,5,6,8,9,9,3,3,3,3,3,,4,6,8,,,4,5,7,8,74,77,8,8,85,87,9,9,94,97,5,53,55,57,6,6,65,67,7,7 3,3,33,35,37,39,4,43,45,48,5 4,8,9,,,4,5,7,8,3,3 5,9,,,,3,4,5,6,8,9 6,5,5,6,6,7,7,8,9,, 7,,,,3,3,4,4,4,5,5 8,,,,,,,,,, 9,,,,,,,,,,,,,,,,,,,, 4,,,, 3, 3, 4, 4, 5, 5, 6,,,,,,,,,, 3 k 9, 9, 9,3 9,4 9,5 9,6 9,7 9,8 9,9,,,,,,,,,,,,,,,,,,,,,4,4 9,4 9,3 8,3 7,3 7, 6, 5, 5, 5 3,4 6,33,, 7, 4,,99,8 7,8 5,7 3 4,3,3,8 3,6 5,5 7,4, 3, 7,,8 6 5,58 9,55,53 5,5 9,48 4,46,43 6,4 3,39,37 9 6,88,855,8,79 6,76 3,73,7 9,688,65 8,63 8 7,4,,9,6 3,3 4, 6,98 9,95,9 6,9 8,3 5,88,6,5 4,3 7,,9,7 5,4 8, 9,3,3 6,3 9,3,3,9,8,7,6 8,5 6,9 7, 5,, 6,3,4 3,44,44,5 3,5,99 8,,3 9,4 8,6 5,8,9 5, 9,,3,75,77,79,8 9,84 7,86 3,888,9,9 5,94 7 3,5,54 6,57 9,59,6 4,64 6,66 8,688,7 8,7 8 4,34 6,36 9,38,39 4,4 7,43,45,47 5,5 7,5 9 5,,,3,5 9,6 9,8 9,99,3 9,33,34 6, 8,,3 5,4,55,6,8 7,9 3,, 7 7,6 8,6 7,77,8 7,8 7,9 8,,, 4, 7 8,33,3 9,3 5,4,4 8,55,5 3,6,6 9,7 8 9,, 5, 9,, 6,, 5,3,3 5,3, 5, 7, 9,, 3, 6, 8,, 4, 7, 7, 8, 9,,, 4, 5, 7, 9, 3, 3, 4, 4, 5, 6, 6, 7, 8, 9 3,,,,,,, 3, 3, 4, 4 4,,,,,,,,,
k,, 3, 4, 5, 6, 7, 8, 9,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, 3,3,,,,,,,,, 4,,5,,,,,,,, 5,,,7,3,,,,,, 6,4,5,5,8,4,,,,, 7,64,43,8,7,,6,3,,, 8,88,65,45,3,9,,7,4,, 9,8,87,66,47,3,,3,8,5,,9,4,85,66,48,34,3,5,9,5,9,4,,84,66,49,35,4,6,,9 3,9 4,4,5 4,9,99,98,6 4,8,95 9,66,8,5,65 4,36,5 8,5,37 9,7,7 6 4,7 6,9 6, 9,6, 6,93 4,8 8,65 9,5 8,38 5,53 8,7 5,88,98, 4,99,9,78 5,65 4,5 7 6,36 4,544,7 5,86 9,96 4,99,966,88 6,77,64 6 7,3 7,38 3,55 9,7 6,84,93,96 3,93 4,86,766 8,4 7,5 3,39,55 3,7 7,83 4,9 3,93 6,9 3,84 9,8 5,6 5,77,4 4,55 6,69,8 9,88 6,9,88 4,44,9,7,8 9,4 7,55 9,69 4,79 7,86,888, 6,5 7, 7,9 6,9 8,4 9,56,688,78 6,84 8, 4,3 5,6 9,, 9,3 6,43,56 4,67 3,766 3,,,3 5,7,3 4,,3 3,43,55 6,66 9 4, 6, 6, 7,44,8 3,4 6,,3 8,44 9,55 9 5, 3, 8,, 3,5 3,9 4,5 6,3 8,33,44 7 6,, 4, 4,,5, 4,6 7,4 6,34 6 7,, 5, 3, 9,3 7,6, 4,7 6,5 3 8,,, 7, 6, 4,33,7 9, 3,8 4 9,, 3, 9, 9, 8,4,77, 3,,, 4,, 3, 4,4 7,8 5 3,,, 6, 3, 6,3 9,5 3 3,, 3, 7, 5,,3 4 33,,, 4, 9, 8, 4 34,,, 5, 35,,, 6, 36,, 3, 7 37,,, 4 38,, 39,
III. táblázat Staa omál elozláú valózíűég változó elozláüggvééek táblázata z z z (z z (z z (z z (z z (z..5.5.698468.4.8583.56.946.4.98383..53989.53.7944.5.8534.57.9479.6.98464..57978.54.754.6.85548.58.94947.8.98537.3.5966.55.7884.7.85769.59.94483..98697.4.55953.56.76.8.85999.6.945..98679.5.59939.57.7566.9.8643.6.9463.4.987455.6.539.58.7943..864334.6.947384.6.98889.7.5793.59.745..8665.63.948449.8.988696.8.5388.6.75747..868643.64.949497.3.98976.9.535856.6.7969.3.8776.65.9559.3.98983..53988.6.7337.4.87857.66.95543.34.99358..543795.63.735653.5.87498.67.9554.36.99863..547758.64.73894.6.876976.68.9535.38.99344.3.5577.65.7454.7.879.69.954486.4.998.4.55567.66.745373.8.88.7.955435.4.994.5.55968.67.74857.9.88977.7.956367.44.99656.6.563559.68.75748..88493.7.95784.46.99353.7.567495.69.75493..88686.73.95885.48.99343.8.5744.7.75836..888768.74.9597.5.99379.9.575345.7.7648.3.8965.75.95994.5.9943..5796.7.76437.4.895.76.96796.54.994457..58366.73.76735.5.89435.77.96636.56.994766..58764.74.7735.6.89665.78.9646.58.9956.3.59954.75.773373.7.897958.79.96373.6.995339.4.594835.76.776373.8.89977.8.9647.6.99564.5.59876.77.77935.9.9475.8.96485.64.995855.6.6568.78.7835.3.93.8.9656.66.99693.7.664.79.78536.3.949.83.966375.68.99639.8.66.8.78845.3.9658.84.9676.7.996533.9.649.8.793.33.984.85.967843.7.996736.3.679.8.79389.34.99877.86.968557.74.99698.3.67.83.79673.35.949.87.96958.76.997.3.6556.84.799546.36.9385.88.969946.78.9978.33.693.85.8337.37.94657.89.976.8.997445.34.6337.86.855.38.967.9.9783.8.997599.35.63683.87.8785.39.97736.9.97933.84.997744.36.64576.88.857.4.9943.9.9757.86.99788.37.64439.89.8367.4.973.93.97397.88.998.38.6487.9.8594.4.996.94.9738.9.99834.39.6573.9.88589.43.9364.95.9744.9.9985.4.6554.9.84.44.9566.96.975.94.998359.4.65997.93.8384.45.9647.97.97558.96.99846.4.66757.94.8639.46.97855.98.97648.98.998559.43.6664.95.88944.47.999.99.97675 3..99865.44.673.96.8347.48.93563..9775 3..99933.45.673645.97.833977.49.93888..9778 3.4.999663.46.6774.98.836457.5.93393..97838 3.6.99984.47.688.99.83893.5.934478.4.97935 3.8.99998.48.684386..84345.5.935745.6.983 4..999968.49.687933..84375.53.93699.8.9837.5.6946..84636.54.938..9836.5.694974.3.848495.55.93949..98997 3
IV. táblázat -elozlá DF.5..5.5..5.5.75.9.95.975.99.995 7.879 6.635 5.4 3.84.76.33.455..6.4....597 9. 7.378 5.99 4.65.773.386.575..3.5.. 3.838.345 9.348 7.85 6.5 4.8.366.3.584.35.6.5.7 4 4.86 3.77.43 9.488 7.779 5.385 3.357.93.64.7.484.97.7 5 6.75 5.86.83.7 9.36 6.66 4.35.675.6.45.83.554.4 6 8.548 6.8 4.449.59.645 7.84 5.348 3.455.4.635.37.87.676 7.78 8.475 6.3 4.67.7 9.37 6.346 4.55.833.67.69.39.989 8.955.9 7.535 5.57 3.36.9 7.344 5.7 3.49.733.8.647.344 9 3.589.666 9.3 6.99 4.684.389 8.343 5.899 4.68 3.35.7.88.735 5.88 3.9.483 8.37 5.987.549 9.34 6.737 4.865 3.94 3.47.558.56 6.757 4.75.9 9.675 7.75 3.7.34 7.584 5.578 4.575 3.86 3.53.63 8.3 6.7 3.337.6 8.549 4.845.34 8.438 6.34 5.6 4.44 3.57 3.74 3 9.89 7.688 4.736.36 9.8 5.984.34 9.99 7.4 5.89 5.9 4.7 3.565 4 3.39 9.4 6.9 3.685.64 7.7 3.339.65 7.79 6.57 5.69 4.66 4.75 5 3.8 3.578 7.488 4.996.37 8.45 4.339.37 8.547 7.6 6.6 5.9 4.6 6 34.67 3. 8.845 6.96 3.54 9.369 5.338.9 9.3 7.96 6.98 5.8 5.4 7 35.78 33.49 3.9 7.587 4.769.489 6.338.79.85 8.67 7.564 6.48 5.697 8 37.56 34.85 3.56 8.869 5.989.65 7.338 3.675.865 9.39 8.3 7.5 6.65 9 38.58 36.9 3.85 3.44 7.4.78 8.338 4.56.65.7 8.97 7.633 6.844 39.997 37.566 34.7 3.4 8.4 3.88 9.337 5.45.443.85 9.59 8.6 7.434 4.4 38.93 35.479 3.67 9.65 4.935.337 6.344 3.4.59.83 8.897 8.34 4.796 4.89 36.78 33.94 3.83 6.39.337 7.4 4.4.338.98 9.54 8.643 3 44.8 4.638 38.76 35.7 3.7 7.4.337 8.37 4.848 3.9.689.96 9.6 4 45.558 4.98 39.364 36.45 33.96 8.4 3.337 9.37 5.659 3.848.4.856 9.886 5 46.98 44.34 4.646 37.65 34.38 9.339 4.337 9.939 6.473 4.6 3..54.5 6 48.9 45.64 4.93 38.885 35.563 3.435 5.336.843 7.9 5.379 3.844.98.6 7 49.645 46.963 43.95 4.3 36.74 3.58 6.336.749 8.4 6.5 4.573.878.88 8 5.994 48.78 44.46 4.337 37.96 3.6 7.336.657 8.939 6.98 5.38 3.565.46 9 5.335 49.588 45.7 4.557 39.87 33.7 8.336 3.567 9.768 7.78 6.47 4.56 3. 3 53.67 5.89 46.979 43.773 4.56 34.8 9.336 4.478.599 8.493 6.79 4.953 3.787 4 66.766 63.69 59.34 55.758 5.85 45.66 39.335 33.66 9.5 6.59 4.433.64.77 5 79.49 76.54 7.4 67.55 63.67 56.334 49.335 4.94 37.689 34.764 3.357 9.77 7.99 6 9.95 88.379 83.98 79.8 74.397 66.98 59.335 5.94 46.459 43.88 4.48 37.485 35.534 7 4..43 95.3 9.53 85.57 77.577 69.334 6.698 55.39 5.739 48.758 45.44 43.75 8 6.3.33 6.63.88 96.578 88.3 79.334 7.45 64.78 6.39 57.53 53.54 5.7 9 8.3 4. 8.4 3.5 7.57 98.65 89.334 8.65 73.9 69.6 65.647 6.754 59.96 4.7 35.8 9.56 4.34 8.5 9.4 99.334 9.33 8.358 77.99 74. 7.65 67.38 4
V. táblázat Stuet- (t- elozlá t DF t.995 t.99 t.975 t.95 t.9 t.8 t.75 t.7 t.6 63.657 3.8.76 6.34 3.78.376..77.35 9.95 6.965 4.33.9.886.6.87.67.89 3 5.84 4.54 3.8.353.638.978.765.584.77 4 4.64 3.747.776.3.533.94.74.569.7 5 4.3 3.365.57.5.476.9.77.559.67 6 3.77 3.43.447.943.44.96.78.553.65 7 3.499.998.365.895.45.896.7.549.63 8 3.355.896.36.86.397.889.76.546.6 9 3.5.8.6.833.383.883.73.543.6 3.69.764.8.8.37.879.7.54.6 3.6.78..796.363.876.697.54.6 3.55.68.79.78.356.873.695.539.59 3 3..65.6.77.35.87.694.538.59 4.977.64.45.76.345.868.69.537.58 5.947.6.3.753.34.866.69.536.58 6.9.583..746.337.865.69.535.58 7.898.567..74.333.863.689.534.57 8.878.55..734.33.86.688.534.57 9.86.539.93.79.38.86.688.533.57.845.58.86.75.35.86.687.533.57.83.58.8.7.33.859.686.53.57.89.58.74.77.3.858.686.53.56 3.87.5.69.74.39.858.685.53.56 4.797.49.64.7.38.857.685.53.56 5.787.485.6.78.36.856.684.53.56 6.779.479.56.76.35.856.684.53.56 7.77.473.5.73.34.855.684.53.56 8.763.467.48.7.33.855.683.53.56 9.756.46.45.699.3.854.683.53.56 3.75.457.4.697.3.854.683.53.56 35.74.438.3.69.36.85.68.59.55 4.74.43..684.33.85.68.59.55 5.678.43.9.676.99.849.679.58.55 6.66.39..67.96.848.679.57.54.67.358.98.658.89.845.677.56.54.576.36.96.645.8.84.674.54.53 5
VI. táblázat =,5 =. 55 F-elozlá ( =,5 DF DF F 3 4 5 6 7 8 9 5 4 3 4 6 6 99 6 5 3 34 37 39 4 4 44 46 48 49 5 5 5 53 54 8.5 9. 9. 9.3 9.3 9.3 9.4 9.4 9.4 9.4 9.4 9.4 9.5 9.5 9.5 9.5 9.5 9.5 9.5 3. 9.55 9.8 9. 9. 8.94 8.89 8.85 8.8 8.79 8.74 8.7 8.67 8.64 8.6 8.59 8.57 8.55 8.53 4 7.7 6.94 6.59 6.39 6.6 6.6 6.9 6.4 6. 5.96 5.9 5.86 6.4 5.77 5.75 5.7 5.69 5.66 5.63 5 6.6 5.79 5.4 5.9 5.5 4.95 4.88 4.8 4.77 4.74 4.68 4.6 4.95 4.53 4.5 4.46 4.43 4.4 4.37 6 5.99 5.4 4.76 4.53 4.39 4.8 4. 4.5 4. 4.6 4. 3.94 4.53 3.84 3.8 3.77 3.74 3.7 3.67 7 5.59 4.74 4.35 4. 3.97 3.87 3.79 3.73 3.68 3.64 3.57 3.5 4. 3.4 3.38 3.34 3.3 3.7 3.3 8 5.3 4.46 4.7 3.84 3.69 3.58 3.5 3.44 3.39 3.35 3.8 3. 3.84 3. 3.8 3.4 3..97.93 9 5. 4.6 3.86 3.63 3.48 3.37 3.9 3.3 3.8 3.4 3.7 3. 3.86.9.86.83.79.75.7 4.96 4. 3.7 3.48 3.33 3. 3.4 3.7 3..98.9.85 3.7.74.7.66.6.58.54 4.84 3.98 3.59 3.36 3. 3.9 3..95.9.85.79.7 3.59.6.57.53.49.45.4 4.75 3.89 3.49 3.6 3. 3..9.85.8.75.69.6 3.49.5.47.43.38.34.3 3 4.67 3.8 3.4 3.8 3.3.9.83.77.7.67.6.53 3.4.4.38.34.3.5. 4 4.6 3.74 3.34 3..96.85.76.7.65.6.53.46 3.34.35.3.7..8.3 5 4.54 3.68 3.9 3.6.9.79.7.64.59.54.48.4 3.9.9.5..6..7 6 4.49 3.63 3.4 3..85.74.66.59.54.49.4.35 3.4.4.9.5..6. 7 4.45 3.59 3..96.8.7.6.55.49.45.38.3 3..9.5..6..96 8 4.4 3.55 3.6.93.77.66.58.5.46.4.34.7 3.6.5..6..97.9 9 4.38 3.5 3.3.9.74.63.54.48.4.38.3.3 3.3..7.3.98.93.88 4.35 3.49 3..87.7.6.5.45.39.35.8. 3..8.4.99.95.9.84 4.3 3.47 3.7.84.68.57.49.4.37.3.5.8 3.7.5..96.9.87.8 4.3 3.44 3.5.8.66.55.46.4.34.3.3.5 3.5.3.98.94.89.84.78 3 4.8 3.4 3.3.8.64.53.44.37.3.7..3 3.3..96.9.86.8.76 4 4.6 3.4 3..78.6.5.4.36.3.5.8. 3..98.94.89.84.79.73 5 4.4 3.39.99.76.6.49.4.34.8.4.6.9.99.96.9.87.8.77.7 6 4.3 3.37.98.74.59.47.39.3.7..5.7 3.37.95.9.85.8.75.69 7 4. 3.35.96.73.57.46.37.3.5..3.6.96.93.88.84.79.73.67 8 4. 3.34.95.7.56.45.36.9.4.9..4 3.34.9.87.8.77.7.65 9 4.8 3.33.93.7.55.43.35.8..8..3.93.9.85.8.75.7.64 3 4.7 3.3.9.69.53.4.33.7..6.9. 3.3.89.84.79.74.68.6 4 4.8 3.3.84.6.45.34.5.8..8..9.84.79.74.69.64.58.5 6 4. 3.5.76.53.37.5.7..4.99.9.84 3.5.7.65.59.53.47.39 3.9 3.7.68.45.9.8.9..96.9.83.75.68.6.55.5.43.35.5 3.84 3..6.37....94.88.83.75.67 3..5.46.39.3..3 6
VII. táblázat =, =. F-elozlá ( =, DF DF F 3 4 5 6 7 8 9 5 4 3 4 6 45 4999 544 564 5764 5859 598 598 6 656 67 657 69 634 66 686 633 634 6366 98.5 99. 99. 99.3 99.3 99.3 99.4 99.4 99.4 99.4 99.4 99.4 99.4 99.5 99.5 99.5 99.5 99.5 99.5 3 34. 3.8 9.5 8.7 8. 7.9 7.7 7.5 7.3 7. 7. 6.9 6.7 6.6 6.5 6.4 6.3 6. 6. 4. 8. 6.7 6. 5.5 5. 5. 4.8 4.7 4.5 4.4 4. 4. 3.9 3.8 3.7 3.7 3.6 3.5 5 6.3 3.3..4..7.5.3.. 9.9 9.7 9.6 9.5 9.4 9.3 9. 9. 9. 6 3.7.9 9.78 9.5 8.75 8.47 8.6 8. 7.98 7.87 7.7 7.56 7.4 7.3 7.3 7.4 7.6 6.97 6.88 7. 9.55 8.45 7.85 7.46 7.9 6.99 6.84 6.7 6.6 6.47 6.3 6.6 6.7 5.99 5.9 5.8 5.74 5.65 8.3 8.65 7.59 7. 6.63 6.37 6.8 6.3 5.9 5.8 5.67 5.5 5.36 5.8 5. 5. 5.3 4.95 4.86 9.6 8. 6.99 6.4 6.6 5.8 5.6 5.47 5.35 5.6 5. 4.96 4.8 4.73 4.65 4.57 4.48 4.4 4.3. 7.56 6.55 5.99 5.64 5.39 5. 5.6 4.94 4.85 4.7 4.56 4.4 4.33 4.5 4.7 4.8 4. 3.9 9.65 7. 6. 5.67 5.3 5.7 4.89 4.74 4.63 4.54 4.4 4.5 4. 4. 3.94 3.86 3.78 3.69 3.6 9.33 6.93 5.95 5.4 5.6 4.8 4.64 4.5 4.39 4.3 4.6 4. 3.86 3.78 3.7 3.6 3.54 3.45 3.36 3 9.7 6.7 5.74 5. 4.86 4.6 4.44 4.3 4.9 4. 3.96 3.8 3.66 3.59 3.5 3.43 3.34 3.5 3.7 4 8.86 6.5 5.56 5.4 4.69 4.46 4.8 4.4 4.3 3.94 3.8 3.66 3.5 3.43 3.35 3.7 3.8 3.9 3. 5 8.68 6.36 5.4 4.89 4.56 4.3 4.4 4. 3.89 3.8 3.67 3.5 3.37 3.9 3. 3.3 3.5.96.87 6 8.53 6.3 5.9 4.77 4.44 4. 4.3 3.89 3.78 3.69 3.55 3.4 3.6 3.8 3. 3..93.84.75 7 8.4 6. 5.9 4.67 4.34 4. 3.93 3.79 3.68 3.59 3.46 3.3 3.6 3.8 3..9.83.75.65 8 8.9 6. 5.9 4.58 4.5 4. 3.84 3.7 3.6 3.5 3.37 3.3 3.8 3..9.84.75.66.57 9 8.8 5.93 5. 4.5 4.7 3.94 3.77 3.63 3.5 3.43 3.3 3.5 3..9.84.76.67.58.49 8. 5.85 4.94 4.43 4. 3.87 3.7 3.56 3.46 3.37 3.3 3.9.94.86.78.69.6.5.4 8. 5.78 4.87 4.37 4.4 3.8 3.64 3.5 3.4 3.3 3.7 3.3.88.8.7.64.55.46.36 7.95 5.7 4.8 4.3 3.99 3.76 3.59 3.45 3.35 3.6 3..98.83.75.67.58.5.4.3 3 7.88 5.66 4.76 4.6 3.94 3.7 3.54 3.4 3.3 3. 3.7.93.78.7.6.54.45.35.6 4 7.8 5.6 4.7 4. 3.9 3.67 3.5 3.36 3.6 3.7 3.3.89.74.66.58.49.4.3. 5 7.77 5.57 4.68 4.8 3.85 3.63 3.46 3.3 3. 3.3.99.85.7.6.54.45.36.7.7 6 7.7 5.53 4.64 4.4 3.8 3.59 3.4 3.9 3.8 3.9.96.8.66.58.5.4.33.3.3 7 7.68 5.49 4.6 4. 3.78 3.56 3.39 3.6 3.5 3.6.93.78.63.55.47.38.9.. 8 7.64 5.45 4.57 4.7 3.75 3.53 3.36 3.3 3. 3.3.9.75.6.5.44.35.6.7.7 9 7.6 5.4 4.54 4.4 3.73 3.5 3.33 3. 3.9 3..87.73.57.49.4.33.3.4.4 3 7.56 5.39 4.5 4. 3.7 3.47 3.3 3.7 3.7.98.84.7.55.47.39.3... 4 7.3 5.8 4.3 3.83 3.5 3.9 3..99.89.8.66.5.37.9....9.8 6 7.8 4.98 4.3 3.65 3.34 3..95.8.7.63.5.35...3.94.84.73.6 6.85 4.79 3.95 3.48 3.7.96.79.66.56.47.34.9.3.95.86.76.66.53.38 6.64 4.6 3.78 3.3 3..8.64.5.4.3.9.4.88.79.7.59.47.33.4 7
VIII. táblázat: Coha-óba (α=5% DF 3 4 5 6 7 8 9 5 4 3 4 6 -,96,9,85,79,7,68,64,59,55,48,39,34,8,3,7,,98,89,76,69,63,57,5,48,45,395,34,8,4,,6,5,67 3,96,8,68,6,55,5,44,4,38,335,85,3,,6,3,9,53 4,9,77,63,56,495,44,39,37,34,95,45,,7,4,,78,43 5,9,73,58,5,455,4,36,335,3,7,,8,5,5,98,68,38 6,86,7,56,48,4,37,335,3,9,45,,65,35,,87,6,33 7,85,68,53,46,4,355,3,95,7,3,9,55,3,5,83,57,3 8,83,65,5,44,38,34,35,8,55,,8,45,,98,76,5,39 9,8,63,5,4,37,35,9,7,45,,7,35,5,9,7,49,38,79,6,48,4,355,3,8,6,35,,6,3,,88,67,47,36,77,58,46,39,34,9,7,45,5,9,5,,5,8,63,43,34 4,75,56,445,375,33,8,55,35,5,8,45,5,98,78,58,4,33 6,73,54,43,365,35,7,5,5,5,75,38,,9,75,55,4,3 8,7,53,4,355,35,6,45,,,7,33,5,9,7,53,38,3,7,5,4,35,95,55,35,5,95,65,3,,87,7,5,37,35 5,68,5,395,34,9,45,3,5,85,55,,98,83,67,5,36,3 3,67,49,38,33,8,35,5,,75,45,8,9,8,63,48,34,3 4,65,47,365,3,65,,5,85,6,35,,85,74,58,45,3,9 5,63,44,35,95,5,,95,75,5,5,5,8,7,55,43,3,8 6,6,43,34,85,4,5,85,65,45,,98,75,65,5,4,8,7 9,58,4,3,65,5,9,7,5,3,,9,7,58,47,37,6,5,56,39,3,5,5,75,6,4,5,,85,65,55,44,35,4,4 4,53,37,8,5,9,6,4,3,,9,75,55,48,38,3,,,49,33,5,9,7,35,,,95,75,65,49,4,3,5,8, 8
I. táblázat: Coha-óba (α=% DF 3 4 5 6 7 8 9 5 4 3 4 6 -,96,94,93,88,83,78,74,69,65,56,46,4,355,9,5,5,,9,85,8,7,67,6,58,54,48,4,34,95,55,,45,89 3,98,87,78,7,63,57,53,48,45,4,34,8,35,5,58,5,7 4,97,84,7,63,56,5,46,45,395,355,95,4,5,7,35,95,57 5,95,8,67,58,5,46,45,39,36,3,65,,8,5,,85,5 6,93,77,64,55,48,43,39,36,33,9,4,9,6,38,,75,43 7,9,75,6,5,45,4,37,34,3,75,5,75,5,3,,7,4 8,9,7,59,49,43,385,35,3,95,55,,65,4,,93,64,36 9,88,69,57,47,4,37,335,35,8,45,95,55,35,,87,59,33,87,68,55,46,4,36,3,9,7,3,9,5,3,8,83,56,3,85,65,53,44,38,34,35,7,5,,75,38,,98,76,5,8 4,83,63,5,4,36,35,9,55,35,5,65,3,,9,7,47,6 6,8,6,48,4,35,35,7,45,5,95,55,3,8,87,66,45,4 8,8,59,47,39,34,3,65,35,,9,5,,3,85,64,43,3,78,58,46,38,33,9,55,5,,8,45,5,98,8,6,4, 5,76,56,44,37,3,7,45,5,,7,35,,94,77,58,39, 3,75,53,4,35,3,55,3,,85,6,3,5,88,7,53,37,9 4,7,5,4,33,75,35,,9,7,5,,95,8,66,5,34,8 5,69,48,38,35,6,,,75,6,4,,9,75,6,47,3,7 6,68,47,36,35,5,,9,65,5,3,7,85,7,57,45,3,6 9,65,44,34,8,3,9,7,5,38,,95,76,6,5,4,7,5,6,4,35,6,5,8,6,4,3,,87,7,57,47,36,5,4 4,57,38,8,35,9,55,4,5,5,38,76,6,5,4,3,,,5,3,5,,7,35,5,,98,5,6,49,4,34,4,8, 9