17_Приложение_Таблицы
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Приложения |
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11 |
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28 |
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1,175 |
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1,701 |
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2,048 |
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2,467 |
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2,763 |
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3,047 |
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3,408 |
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3,674 |
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1,313 |
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29 |
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1,174 |
1,311 |
1,699 |
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2,045 |
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2,462 |
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2,756 |
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3,038 |
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3,396 |
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3,660 |
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30 |
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1,173 |
1,310 |
1,697 |
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2,042 |
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2,457 |
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2,750 |
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3,030 |
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3,385 |
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3,646 |
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40 |
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1,167 |
1,303 |
1,684 |
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2,021 |
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2,423 |
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2,704 |
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2,971 |
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3,307 |
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3,551 |
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50 |
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1,164 |
1,299 |
1,676 |
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2,009 |
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2,403 |
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2,678 |
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2,937 |
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3,261 |
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3,496 |
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60 |
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1,162 |
1,296 |
1,671 |
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2,000 |
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2,390 |
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2,660 |
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2,915 |
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3,232 |
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3,460 |
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70 |
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1,160 |
1,294 |
1,667 |
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1,994 |
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2,381 |
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2,648 |
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2,899 |
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3,211 |
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3,435 |
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80 |
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1,159 |
1,292 |
1,664 |
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1,990 |
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2,374 |
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2,639 |
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2,887 |
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3,195 |
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3,416 |
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90 |
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1,158 |
1,291 |
1,662 |
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1,987 |
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2,368 |
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2,632 |
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2,878 |
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3,183 |
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3,402 |
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100 |
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1,157 |
1,290 |
1,660 |
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1,984 |
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2,364 |
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2,626 |
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2,871 |
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3,174 |
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3,390 |
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200 |
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1,154 |
1,286 |
1,653 |
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1,972 |
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2,345 |
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2,601 |
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2,838 |
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3,131 |
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3,340 |
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12
ПРИЛОЖЕНИЕ 5
F-распределение Фишера-Снедекора
Приложения |
13 |
ПРИЛОЖЕНИЕ 5 (продолжение)
14
ПРИЛОЖЕНИЕ 5 (продолжение)
Таблица 5
Квантили F-распределения Фишера-Снедекора k1 - число степеней свободы большей дисперсии (числитель) k2 - число степеней свободы меньшей дисперсии (знаменатель)
Уровень значимости a = 0,01
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k1 |
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k2 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
1 |
4052,24999,35403,55624,3 |
5764 |
5859 5928,3 5981 6022,46055,96083,46106,76125,8 6143 |
6157 |
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2 |
98,502 |
99 |
99,16499,25199,30299,33199,35799,375 99,39 99,39799,40899,41999,42299,42699,433 |
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3 |
34,11630,81629,457 28,71 28,23727,91127,67127,48927,34527,22827,13227,05226,98326,92426,872 |
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4 |
21,198 |
18 |
16,69415,97715,52215,20714,97614,79914,65914,54614,45214,37414,30614,24914,198 |
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5 |
16,25813,274 |
12,06 |
11,392 |
10,96710,67210,45610,28910,15810,0519,96269,88839,8248 |
9,77 |
9,7223 |
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6 |
13,74510,9259,77969,14848,7459 8,466 |
8,26 |
8,1017 7,976 7,87427,78967,71837,6575 7,605 |
7,559 |
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7 |
12,2469,54658,45137,84677,46047,19146,99296,84016,71886,62016,53816,4691 |
6,41 |
6,359 6,3144 |
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8 |
11,2598,6491 |
7,591 |
7,00616,63186,37076,17766,02885,91065,81435,73435,66675,60895,55885,5152 |
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9 |
10,5628,0215 |
6,992 |
6,42216,05695,80185,61285,46715,35115,25655,17795,11155,05455,00524,9621 |
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10 |
10,0447,55956,55235,99445,63645,38585,20015,05674,94244,84914,77164,70584,64964,60084,5582 |
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11 |
9,64617,20576,21675,6683 |
5,316 5,0692 4,886 4,74454,63154,53934,46244,39744,34164,29334,2509 |
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12 |
9,33036,92665,95255,41195,06444,82054,63954,49944,38754,29614,21984,15534,09984,05174,0096 |
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13 |
9,07386,70095,73945,20534,86164,6203 4,441 4,30214,19114,10034,02453,96033,90523,85733,8154 |
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14 |
8,86176,51495,56395,0354 |
4,695 4,45584,2779 |
4,14 |
4,02973,9394 3,864 3,80023,74523,69763,6557 |
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15 |
8,68326,3588 |
5,417 |
4,89324,55564,31834,14164,00443,89483,80493,72993,66623,61153,56393,5222 |
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16 |
8,53096,22635,29224,77264,43744,20164,02593,88963,78043,69093,61623,55273,49813,4506 3,409 |
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17 |
8,39986,1121 |
5,185 |
4,6689 |
4,336 4,10153,92673,79093,68233,59313,51853,45523,40073,35333,3117 |
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18 |
8,28556,01295,0919 4,579 4,24794,01463,84063,70543,59713,50813,43383,37063,31623,26893,2273 |
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19 |
8,185 5,92595,01034,50024,17083,93863,76533,63053,52253,43383,35963,29653,24223,19493,1533 |
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20 |
8,096 |
5,849 4,93824,43074,10273,87143,69873,56443,45673,36823,29413,23113,17693,1296 3,088 |
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Приложения |
15 |
ПРИЛОЖЕНИЕ 5 (продолжение)
Уровень значимости a = 0,02
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k1 |
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k2 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
1 |
1012,51249,51350,51405,81440,61464,41481,8 1495 1505,41513,71520,61526,31531,21535,4 |
1539 |
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2 |
48,505 |
49 |
49,16549,24949,29849,33249,35649,37349,38749,39849,40749,41549,42249,427 |
49,431 |
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3 |
20,61818,858 18,11 17,69417,42917,245 17,11 17,00716,926 16,86 16,80516,759 16,72 16,686 |
16,657 |
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4 |
14,04 12,14211,34310,89910,61610,41910,27410,16210,07410,0039,94369,89389,85149,8148 |
9,7829 |
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5 |
11,3239,45448,6702 8,233 |
7,953 7,75767,6137 7,503 7,41517,34387,28477,23487,19237,1555 |
7,1234 |
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6 |
9,87648,0521 7,287 6,85946,58476,39286,25086,14156,05465,98395,92525,87575,83345,7968 |
5,7648 |
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7 |
8,98777,20266,45396,03475,76475,57565,43555,32735,24135,17125,11285,06365,0214 |
4,985 |
4,9531 |
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8 |
8,38956,63665,90145,48895,22275,03594,8972 |
4,79 |
4,70464,63484,57684,52774,48574,4493 |
4,4174 |
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9 |
7,9605 6,234 5,50975,10274,83954,65454,51694,41054,3255 4,256 4,19824,14934,10734,0709 |
4,039 |
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10 |
7,63845,93365,21824,8157 4,555 4,37144,23474,12884,0442 3,975 3,91733,86843,8264 |
3,79 |
3,7581 |
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11 |
7,38795,70124,99324,59434,33574,15334,01743,91193,82753,75843,70083,65193,60993,5735 |
3,5415 |
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12 |
7,18775,51634,81454,41874,16173,9804 3,845 3,73983,65573,5867 3,529 3,48023,43813,4017 |
3,3696 |
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13 |
7,02415,36574,6692 4,276 4,02053,83993,70513,60013,51613,44723,38963,34073,2986 |
3,262 |
3,2299 |
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14 |
6,88795,24074,54884,15783,90363,72373,58923,48453,40063,33173,27413,2252 3,183 3,1464 |
3,1142 |
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15 |
6,77295,13554,44744,05843,8052 3,626 3,49183,38733,30353,2346 3,177 |
3,128 3,0858 |
3,049 |
3,0168 |
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16 |
6,67445,04554,36093,97373,72143,54263,40873,30443,22063,15183,0941 3,045 3,0028 |
2,966 |
2,9336 |
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17 |
6,58924,96784,28633,90063,64913,47073,33713,23293,14923,08033,02262,97352,93122,8943 |
2,8619 |
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18 |
6,51474,90014,22133,83683,58613,40813,27473,17063,0869 3,018 2,96032,91122,86882,8318 |
2,7993 |
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19 |
6,449 4,84044,16413,78093,53073,35313,21993,11593,03222,96332,90552,85632,81392,7769 |
2,7443 |
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20 |
6,39074,78764,11343,73133,48173,30443,17133,06742,98372,9148 2,857 2,80772,76522,7281 |
2,6955 |
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16
ПРИЛОЖЕНИЕ 5 (продолжение)
Уровень значимости a = 0,05
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k1 |
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k2 |
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1 |
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6 |
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9 |
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11 |
12 |
13 |
14 |
15 |
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1161,45 199,5 215,71224,58230,16233,99236,77238,88240,54241,88242,98 243,9 244,69245,36245,95
218,513 19 19,16419,24719,29619,32919,35319,37119,38519,39619,40519,41219,41919,42419,429
310,1289,55219,27669,11729,01348,94078,88678,84528,81238,78558,76338,74478,72868,71498,7028
47,70866,94436,59146,38826,25616,16316,0942 6,041 5,99885,96445,93585,91175,89115,87335,8578
56,60795,78615,40945,19225,05034,95034,87594,81834,77254,7351 4,704 4,67774,65524,63584,6188
6 |
5,98745,14324,75714,53374,38744,28394,20674,1468 4,099 |
4,06 |
4,02743,99993,97643,95593,9381 |
75,59154,73744,34684,12033,9715 3,866 3,78713,72573,67673,6365 3,603 3,57473,55033,52923,5107
85,3176 4,459 4,06623,83793,68753,58063,50053,43813,38813,34723,31293,2839 3,259 3,23743,2184
95,11744,25653,86253,63313,48173,37383,29273,22963,17893,13733,10253,07293,04753,02553,0061
10 4,96464,10283,7083 3,478 3,32583,21723,13553,07173,02042,9782 2,943 2,913 2,88722,8647 2,845
11 4,84433,98233,58743,35673,20393,09463,0123 2,948 2,89622,85362,81792,78762,76142,73862,7186
12 4,74723,88533,49033,25923,10592,99612,91342,84862,79642,75342,71732,68662,66022,63712,6169
13 4,66723,80563,41053,17913,02542,91532,83212,76692,7144 2,671 2,63462,60372,57692,55362,5331
14 4,60013,73893,34393,11222,95822,84772,76422,69872,64582,60222,56552,53422,50732,4837 2,463
15 4,54313,68233,28743,05562,90132,79052,70662,64082,58762,54372,50682,47532,44812,42442,4034
16 4,494 3,63373,23893,00692,85242,74132,65722,59112,53772,49352,45642,42472,39732,37332,3522
17 4,45133,59153,19682,9647 2,81 2,69872,6143 2,548 2,49432,44992,41262,38072,3531 2,329 2,3077
18 4,41393,55463,15992,92772,77292,66132,57672,51022,45632,41172,37422,34212,3143 2,29 2,2686
19 4,38083,52193,12742,89512,74012,62832,54352,47682,42272,37792,3402 2,308 2,28 2,25562,2341
20 4,35133,49283,09842,86612,7109 2,599 2,514 2,44712,39282,3479 2,31 2,27762,2495 2,225 2,2033
Приложения |
17 |
ПРИЛОЖЕНИЕ 5 (продолжение)
Уровень значимости a = 0,1
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k1 |
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k2 |
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11 |
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15 |
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139,864 49,5 53,593 55,833 57,24 58,204 58,906 59,439 59,857 60,195 60,473 60,705 60,902 61,073 61,22
28,5263 9 9,1618 9,2434 9,2926 9,3255 9,3491 9,3668 9,3805 9,3916 9,4006 9,4082 9,4145 9,42 9,4247
35,5383 5,4624 5,3908 5,3427 5,3091 5,2847 5,2662 5,2517 5,24 5,2304 5,2224 5,2156 5,2098 5,2047 5,2003
44,5448 4,3246 4,1909 4,1072 4,0506 4,0097 3,979 3,9549 3,9357 3,9199 3,9067 3,8955 3,8859 3,8776 3,8704
54,0604 3,7797 3,6195 3,5202 3,453 3,4045 3,3679 3,3393 3,3163 3,2974 3,2816 3,2682 3,2567 3,2468 3,238
63,776 3,4633 3,2888 3,1808 3,1075 3,0546 3,0145 2,983 2,9577 2,9369 2,9195 2,9047 2,892 2,8809 2,8712
73,5894 3,2574 3,0741 2,9605 2,8833 2,8274 2,7849 2,7516 2,7247 2,7025 2,6839 2,6681 2,6545 2,6426 2,6322
83,4579 3,1131 2,9238 2,8064 2,7264 2,6683 2,6241 2,5893 2,5612 2,538 2,5186 2,502 2,4876 2,4752 2,4642
93,3603 3,0064 2,8129 2,6927 2,6106 2,5509 2,5053 2,4694 2,4403 2,4163 2,3961 2,3789 2,364 2,351 2,3396
10 3,285 2,9245 2,7277 2,6053 2,5216 2,4606 2,414 2,3771 2,3473 2,3226 2,3018 2,2841 2,2687 2,2553 2,2435
11 3,2252 2,8595 2,6602 2,5362 2,4512 2,3891 2,3416 2,304 2,2735 2,2482 2,2269 2,2087 2,193 2,1792 2,1671
12 3,1766 2,8068 2,6055 2,4801 2,394 2,331 2,2828 2,2446 2,2135 2,1878 2,166 2,1474 2,1313 2,1173 2,1049
13 3,1362 2,7632 2,5603 2,4337 2,3467 2,283 2,2341 2,1953 2,1638 2,1376 2,1155 2,0966 2,0802 2,0658 2,0532
14 3,1022 2,7265 2,5222 2,3947 2,3069 2,2426 2,1931 2,1539 2,122 2,0954 2,073 2,0537 2,037 2,0224 2,0095
15 3,0732 2,6952 2,4898 2,3614 2,273 2,2081 2,1582 2,1185 2,0862 2,0593 2,0366 2,0171 2,0001 1,9853 1,9722
16 3,0481 2,6682 2,4618 2,3327 2,2438 2,1783 2,128 2,088 2,0553 2,0281 2,0051 1,9854 1,9682 1,9532 1,9399
17 3,0262 2,6446 2,4374 2,3077 2,2183 2,1524 2,1017 2,0613 2,0284 2,0009 1,9777 1,9577 1,9404 1,9252 1,9117
18 3,007 2,6239 2,416 2,2858 2,1958 2,1296 2,0785 2,0379 2,0047 1,977 1,9535 1,9333 1,9158 1,9004 1,8868
19 2,9899 2,6056 2,397 2,2663 2,176 2,1094 2,058 2,0171 1,9836 1,9557 1,9321 1,9117 1,894 1,8785 1,8647
20 2,9747 2,5893 2,3801 2,2489 2,1582 2,0913 2,0397 1,9985 1,9649 1,9367 1,9129 1,8924 1,8745 1,8588 1,8449
18
ПРИЛОЖЕНИЕ 6
Критерий Колмогорова
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∞ |
K (x)= lim P (λn < x)=1+2∑(−1)k e−2k2 x2 , x ≥ 0 . |
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n→∞ |
k =1 |
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Приложения |
19 |
ПРИЛОЖЕНИЕ 6 (продолжение)
x |
K(x) |
x |
K(x) |
x |
K(x) |
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0.200 |
5.0515148e-13 |
0.825 |
0.4959458 |
1.450 |
0.9701585 |
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0.225 |
2.9067959e-10 |
0.850 |
0.5346808 |
1.475 |
0.9742187 |
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0.250 |
2.6823810e-8 |
0.875 |
0.5718426 |
1.500 |
0.9777820 |
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0.275 |
7.4978976e-7 |
0.900 |
0.6072693 |
1.525 |
0.9809007 |
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0.300 |
9.3058013e-6 |
0.925 |
0.6408494 |
1.550 |
0.9836226 |
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0.325 |
6.5259653e-5 |
0.950 |
0.6725145 |
1.575 |
0.9859917 |
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0.350 |
3.0285263e-4 |
0.975 |
0.7022323 |
1.600 |
0.9880480 |
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0.375 |
1.0351449e-3 |
1.000 |
0.7300003 |
1.625 |
0.9898279 |
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0.400 |
2.8076732e-3 |
1.025 |
0.7558406 |
1.650 |
0.9913643 |
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0.425 |
6.3737237e-3 |
1.050 |
0.7797944 |
1.675 |
0.9926870 |
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0.450 |
0.0125894 |
1.075 |
0.8019187 |
1.700 |
0.9938226 |
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0.475 |
0.0222693 |
1.100 |
0.8222818 |
1.725 |
0.9947948 |
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0.500 |
0.0360548 |
1.125 |
0.8409611 |
1.750 |
0.9956250 |
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0.525 |
0.0543280 |
1.150 |
0.8580401 |
1.775 |
0.9963320 |
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0.550 |
0.0771832 |
1.175 |
0.8736065 |
1.800 |
0.9969324 |
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0.575 |
0.1044449 |
1.200 |
0.8877503 |
1.825 |
0.9974409 |
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0.600 |
0.1357172 |
1.225 |
0.9005625 |
1.850 |
0.9978705 |
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0.625 |
0.1704469 |
1.250 |
0.9121336 |
1.875 |
0.9982323 |
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0.650 |
0.2079870 |
1.275 |
0.9225530 |
1.900 |
0.9985364 |
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0.675 |
0.2476524 |
1.300 |
0.9319078 |
1.925 |
0.9987912 |
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0.700 |
0.2887648 |
1.325 |
0.9402825 |
1.950 |
0.9990041 |
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0.725 |
0.3306849 |
1.350 |
0.9477581 |
1.975 |
0.9991816 |
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0.750 |
0.3728330 |
1.375 |
0.9544122 |
2.000 |
0.9993291 |
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0.775 |
0.4147012 |
1.400 |
0.9603181 |
2.025 |
0.9994514 |
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0.800 |
0.4558576 |
1.425 |
0.9655452 |
2.050 |
0.9995525 |
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20
ПРИЛОЖЕНИЕ 7
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Биномиальные коэффициенты |
Cnm = |
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n! |
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m!(n |
−m)! |
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0 |
1 |
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6 |
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23 2425 |
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0 1 |
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1 1 |
1 |
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2 1 |
2 |
1 |
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3 1 |
3 |
3 |
1 |
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4 1 |
4 |
6 |
4 |
1 |
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5 1 |
5 |
10 |
10 |
5 |
1 |
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6 1 |
6 |
15 |
20 |
15 |
6 |
1 |
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7 1 |
7 |
21 |
35 |
35 |
21 |
7 |
1 |
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8 1 |
8 |
28 |
56 |
70 |
56 |
28 |
8 |
1 |
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9 1 |
9 |
36 |
84 |
126 |
126 |
84 |
36 |
9 |
1 |
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101 |
10 |
45 |
120 |
210 |
252 |
210 |
120 |
45 |
10 |
1 |
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111 |
11 |
55 |
165 |
330 |
462 |
462 |
330 |
165 |
55 |
11 |
1 |
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121 |
12 |
66 |
220 |
495 |
792 |
924 |
792 |
495 |
220 |
66 |
12 |
1 |
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131 |
13 |
78 |
286 |
715 |
1287 |
1716 |
1716 |
1287 |
715 |
286 |
78 |
13 |
1 |
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141 |
14 |
91 |
364 |
1001 |
2002 |
3003 |
3432 |
3003 |
2002 |
1001 |
364 |
91 |
14 |
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1 |
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15115105 |
455 |
1365 |
3003 |
5005 |
6435 |
6435 |
5005 |
3003 |
1365 |
455 |
105 |
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15 |
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1 |
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|||
16116120 |
560 |
1820 |
4368 |
8008 |
11440 |
12870 |
11440 |
8008 |
4368 |
1820 |
560 |
|
120 |
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16 |
1 |
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17117136 |
680 |
2380 |
6188 |
12376 |
19448 |
24310 |
24310 |
19448 |
12376 |
6188 |
2380 |
|
680 |
|
136 |
17 |
1 |
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18118153 |
816 |
3060 |
8568 |
18564 |
31824 |
43758 |
48620 |
43758 |
31824 |
18564 |
8568 |
|
3060 |
|
816 |
153 |
18 |
1 |
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19119171 |
969 |
387611628 |
27132 |
50388 |
75582 |
92378 |
92378 |
75582 |
50388 |
27132 |
|
11628 |
|
3876 |
969 |
171 |
19 |
1 |
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|||||
201201901140 |
484515504 |
38760 |
77520 |
125970 |
167960 |
184756 |
167960 |
125970 |
77520 |
|
38760 |
|
15504 |
4845 |
1140 |
190 |
20 |
1 |
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||||||
211212101330 |
598520349 |
54264116280 |
203490 |
293930 |
352716 |
352716 |
293930 |
203490 |
|
116280 |
|
54264 |
20349 |
5985 |
1330 |
210 |
21 |
1 |
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|||||||
221222311540 |
731526334 |
74613170544 |
319770 |
497420 |
646646 |
705432 |
646646 |
497420 |
|
319770 |
|
170544 |
74613 |
26334 |
7315 |
1540 |
231 |
22 |
1 |
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|||||||
231232531771 |
885533649100947245157 |
490314 |
8171901144066135207813520781144066 |
|
817190 |
|
490314 |
245157 |
100947 |
33649 |
8855 |
1771 |
253 |
23 |
1 |
|
||||||||||||
2412427620241062642504134596346104 |
7354711307504196125624961442704156249614419612561307504 |
735471 |
346104134596 |
4250410626 |
2024 |
276 |
24 |
1 |
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251253002300126505313017710048070010815752042975326876044574005200300520030044574003268760204297510815754807001771005313012650230030025 1