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Начало temp_dir Вероятности и статистика - избрани задачи    English
Факултет по математика и информатика - Вероятности и статистика - избрани задачи

 Данни от сборника

 

ВЕРОЯТНОСТИ   

И   

СТАТИСТИКА 

 

ИЗБРАНИ ЗАДАЧИ

 

П. Копанов                   В. Нончева                   С. Христова

Пловдив    2010

 

Част втора.   СТАТИСТИКА

 

12.  Основни понятия в статистиката.  Описателна статистика

Основни функции на R: mean (); var(); sd(); summary (); hist ();

12.1.  

Доходи 

(в долари)

20 000 -29 999

30 000 -39 999

40 000 - 49 999

50 000 - 59 999

60 000 -69 999

70 000 -79  999

над      80 000

Брой (адвокати)

20

80

230

400

1700

70

30

 

12.2.                3,7      3,3     3,3    3,0   3,0    3,0     3,0     2,7     2,7     2,3

12.3  

12.4.   

Oтговори на въпроса  “ИЗПИТВАТЕ ЛИ ЧУВСТВО НА САМОТА?”

4,3,2,3,3,2,3,3,2,3,2,3,3,2,3,4,3,3,4,2,3,4,4,3,4,3,3,3,4,4,3,3,4,3,3,3,3,3,3,3,3,3,2,3,1,3,3,3,3,3,4,4,3,2,1,3,4, 4,4,4,3,2,3,3,3,3,3,3,3,3,3,4,3,4,4,4,3,2,3,3,3,4,4,3,3,3,3,2,1,4,3,3,3,4,4,4,3,3,4,3,2,3,4,3,3,4,3,3,3,2,2,3,2,3

 

12.5.   

 

омега 7

90, 185, 169, 243, 120, 175, 100, 88, 92, 80, 175, 37, 100, 185, 90, 112, 189, 41, 180, 60, 179, 30, 232, 50, 187, 60, 108, 169, 87, 170, 173, 221, 197, 117, 52, 183, 198, 182,  53, 166, 130, 181, 73, 121, 147, 176, 104, 159, 86, 119, 157, 174, 100, 180, 90, 60, 157, 181, 86, 154, 95, 30, 159, 109, 70, 78, 246, 166, 160, 106, 237, 226, 236, 162, 93, 188, 201, 151, 80, 70, 96, 95, 58 ,165, 154, 58, 163, 100, 110, 167, 100, 104, 130, 231, 157, 90, 204, 108, 133, 167, 90, 76, 168, 106, 98, 175, 170, 55, 80, 255, 58, 158, 206, 85, 70, 159, 173, 90, 55, 166

омега 9

7800, 6842, 6875, 6962, 7600, 6876, 7045, 7353, 7356, 7760, 7129, 7955, 7710, 6956, 7780, 7007, 6752, 7815, 6895, 7945, 7034, 7995, 6715, 7900, 6861, 7945, 7343, 7011, 7144, 6804, 6843, 6415, 7003, 7351, 8018, 6867, 6681, 6965, 7703, 7190, 7550, 6813, 7709, 7285, 7197, 6909, 7355, 7017, 7359, 7130, 7018, 6993, 7520, 6752, 7580, 7955, 7140, 7147, 7403, 6917, 7405, 7955, 7019, 7335, 7975, 7421, 6444, 7006, 6911, 7025, 6571, 6595, 6607, 6772, 7324, 6697, 6803, 7319, 7520, 7955, 7351, 7035, 7940, 7025, 6991, 7743, 6888, 7600, 7720, 6883, 7620, 7375, 7530, 6437, 7132, 7700, 6732, 7403, 7425, 6959, 7780, 7553, 7100, 7209, 7320, 6883, 6838, 7329, 7800, 6628, 7950, 7160, 6953, 7445, 7977, 7009, 7038, 7680, 7900, 6902

 

13.  Оценки на параметри на разпределението. Точкови оценки. Интервални оценки

Основни функции на R:   mean (); var(); sd(); t.test ()

13.1.  

13.2.  

13.3.    

13.4.  

55,95   56,54   57,58   55,13   57,48   56,06   59,93   58,30  52,57     58,48

 

13.5.  

13.6.  

4,4     3,8     5,1              4,6   4,5     4,5     4,8             4,1     3,9     4,2     4,4             4,9

5,0     4,3     4,4              3,6   5,2     4,8     4,4              4,6  4,6     5,0     4,0              4,5

 

13.7.  

13.8.  

13.9.  

13.10.  

13.11.  

0,79; 3,60; 6,83; 26,14; 1,38; 14,06; 10,83; 2.35; 0,06; 9,80; 24,69; 3,09; 15,20; 11,73; 21,80; 20,05; 6.89; 7,56; 0.14; 1,45; 5,96; 14,42; 1,53; 11,30; 6,05.

13.12.  

3,74; 5,34; 3,75; 4,29; 4,67; 4,51; 5,94; 5,84; 5,82; 5,11; 3,84; 5,69;   4,25;   5,38;    3,73;   5,98;    4,38;    5,10; 5,00.

13.13.  

13.14.  

0,20; 1,25; 1.28; 0,02; 1,62; 0.88; 1.02; 3,08; 2.63; 1,93; 2,04; 2,42; 2,45; 0,12; 0,28; 0,24; 2,48; 2,59; 0,35; 0.11; 1,04; 0,66; 0,39; 1,64; 1,29; 0,15; 2,74; 2,10;  2,36; 0,02;  2,16; 1.70;   1,24; 0,90; 2,96; 1.27

13.15.  

13.16.  

49, 50, 51, 50, 52, 49, 50, 51  

51, 47, 53, 52, 50, 51, 49   

 

13.17.  

7120, 7065, 7080, 7120, 6990, 7007, 6971, 7130, 6882, 7043, 7145, 7065, 7162, 7144, 7020, 7123, 7164, 7159, 7085, 7103, 7068, 7170, 7076, 7243, 7068,  7080,  7035,  7135, 7062,  7200,  7085,  7006,  7025

 

13.18.  

7425, 6510, 6801, 6838, 7277, 7770, 7605, 7616, 7815, 7714, 7576, 7235, 7416, 7870, 7747, 7329, 7020, 7328, 7045, 6876, 6962, 6917, 6994, 7189, 7110, 7374, 7593, 7553, 7375, 7743, 7719, 7692, 7527, 7445, 7405, 7471

 

13.19.  

Материал А

2.915, 2.6, 4.061, 4.398, 4.025, 2.84, 3.253, 2.25, 4.83, 2.406, 4.502, 4.547, 4.132, 2.812, 1.736, 4.403, 3.794, 4.396, 4.259, 3.132

Материал В

4.39, 4.694, 3.388, 4.226, 4.505, 5.608, 2.75, 3.199, 3.604, 2.451, 2.469, 3.516, 4.323, 5.175, 5.004, 4.202, 4.41, 3.577, 4.946, 3.57, 4.492, 4.633, 3.368, 4.967, 3.378

 

стойности Xj

7,85

7,9

7,95

8

8,05

честота nj

1

2

3

2

3

 

 

 

 

 

 

 

13.20.    

 

13.21.  

СТОЙНОСТИ Xj

24,85

24,95

25,00

25,10

25,15

25,20

честота nj

2

3

4

2

1

1

 

 

 

 

13.22.  

стойности Xj

108

109

109,5

110

110,5

честоти nj

1

2

2

4

1

 

 

 

 

13.23.  

260      216      259      206      265      284      291      229      249

13.24.

135.25,  186.09,  110.94,  211.20,  209.40,  159.54,  164.40,  154.90,  230.50,   207.10, 192.98,  210.90, 156.39.   

14. Проверка на хипотези за средна стойност на нормална популация

Функция на R: t.test() 

14.1.  

Резултати от IQ теста

115, 124, 107, 106, 109,  99, 121,  95, 118, 111, 115, 114, 131,  119,  104,  125,  115, 119,  94, 122, 116, 116, 119, 124, 106, 107, 122, 113, 105, 120, 105, 110, 106, 119, 115

 

14.2.  

14.3.  

     55,95          56,54               57,58              55,13               57,48                 56,06 59,93               58,30               52,57            58,48

14.4.    

 

14.5.  

4,4       3,8       5,1       4,6       4,5       4,5       4,8       4,1       3,9       4,2

4,4       4,9       5,0       4,3       4,4       3,6       5,2       4,8       4,4       4,6

4,6       5,0       4,0       4,5

14.6.   

14.7.  

14.8.  

 

14.9.  

14.10.  

14.11.  

14.12.  

14.13.  

1.006

1.013

1.015

0.987

1.006

0.997

1.002

1

1.006

1.013

0.996

0.997

0.986

0.99

1.012

0.999

0.993

0.986

1.003

0.986

0.995

0.992

0.994

1.012

1.003

1.009

0.992

0.999

1.013

1.002

0.989

1.007

0.997

0.987

1.001

0.995

0.998

0.989

0.993

0.996

1

0.997

1.008

1.008

1.006

1.006

0.987

0.998

0.994

1.002

1.009

0.988

0.999

1.003

0.992

0.996

0.994

0.99

0.988

0.992

0.992

0.995

1.012

1.013

0.997

0.986

1.001

0.99

1.008

1.004

1.005

1

0.999

1.002

1.008

0.988

1.009

0.993

0.99

1.01

0.997

1.008

1.011

1.007

1.006

0.993

1.001

0.986

0.987

1.002

1.014

1.006

1.001

0.986

1.009

0.991

1.001

0.993

1.01

1.007

1.008

1.008

1.012

0.989

0.999

0.988

0.988

0.99

0.987

0.996

1.013

1.009

1.014

0.989

0.993

0.988

0.988

1

0.99

1.007

0.997

0.995

1.008

1.013

1.011

0.996

1.013

1.01

0.996

0.989

1.008

1.014

0.996

0.991

0.989

1.002

1.005

1.006

0.991

0.993

0.988

1.013

0.993

0.996

1.014

 

14.14.  

6, 9, 7, 5, 11, 5, 10, 8, 7, 10, 8, 8, 7, 2, 9, 6, 5, 8, 4, 5, 4, 6, 8, 10, 6, 6, 6, 5, 8, 7, 9, 6, 9, 8, 8, 7, 10, 10, 9, 9, 8, 10, 3, 7, 4, 9, 4, 8, 5, 8, 12, 7, 6, 4, 10, 5, 7, 5, 11, 7, 9, 6, 5, 8, 6, 8, 9, 7, 9, 3, 7, 9, 8, 7, 8, 7, 9, 4, 4, 7

 

 

 

14.15.  

Твърдост по Бринел на сферографитен чугун

172.24, 179.88, 176.99, 191.35, 175.90, 179.92, 177.00, 187.77, 184.93, 182.19, 171.38, 181.13, 185.22, 175.30, 181.31, 201.29, 191.54, 151.34, 186.30, 165.46, 173.65, 177.61, 174.70, 179.30, 181.36, 176.29, 176.90, 161.14,   183.94,  179.57,   190.46,  188.39,   186.98,  177.08,   187.02

 

14.16.  

Якост на стоманена нишка след въвеждането на новия производствен процес

61.05, 47.18, 48.41, 51.48, 53.55, 48.25, 55.07, 43.93, 47.78, 56.46, 56.93, 47.93, 52.01, 47.82, 49.61, 54.98, 65.29, 45.62, 50.80, 46.95, 57.68, 52.27, 53.92, 60.84, 59.50, 62.60, 59.27, 54.96, 42.76, 54.40, 50.66, 53.44, 56.63, 50.35,  43.24,  50.66,  60.32, 45.84,  54.88,  41.32

 

15. Точкова оценка, доверителен интервал и  проверка на хипотези за алтернативни популации.

15.1.  

15.2.  

15.3.  

15.4.  

 

15.5.  

15.6.  

15.7.    

8/56

13/55

12/58

13/56

14/57

5/54

14/56

15/57

11/54

13/55

10/57

8/59

10/54

11/55

12/56

11/57

6/54

7/58

12/58

14/58

 

15.8.  

15.9.  

15.10.  

16. Проверка на хипотези за две популации 

Основни функции на R:   t.test (); var.test ()

16.1.  

Бял щъркел

4.58, 3.06, 2.45, 3.98, 1.40, 5.71, 4.08, 4.70, 2.55, 2.37, 3.70, 4.10, 2.12, 4.10, 3.07, 4.20, 3.98, 2.46, 3.17, 3.94, 2.67, 2.72, 4.01, 2.49, 2.75, 3.44, 4.00, 3.40, 2.61, 3.23, 4.87, 3.04, 4.15, 3.10, 0.81, 3.93,  3.43, 4.36,  3.76,  2.26, 3.54,  2.88

Черен щъркел

3.01, 2.96, 2.98, 2.92, 3.02, 3.04, 3.00, 3.03, 2.97, 2.97, 2.94, 3.04, 2.96, 2.97, 3.01, 2.82, 3.03, 3.03, 3.01, 3.02, 2.92, 3.01, 2.91, 2.98, 3.03, 3.02, 2.95, 3.04, 3.06, 3.02, 3.08, 2.97, 3.02, 2.87, 2.97

 

 

 

 

 

 

16.2.  

Шофьор

1

2

3

4

5

Марка A

150

146

160

155

152

Марка  B

152

145

160

157

154

 

16.3.  

 

Брой телефони

Брой дефектни

Клон A

100

1

Клон B

100

5

 

16.4.  

 

Момчета

Момичета

брой

40

40

Средно време

10

11

Стандартно отклонение

3

2

 

16.5.  

касиер

1

2

3

4

5

6

7

стара

60

70

55

75

62

52

58

нова

65

71

55

75

65

57

57

 

16.6.  

Вид сблъсък

разходи-  Neon

разходи- Civic

Предна броня в бариера

363

420

Задна броня в бариера

88

462

Предна броня в наклонена бариера

420

409

Задна броня в стълб

1,131

236

 

16.7.    

 

Група с Zyprexa

Група с плацебо

брой

55

60

Средно въздействие

14,8

8.1

Стандартно отклонение

12.5

12.7

 

16.8.   

16.9.  

С лекарство

2.1

5.3

1.4

4.6

0.9

Без лекарство

1.9

0.5

2.8

3.1

 

 

16.10.  

16.11.   

16.12.  

Ca

7

-4

18

17

-3

-5

1

10

11

-2

 

Placebo

-1

12

-1

-3

3

-5

5

2

-11

-1

-3

 

16.13.  

 

Съдържание на линолевата киселина в зехтин (в %x100)

Източна Лигурия

 

1020, 1000, 1030,  990, 1050,  830,  880,  900,  970,  980,  990,  850,  860,  910, 1040,  940,  930, 1010,  730,  690,  960, 1020, 1010,  850, 1030,  940,  820,  810,  920, 1010,  930,  910,  900,  830,  840,  910,  850, 830, 800, 770, 760, 810, 750, 950, 870, 790, 810, 970, 870, 740

Калабрия

832, 950, 874, 940, 903, 892, 915, 870, 820, 823, 798, 829, 819, 840, 866, 870, 877, 928, 897, 757, 839, 786, 939, 925, 780, 743, 787, 872, 771, 819, 828, 618, 818, 633, 616, 923, 638, 609, 759, 869, 702, 855, 857, 823, 949, 790, 783, 738, 763, 780, 826, 810, 709, 898, 861, 848

 

16.14.   

Година

Температура на морската вода

 

1993

22.68, 24.01, 23.42, 22.89, 23.54, 23.91, 23.37, 21.84, 23.88, 22.81, 22.81, 24.43, 23.41, 24.05, 23.67, 23.93, 24.43, 23.95, 21.99, 24.55, 24.08, 22.59, 23.50, 24.62, 23.43

 

1997

28.08, 28.51, 28.78, 28.25, 28.35, 26.85, 26.64, 26.83, 27.68, 28.05, 27.59, 28.26, 28.03, 28.20, 26.64, 27.60, 27.62, 28.55, 28.81, 28.94, 27.51, 28.45, 28.28, 28.24, 28.24

 

16.15.  

Съдържанието на мазнините в % за 100 гр продукт

2.343, 1.922, 1.587, 1.736, 0.461, 1.800, 1.409, 0.884, 2.999, 3.519, 2.219, 2.399, 1.037, 2.345, 0.865, 3.397, 2.744, 2.484, 2.828, 2.470, 3.136, 1.403, 0.691, 0.865, 1.974, 2.150, 0.666, 1.409, 2.443, 1.658

2.098, 1.689, 2.269, 3.579, 2.703, 3.327, 1.631, 2.778, 2.458, 1.899, 1.120, 3.048, 2.375, 2.909, 1.757, 1.561, 0.480, 2.791, 2.353, 2.639, 1.896, 2.116, 1.500, 1.220, 2.091, 3.863, 1.720, 2.041, 2.323, 1.065

16.16.  

Съдържание на белтъчини

Съдържание на въглехидрати

3.52, 3.52, 3.46, 3.60, 3.58, 3.54, 3.48, 3.50, 3.52, 3.35, 3.57, 3.43, 3.47, 3.45, 3.49, 3.49, 3.52, 3.59, 3.47, 3.49, 3.48, 3.54, 3.55, 3.45, 3.51, 3.44, 3.56, 3.65, 3.43, 3.47, 3.46, 3.47, 3.49, 3.44, 3.41, 3.42, 3.53, 3.47, 3.48, 3.57, 3.40, 3.48, 3.43, 3.46, 3.60

4.24, 4.19, 4.23, 4.13, 4.14, 4.26, 4.12, 4.30, 4.20, 4.12, 4.06, 4.23, 4.17, 4.16, 4.15, 4.16, 4.23, 4.19, 4.18, 4.20, 4.29, 4.17, 4.14, 4.26, 4.24, 4.34, 4.21, 4.21, 4.24, 4.16, 4.22, 4.31, 4.12, 4.25, 4.14, 4.20, 4.26, 4.24, 4.14, 4.22, 4.27, 4.24, 4.26, 4.12, 4.22

 

16.17.  

пациент

1

2

3

4

5

6

7

8

Окото с глаукома

488

478

480

426

440

410

458

460

Окото без глаукома

484

478

492

444

436

398

464

476

 

16.18.  

Северна област: 157; 202; 175; 174; 199; 194; 195; 201;178 179; 170; 194; 158; 180; 205; 204; 162; 203; 203; 181; 174; 198

Централна област: 186; 169; 159; 173; 177; 159; 160; 194; 177; 161; 185; 201; 165; 163; 171; 173; 189; 193; 195; 162; 156; 174; 178; 196; 161; 203; 180; 182; 176; 158; 191; 158; 194; 174; 203; 195; 155; 196; 177; 180; 158; 183

Южна област: 183; 190; 165; 184; 165; 179; 183; 180; 177; 192; 184; 167; 161; 188; 167; 186; 194; 190; 180; 194; 195; 168; 192; 180; 159; 182; 180; 157; 164; 192; 169; 170; 156 

17. Проверка на хипотези за нормалност на популация.

Основни функции на R:   shapiro.test (); ks.test().

17.1.  

Женски сурикат

45.05, 45.30, 46.19, 46.19, 44.72, 45.09, 44.86, 44.25, 46.72, 46.14, 46.94, 45.26, 47.14, 46.03, 46.82, 44.89, 44.36, 46.51, 45.92, 45.02, 44.41, 45.23, 46.06, 45.90, 45.65, 46.56, 48.29, 46.30, 45.65, 45.63, 46.16, 45.88, 45.59, 46.80, 45.10, 47.99, 44.43, 43.81, 46.00, 47.31, 46.53, 46.62, 46.20, 46.27, 46.14, 45.71, 44.52, 45.50, 45.24, 45.38, 44.58, 46.59, 46.95, 46.37, 47.11, 46.44, 46.11, 43.88, 45.46, 46.29, 45.82,  45.67, 47.40, 45.87, 45.71, 46.13, 47.80, 45.53,  46.87, 44.63

Мъжки сурикат

50.84, 50.82, 48.36, 49.89, 49.49, 49.81, 51.28, 49.77, 48.79, 49.86, 49.60, 48.49, 51.39, 50.37, 49.74, 49.80, 49.97, 49.84, 50.55, 49.41, 48.58, 50.32, 50.78, 48.29, 47.63, 49.54, 49.67, 51.72, 51.08, 48.74, 49.32, 49.47, 51.76, 49.86, 50.24, 51.00, 49.67, 49.50, 50.05, 47.72, 52.26, 48.48, 50.60, 49.99, 48.71, 49.77, 50.07, 48.43, 47.95, 49.61, 49.38, 49.56, 51.83, 50.29, 50.44, 50.42, 47.58, 49.88, 49.82, 48.80, 50.30, 49.27, 47.42, 49.73, 49.60, 51.12, 50.49, 50.12, 48.80, 50.85, 49.74, 50.31, 50.54, 52.36, 49.92

 

17.2.  

АФРИКАНСКИ СЛОН

6.69 6.25 6.02 6.79 6.41 6.16 6.25 6.41 6.19 6.06 6.04 7.67 6.89 6.39 6.29 6.81 6.74 6.37 6.47 6.41 6.59 6.33 6.35 6.35 6.10 6.24 5.91 6.12 6.32 5.54 6.36 6.05 5.96 6.70 6.90 6.64 6.36 6.63 6.51 6.24 6.08 6.92 6.48 6.51 6.74 6.15 6.57 6.61 6.39 5.86 6.49 6.57 6.28 6.37 6.64 6.10 6.62 6.76 6.24 6.34 5.33 5.58 6.47 6.24 6.23 6.92 6.94

 

АЗИАТСКИ СЛОН

6.18 6.16 6.22 6.26 6.25 6.262 6.19 6.20 6.12 6.19 6.17 6.20 6.18 6.16 6.25 6.20 6.20 6.17 6.26 6.26 6.22 6.25 6.20 6.28 6.17 6.21 6.17 6.21 6.23 6.19 6.17 6.16 6.22 6.13 6.12 6.23 6.16 6.19 6.12 6.16  6.23 6.15 6.29 6.18 6.20 6.16 6.19 6.20 6.21 6.17 6.24 6.21 6.19 6.23 6.17 6.17 6.18 6.22 6.25 6.16 6.18 6.26 6.30 6.17 6.19 6.27 6.11 6.19 6.27 6.23 6.25 6.24 6.19

 

17.3.  

Температура на въздуха около Коледа 1997 година

27.79, 27.13, 27.05, 28.30, 27.27, 26.91, 26.99, 27.23, 27.59, 26.36, 26.35, 27.79, 27.43, 26.94, 26.67, 28.18, 26.39, 26.74, 26.59, 28.40, 27.68, 26.91, 27.28, 26.98, 27.67, 27.09, 28.37, 27.74, 27.28, 27.67

 

Температура на въздуха около Коледа 1993 година

22.35, 22.83, 23.62, 24.42, 24.34, 23.62, 23.26, 22.22, 22.94, 23.78, 22.09, 22.19, 23.54, 23.20, 22.86, 22.69, 23.75, 22.35, 24.62, 23.94, 23.65, 22.55, 24.80, 22.24, 22.83, 24.80, 23.65, 23.38, 23.38, 22.98

 

17.4.  

Процентно съдържание на олеинова киселина (в %x100) в 33 шишета италиански зехтин, произведен в остров Сардиня

7172, 7820, 7417, 7650, 6928, 6806, 7840, 7900, 6499, 6504, 7620, 6608, 6948, 7771, 7323, 7025, 7030, 7123, 7277, 7416, 7375, 7714, 7955, 6913, 7553, 7650, 7229, 7086, 6595, 7011, 7540, 8018, 6752, 7130, 7760, 6737, 7000, 6994, 7955, 7395, 7380, 7285, 6961, 7327, 6923, 7680, 7415, 7965, 7383, 7580, 7620, 6630, 7107, 6300, 7105, 6898, 7958, 7103, 7006, 6997

 

17.5.    

Материал А

7.4,  6.25,  7.94,  7.47,  7.83,  9.5,  7.36,  7.34, 12.45,  9.53,  7.63, 10.07,  6.97,   7.77,  7.88,  7.98,  6.6,  6.18, 10.29,  4.49,  6.66,  8.07, 10.26,  9.35,  9.48,  6.34,  5.46,  6.71, 12.62,  7.03

Материал В

9.17, 10.65, 11.60, 11.36, 12.42,  9.6,  8.92, 11.48, 10.71,  7.54,  8.29,  4.92,  9.57,   9.39,  6.42, 11.89,  9.35,  8.08,  8.58,  8.25,  6.91,  7.88,  6.13, 11.03,  8.82, 11.65,  10.62,  5.01,  9.55, 12.69

 

17.6.  

2,20; 1,27; 1,28; 1,02; 1,42; 0,88; 1,65; 3,08; 2,63; 1,95; 2,44; 2,77; 2,45; 0,52; 0,28; 0,35; 2,48; 2,60; 0,45; 0.11.

17.7.  

интервали (aj-1,aj]

(100;108]

(108;116]

(116;124]

(124;132]

(132;140]

абсолютни честоти nj

3

7

12

6

2

 

17.8.  

интервали (aj-1,aj]

(3,8; 4,4]

(4,4; 5,0]

(5,0 ; 5,6]

(5,6; 6,2]

абсолютни честоти nj

1

7

9

2

 

 

 

18. Непараметрични тестове

Основни функции на R:   wilcox.test (); bartlett.test()

18.1.  

Данни за отклонението на нивото на водата на язовир около желаното

0.38, -1.04, -1.85, -0.43,  0.94, -0.77, -0.52, -1.57, -0.27, -1.80,   -1.32, -0.30, -1.52,  0.68, -1.04, -1.46, -1.87, -2.13, -0.26,  2.89,  1.02, -1.59,  0.20,  0.28, -2.00, -2.30, -2.12, -2.06, -0.12,  0.44

 

18.2.  

18.3.  

808

882

1062

970

909

802

374

416

784

997

61

716

438

1420

1425

948

1050

976

572

403

626

774

1253

549

1325

446

465

696

671

1269

1156

684

1933

748

1203

2436

1255

110

1025

2610

 

18.4.  

Съдържание на еритроцити в кръвта на мъжете:

0.52 0.48 0.58 0.48 0.40 0.44 0.42 0.52 0.48 0.47 0.43 0.51 0.43 0.40 0.39 0.48 0.42 0.41 0.37 0.49 0.40 0.47 0.54 0.44 0.44 0.36 0.40 0.48 0.40 0.49 0.43 0.38 0.46 0.41 0.50 0.35 0.61 0.36 0.43 0.54 0.41 0.48 0.52 0.43 0.49 0.42 0.44 0.50 0.52 0.54 0.45 0.42 0.53 0.51 0.44 0.52  0.43 0.50 0.47 0.51 0.49 0.47 0.38 0.49 0.53 0.59 0.47 0.40 0.42 0.52 0.45 0.55 0.44 0.33 0.31 0.55 0.40 0.46 0.54 0.45 0.49 0.43 0.56 0.47 0.41 0.48 0.52 0.52 0.42 0.41 0.33 0.35 0.40 0.36 0.41 0.29 0.50 0.47 0.57 0.47 0.44 0.46 0.51 0.39 0.49 0.48 0.46 0.49 0.49 0.43 0.49 0.47 0.54 0.50 0.46 0.41 0.40 0.51 0.48 0.40

Съдържание на еритроцити в кръвта на жените:

0.41 0.45 0.49 0.43 0.38 0.48 0.47 0.40 0.43 0.39 0.48 0.46 0.38 0.37 0.45 0.47 0.39 0.46 0.40 0.43 0.39 0.47 0.49 0.43 0.39 0.44 0.49 0.42 0.43 0.45 0.49 0.51 0.53 0.44 0.43 0.44 0.46 0.46 0.35 0.31 0.46 0.42 0.37 0.39 0.49 0.44 0.49 0.38 0.41 0.40 0.45 0.46 0.35 0.42 0.33 0.49 0.42 0.33 0.41 0.41 0.33 0.41 0.39 0.44 0.40 0.35 0.44 0.40 0.44 0.40 0.37 0.37 0.44 0.37 0.45 0.45 0.39 0.38 0.49 0.40 0.43 0.51 0.46 0.36 0.47 0.39 0.46 0.43 0.30 0.36 0.54 0.37 0.45 0.43 0.35 0.38 0.42 0.44 0.50 0.43 0.44 0.43 0.43 0.42 0.49 0.36 0.34 0.42 0.41 0.32 0.42 0.45 0.47 0.44 0.54 0.38 0.53 0.45 0.40 0.32 0.41 0.44 0.44 0.40 0.42 0.38 0.47 0.46 0.41 0.45 0.49 0.40 0.39 0.48 0.35 0.35 0.35 0.38 0.44 0.38 0.50 0.38 0.44 0.44 0.38 0.43 0.47 0.43 0.48 0.42 0.46 0.45 0.41 0.38 0.38 0.41 0.40 0.48 0.49 0.44 0.48 0.45 0.47 0.41 0.42 0.33 0.46 0.37 0.38 0.42 0.41 0.45 0.30

 

18.5.  

Дължини на полипептидни верига при Drosophila melanogaster

938   940 1014  990  1011 1025 1085 1083 1074   961  114 3042 1050  974  1045  968  995  968   989   971 1000   963 1160 1101   958 1031 1140 1062  959 1095 1110 1046  926  961 1048 1028 1085 1029 1020 1046

Дължини на полипептидни вериги при Arabidopsys thaliana

1055 1073 1033 1103 1180 1169 1037 1133   998 1126 1094 1130 1161 1031 1121 1032 1072 1086 1229   996 1144 1069 1051 1056 1133 1137 1017 1178 1151 1125 1125 1056 1075 1014 1172 1100 1160 1085 1196 1043

 

18.6.  

Размерите на невронните клетки от извадката:

31.50, 36.41, 40.80, 40.84, 37.83, 42.88, 41.08, 39.18, 38.92, 36.46, 45.95, 43.83, 39.20, 41.80, 35.95, 33.54, 35.13, 40.84, 43.42, 40.00, 38.22, 47.22, 36.17, 44.61, 40.41, 41.13, 35.81, 37.48, 38.97, 43.78

Размерите на мускулните влакна от извадката:

11.03, 10.96, 11.01, 11.00, 10.98, 10.98, 11.00, 10.93, 11.06, 11.03, 11.03, 11.02, 10.90, 10.87, 10.96, 11.02, 11.01, 11.05, 11.03, 11.07, 11.03, 10.99, 10.96, 10.95, 10.96, 11.11, 11.10, 11.03, 11.07, 11.00

 

18.7

 

 

1970

1980

1990

1995

2000

2005

2006

2007

2008

Градове

18.0

15.7

12.6

8.8

9.5

9.6

10.1

10.4

10.8

Села

14.6

12.4

10.9

8.0

8.1

8.1

8.3

8.5

8.7

 

 

 

 

 

18.8

Височина на плевенските коне от извадката:

161.48, 161.54, 161.21, 162.05, 163.20, 161.56, 159.94, 161.27, 161.71, 161.31, 161.53, 161.63, 162.23, 160.17, 161.22, 161.07, 162.96, 161.47, 161.50, 161.66, 161.35, 161.22, 161.74, 161.96, 162.18, 161.62, 162.46, 160.55, 161.17, 161.77, 161.94, 161.93, 162.53, 160.72, 161.60

Височина на  каракачанските коне от извадката:

127.70, 127.23, 128.07, 127.02, 127.57, 127.63, 127.69, 127.81, 128.07, 127.91, 127.80, 128.09, 128.62, 127.90, 128.72, 127.66, 127.94, 127.64, 127.92, 128.23, 128.32, 127.62, 127.70, 128.21, 127.75, 128.35, 127.89, 128.23

 

 

 

 

 

 

 

 

 

18.9.  

 

 

18.10.  

пенсионери

39, 44, 44, 40, 42, 43, 44, 43, 38, 39, 39, 38, 43, 40, 40, 42, 38, 44, 41, 46, 44, 41, 45, 44, 42, 44, 40, 35, 45, 41, 47, 46, 40, 45, 43, 40, 41, 39, 38, 36, 41, 39, 42, 39, 40, 46, 39, 39, 39, 45

тийнейджъри

33, 13, 19, 27, 18, 30, 12, 33, 25, 24, 28, 26, 24, 29, 26, 27, 23, 23, 25, 26, 30, 21, 16, 24, 25, 26, 27, 21, 30, 26, 28, 28, 29, 20, 19, 27, 16, 23, 26, 29, 22, 20, 23, 24, 27, 27, 18, 20, 13, 30, 24, 25, 26, 27, 21, 30, 26, 28, 28, 29

 

18.11.  

Пол

Тегло (g)

♂ (9)

1234, 1080, 1182,  820, 1120, 1498, 929 ,1090, 1029

♀ (14)

1080,  676,  981,  997, 1053,  739,  709, 1066, 1043,  760,  840,  888, 1015

19. Елементи на регресионния анализ

Основни функции на R са:    lm(); plot(); cor(); summary()

19.1.

Мастни киселини

Съдържанието на палмитиновата и стеариновата мастни киселини в извадка от 60 липидни фракции на италиански зехтин (% x100)

almitic

1213, 1348, 1272, 1020, 1131, 1105, 1527, 1283, 1092, 1387, 1284, 1306, 1020, 1076, 1255, 1065, 1336, 1075, 1252, 1340, 1085,  961, 1590, 1463, 1355, 1290, 1176, 1267, 1160, 1412, 1107, 1514, 1100, 1040,  911, 1070, 1178, 1457, 1180, 1118, 1120, 1090, 1090, 1055p, 1387, 1394, 1360, 1220, 1393, 1090, 1438,  960, 1241, 1060,  905, 1517, 1400, 1419, 1207, 1140

stearic

245, 183, 205, 220, 208, 373, 232, 196, 210, 204, 265, 226, 260, 202, 223, 245, 223, 200, 181, 189, 180, 195, 195, 183, 214, 260, 205, 300, 230, 217, 220, 298, 250, 250, 268, 188, 241, 267, 250, 199, 240, 190, 220, 175, 206, 223, 176, 240, 211, 192, 248, 200, 268, 175, 288, 249, 270, 207, 156, 220

 

 

x

4.11

5.18

4.52

5.49

4.89

1.11

y

56.2

40.0

45.9

45.3

38.5

32.4

 

 

 

 

 

 

 

 

 

 

 

 

19.2.  

 

x

5.35

2.09

0.6

6.53

1.40

3.80

y

31.0

50,0

18.2

30.1

45.8

56.1

 

 


 

19.3.  

мастна киселина

Процентно съдържание на оmega ненаситените мастни киселини, открити в 60 липидни фракции на италиански зехтин (% x100)

Оmega-7

(palmitoleic)

112, 154, 207, 100,  87,  69, 260, 153,  37, 154,  93, 149,  90,  77, 103,  45, 185,   91, 180, 114,  70,  70, 241, 183, 144,  60,  75, 101,  70, 185,  75, 162,  90,  90,  49,  75,  92, 182,  80,  85,  90,  60,  60,  60, 182, 164, 163,  80, 128,  58, 206,  90,  97,  75,  49, 206,  90, 192, 151, 180

Оmega-9

(oleic)

7007, 6917, 7152, 7530, 7170, 7714, 6488, 7107, 7955, 6991, 7235, 7082, 7620, 7243, 7395, 7779, 6956, 7410, 7055, 7337, 7955, 7958, 6705, 6747, 6972, 7550, 7396, 7230, 7860, 6842, 7399, 6725, 7680, 7780, 7924, 7980, 7006, 7020, 7870, 7415, 7068, 7950, 7890, 7985, 7100, 7086, 6901, 7610, 7189, 7950, 6806, 7810, 7499, 7975, 7747, 6680,  7420, 6996, 7159, 7610

 

 

 

 

 

 

 



 

 

19.4.  

 

Обявена цена

Продажна цена

 

Обявена цена

Продажна цена

 

Обявена цена

Продажна цена

1

382000

399900

21

222000

249900

41

66400

69900

2

166000

189900

22

285000

323900

42

154000

158900

3

145000

154900

23

320000

379000

43

70900

70900

4

465000

479500

24

145000

154888

44

280000

299000

5

105000

107500

25

118000

139000

45

190000

205000

6

190000

199900

26

205000

214900

46

89900

89900

7

132000

139900

27

147500

159000

47

638000

675000

8

273000

289000

28

309000

319000

48

384900

384900

9

50000

50000

29

166000

174900

49

173000

184900

10

167000

189900

30

114500

117000

50

126000

134900

11

191150

191900

31

355000

369900

51

430000

439900

12

210000

219900

32

176000

179000

52

825000

875000

13

235000

243000

33

250000

250000

53

290000

314900

14

202500

225000

34

158000

165000

54

149000

149900

15

275000

295000

35

315000

315000

55

182000

182000

16

142750

145500

36

71000

75000

56

179000

179000

17

71900

73900

37

71000

79900

57

440000

459000

18

249900

249900

38

280000

289000

58

63750

74900

19

103000

105500

39

150000

159000

59

350000

359000

20

428000

439000

40

158000

165000

 

 

 

 

19.5.   

           Кости  Мускули  Черен дроб  Кожа

[1]      1.755      1.617       7.389                    1.731

[2]      1.886      1.671       10.347        1.970

[3]      1.780      1.578        5.036         1.338

[4]      0.790       0.657       3.439         1.046

[5]      1.278       1.629       10.426       1.495

[6]      1.687       2.231       14.749       2.363

[7]      1.906       1.060        8.401        1.519

[8]      0.875       0.905        3.658        1.229

[9]      1.467       1.102        3.357        1.603

[10]     1.776       1.085        5.624        1.887

[11]     1.199       0.903        2.043        1.633

[12]     1.056       0.760        3.017        1.046

[13]     1.871       1.193        4.122        2.081

[14]     1.796       1.212        8.270        2.926

[15]     1.192       0.540        3.233        1.962

[16]     1.379       0.950        3.273        1.679

[17]     1.856       1.338        3.977        1.295

[18]      2.189      1.846       13.911       1.723

[19]      0.859      1.313       10.788       1.253

[20]      1.039      0.690        6.519        1.154

[21]      1.741      1.543        4.893        2.109

[22]      2.877      1.717       16.344       2.646

[23]      2.024      1.585       11.233       1.670

[24]      0.934       0.777        5.331       1.063

[25]      0.316       0.187        1.888       0.778

[26]      1.050       1.022        2.395       1.200

[27]      1.180       0.588        2.003       0.801

[28]      0.430       0.116        1.999       0.894

[29]      0.505       0.182        1.833       0.998

[30]      0.892       0.521        3.200       1.112

[31]      0.480       0.112        1.321       0.996

[32]      0.347       0.096        1.160       0.979

[33]      0.218       0.151        2.005       0.546

[34]      0.339       0.108        2.615       0.566

[35]      0.270       0.127        2.378       0.519

[36]      0.219       0.050        2.335       0.345

              Кости    Мускули  Черен дроб  Кожа

[37]      0.586       0.345        3.213       0.420

[38]      0.810       0.351        5.073       0.473

[39]      0.355       0.276        1.843       0.265

[40]      0.275       0.187        1.385       0.182

[41]      1.031       0.230        5.757       0.801

[42]      1.352       0.984       11.150       0.709

[43]      0.663       0.896        4.325       0.680

[44]      0.346       0.913        3.175       0.777

[45]      1.401       0.700        7.805       0.992

[46]      1.778       1.220       17.003      1.042

[47]      0.911       0.700        4.325       0.854

[48]      0.920       0.550        4.400       0.645

[49]      0.422       0.048        0.620       0.603

[50]      1.230       0.258        2.664       0.820

[51]      0.686       0.095        2.606       0.864

[52]      0.518       0.097        1.887       0.778

[53]      0.975       0.162        3.798       1.095

[54]      1.075       0.101        3.868       1.209

[55]      1.619       0.446        9.206       1.962

[56]      1.545       0.123        4.497       1.859

[57]      0.280       0.045        0.816       0.270

[58]      0.969       0.338        3.309       0.539

[59]      0.873       0.305        3.207       0.510

[60]      0.491       0.148        1.900       0.396

[61]      0.381       0.212        2.214       1.087

[62]      0.610       0.251        2.762       1.253

[63]      0.998       0.885        4.900       1.295

[64]      0.695       0.413        3.759       1.383

[65]      1.060       0.085        2.400       1.070

[66]      1.467       0.679        5.610       1.788

[67]      1.436       0.255        3.142       1.414

[68]      1.680       0.214        2.483       1.398

[69]      1.072       0.261        4.521       2.175

[70]      1.419       0.750        5.011       2.109

[71]      1.505       1.091        7.932       1.764

[72]      1.529       1.175        7.252       1.485

 

19.6.  

X 

80

80

80

80

80

100

100

Y 

55

60

65

70

75

65

70

X 

140

140

140

140

160

160

160

Y 

103

108

113

115

102

107

110

X 

200

220

220

220

220

220

220

Y

145

135

137

140

152

157

160

X

100

100

100

100

120

120

120

Y

74

80

85

88

79

84

90

X

160

160

160

180

180

180

180

Y

116

118

125

110

115

120

130

X

220

240

240

240

240

240

240

Y

162

137

145

155

165

175

189

X

120

120

140

140

140

140

 

Y

94

98

80

93

95

103

 

X

180

180

200

200

200

200

 

Y

135

140

120

136

140

144

 

X

260

260

260

260

260

260

260

Y

150

152

175

178

180

185

191

 

 

19.7.  

 

x

2.5  0.5    2  3.5    1  0.5  2.5  2.6    3     2   0.5   0.4   0.6     4   0.5   3.5   3.9   4.7   1.9   0.9     5 1.5  0.8   1.5   2.7   1.7   1.7   0.7    4     5   1.2   1.9   2.6   3.6   0.5   3.6   4.4   4.8   0.8   5.2

y

2, 3, 2, 1, 2, 3, 2, 2, 1, 2, 3, 3,  3, 1, 3, 1, 1, 1, 2, 2, 1, 2, 3, 2, 2, 2, 2, 3, 1, 1, 2, 2, 1, 1, 3, 1,  1, 1, 2, 1

 

 

 

 

 

 

19.8.  

i

13.64

-19.74

-19.11

-21.98

-19.4

-6.33

-35.08

-30.84

SP500

909.73

843.74

827.5

845.14

845.85

835.19

778.94

752.83

i

20

9.65

5.37

0.63

-5.13

-13.85

-1.67

5.26

SP500

1150.24

1122.97

1102.94

1106.75

1078.47

1063.11

1084.53

1116.48

i

15

26.23

0

13.69

7.31

7.92

0

10.91

SP500

1141.69

1115.1

1126.48

1096.08

1102.35

1099.92

1094.9

1094.9

i

-33.34

4.77

13.52

-6.14

8.07

-5.46

2.14

-6.67

SP500

1066.63

1092.91

1096.56

1065.48

1029.85

1050.78

1065.49

1044.14

i

-8.25

-26.74

-30.67

5.49

20.52

0

-13.1

 

SP500

906.83

882.68

931.8

1165.83

1148.46

1087.24

918.37

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

20. Комплексни задачи по статистика

20.1.  

Използвайте следното име за променливата: Kidney_Pb и данните:

11.9250 20.9268  7.9227  2.5272 13.5000 22.5000  8.2170  3.0807 14.4171  9.0189  5.9733  5.1804  6.0417 12.9393  6.4377  5.5404 14.1426 28.8198 13.9995  4.6215 14.7537 30.9618 15.3000  5.4099  2.9286  4.4073  2.9889 3.1104  3.4200  5.8950  3.8250  2.8458  3.0375  3.8574  2.6370  2.3040 3.3606  6.1479  2.3445  1.9710  6.3018 14.3730  4.0995  3.3183 32.6970 33.750  7.5357  7.2018  1.2438  4.4622  3.7179  3.1635  4.3659  4.4622 6.9480  6.5115  0.9900  3.9600  2.0862  2.0790  1.6065  1.7100  3.7098  3.6360   5.4000  8.3808   7.4250   6.8175   7.7274   8.091  19.9431 16.4997

20.2.  

Използвайте следното име за променливата: Liver_Pb и данните:

6.7401  9.4023  4.6224  3.1851  9.4734 13.3641  7.6509  3.3822  3.1113  5.1516  1.9287  2.8053  3.7998  7.5330  2.9997  3.0357  3.6693 12.6099 9.7992  5.9571  4.4937 14.7996 10.1997  4.8879  1.7892  2.2455  1.8927  1.8891  1.7397  2.9700  1.2789  1.1340  1.8945  2.4435  2.2302  2.1915 2.9817  4.6557  1.7487  1.3365  5.2713 10.1250  3.9825  2.9475  7.1145 15.3927  3.9825  4.0500  0.6480  2.4876  2.4354  1.7883  3.5082  3.5712 8.3754  4.1373  0.8244  3.0681  2.9763  1.8000  2.0826  2.5758  4.5000  3.4731  2.2500  5.1390  2.9178  2.3247  4.1589  4.5999  7.2288  6.6168

20.3.  

Използвайте следното име за променливата: Gills_Pb и данните:

1.7001 1.8810 1.3104 0.9558 1.7928 2.4822 1.2951 1.0719 1.2222 2.2248 1.5363 0.9702 1.4103 2.3157 1.7001 1.2879 1.6551 1.7136 1.2069 1.0593 2.8143 4.8384 1.9251 2.6127 0.1548 0.1926 0.1458 0.1881 0.5139 0.9936 0.3807 0.1521 0.1899 0.4950 0.2142 0.1881 0.3528 0.3591 0.2214 0.1800 0.9189 1.2825 1.0710 0.8316 1.3257 1.5147 1.0224 0.6570 0.1512 0.2475 0.3051 0.3528 0.9342 1.6425 1.7514 0.2889 0.1782 0.2853 0.2358 0.2187 1.0917 1.0971 1.7136 1.2312 1.1898 1.9314 1.8900 1.8000  2.3157  2.4300 2.6127  2.4084

20.4.  

Използвайте следното име за променливата: Skin_Pb и данните:

1.5849 1.8000 1.2312 0.9684 1.3725 2.1537 1.3941 1.1331 1.4697 1.7253 1.4967 0.9684 1.8999 2.6604 1.7928 1.5381 1.1925 1.5777 1.1547 1.0656 1.9251 2.4084 1.5300 0.9837 0.7272 1.1070 0.7479 0.8316 0.9252 1.0278 0.9234 0.9081 0.5184 0.5364 0.4941 0.3375 0.4050 0.4527 0.2655 0.1908 0.7479 0.6651 0.6390 0.7263 0.9198 0.9648 0.7956 0.6075 0.5697 0.7650 0.8046 0.7272 1.0125 1.1151 1.7928 1.7001 0.2700 0.5121 0.4860 0.3834 1.0053 1.1547 1.1925 1.2717 0.9900 1.6362 1.2996 1.2852 1.9845  1.9251  1.6146 1.3635

20.5.  

Използвайте следното име за променливата: Bones_Pb и данните:

1.5975 1.7154 1.6200 0.7290 1.1682 1.5363 1.7334 0.8055 1.3383 1.6164 1.0971 0.9684 1.7019 1.6344 1.0908 1.2591 1.6884 1.9881 0.7911 0.9531 1.5849 2.6073 1.8396 0.8586 0.3024 0.9630 1.0800 0.4050 0.4725 0.8208 0.4500 0.3303 0.2142 0.3231 0.2610 0.2151 0.5454 0.7470 0.3375 0.2655 0.9459 1.2348 0.6147 0.3294 1.2789 1.6182 0.8379 0.8460 0.3978 1.1250 0.6354 0.4842 0.8955 0.9855 1.4751 1.4085 0.2700 0.8901 0.8037 0.4599 0.3609 0.5670 0.9162 0.6435 0.9720 1.3383 1.3104 1.5300  0.9828 1.2951  1.3725  1.3941

20.6.  

Използвайте следното име за променливата: Muscle_Pb и данните:

1.4823 1.5309 1.4472 0.6183 1.4931 2.0349 0.9810 0.8415 1.0188 1.0035 0.8397 0.7110 1.1007 1.1178 0.5130 0.8820 1.2312 1.6884 1.2087 0.6480 1.4157 1.5723 1.4535 0.7263 0.1953 0.9468 0.5562 0.1314 0.1908 0.4959 0.1278 0.1134 0.1629 0.1242 0.1413 0.0720 0.3375 0.3429 0.2754 0.1953 0.2340 0.9126 0.8334 0.8487 0.6570 1.1250 0.6570 0.5220 0.0702 0.2592 0.1125 0.1143 0.1728 0.1179 0.4284 0.1377 0.0675 0.3312 0.3015 0.1602 0.2178 0.2529 0.8235 0.3987 0.1035 0.6381 0.2565 0.2196 0.2619 0.7020 1.0089 1.0845

20.7.  

Използвайте следното име за променливата: Kidney_Cd и данните:

8.3205  9.1809  4.6926  2.9250 17.5689 15.6609 13.5225 11.6865  2.9259  7.3116  4.7169  3.5901 20.9259 16.7616 15.5169 15.0201 11.9619 17.0316 15.5169 15.2811 20.8719 26.0586 25.1055 24.2811  6.4575  8.3709  3.2868  2.0610 16.8750 18.0108 17.3709 15.7500  2.0250  7.0254  3.7260  2.8422 5.4918 11.2806  9.0909  3.6153 11.2500 14.2200 13.5099 13.7790 14.6250 28.1250 25.1109 15.3261  0.6750  0.8442  0.7290  0.5454  1.1025  2.0673 2.6910  1.5750  0.1143  0.4887  0.3015  0.2970  1.0647  1.6155  1.5192  1.3896  2.2500  3.3300  3.1950  1.3500  2.4750  3.9078  3.5100  2.0124

20.8.  

Използвайте следното име за променливата: Liver_Cd и данните:

1.8945  2.2869  1.8135  1.8090  3.7422  6.8922  5.4045  5.1102  1.3212  2.0826  1.0359  2.4759  9.4212 14.5926 12.1959 11.4813  4.8852  9.1926 6.4719  5.1399 14.0652 15.3216 17.2719 15.0399  0.9360  1.4139  1.0035  0.6750  2.8422  9.6390  3.9060  2.0799  0.8478  1.0242  1.0044  1.5750 2.1519  3.1221  1.4850  1.3941  4.0410  8.5725  5.2182  1.1565  7.0875 18.0108 14.7600  5.6520  0.2295  0.2250  0.1233  0.1620  0.1665  0.2790 0.7875  0.1611  0.0909  0.1980  0.2700  0.2889  0.5877  0.9603  0.9027  0.4491   0.2925   0.7560   0.5454   0.5049  1.2861   3.5064   3.4767  1.5750

20.9.  

Използвайте следното име за променливата: Gills_Cd и данните:

1.1718 1.2312 1.1034 1.0584 1.1781 1.1412 1.0044 0.9981 1.1889 1.0782 0.9801 0.9990 1.3869 1.1916 1.0161 1.0080 1.2204 1.0575 1.0899 1.0089 1.7883 1.7775 1.7199 1.6389 0.2718 0.3312 0.2034 0.1584 0.2781 2.0700 0.3456 0.3321 0.1188 0.2520 0.1656 0.0990 0.3879 0.4104 0.3825 0.2115 0.3015 0.6426 0.5418 0.3015 0.8748 1.1916 0.5508 0.5418 0.0810 0.0747 0.0630 0.0378 0.0828 0.0954 0.1017 0.0693 0.0180 0.0810 0.0477 0.0441 0.0603 0.0594 0.0576 0.0450 0.1719 0.2250 0.1728 0.1611 0.3150 0.5247 0.3510 0.1800

20.10.   

Използвайте следното име за променливата: Skin_Cd и данните:

1.0836 1.1691 1.2978 0.9918 1.1826 1.1943 1.3491 1.4418 1.0890 1.1889 1.4049 0.9189 1.3590 1.3239 1.4022 1.2789 1.0890 1.2789 1.4301 0.9504 1.4490 1.7289 1.7901 1.3104 0.1836 0.2691 0.2196 0.1899 0.3816 0.9450 0.4770 0.3879 0.3348 0.3771 0.2511 0.2691 0.3843 0.5256 0.5238 0.2781 0.1548 0.4752 0.3825 0.1008 0.3411 0.8550 0.5202 0.3501 0.0747 0.0927 0.0711 0.0441 0.0927 0.0945 0.0954 0.0522 0.0351 0.0639 0.0459 0.0342 0.0486 0.1035 0.0243 0.0252 0.1638 0.1062 0.1629 0.0909 0.2700 0.2997 0.1845 0.1440

20.11.  

Използвайте следното име за променливата: Bones_Cd и данните:

0.2169 0.5211 0.8865 0.5589 0.6399 0.8100 0.7965 0.6489 0.8865 0.7866 0.5886 0.3582 0.7785 0.8766 0.6786 0.8082 0.7965 0.8766 0.6786 0.3222 0.7974 0.8073 0.5886 0.4122 0.0621 0.3771 0.1026 0.1143 0.3879 0.6129 0.2700 0.2484 0.2583 0.2232 0.2061 0.1899 0.3708 0.8028 0.6552 0.5697 0.1953 0.4221 0.2583 0.2034 0.2988 0.6201 0.4977 0.2718 0.1710 0.1728 0.3897 0.0900 0.1431 0.1710 0.1080 0.1251 0.0540 0.0441 0.0441 0.0459 0.1629 0.2790 0.2610 0.2124 0.1233 0.2367 0.1431 0.0900 0.2475 0.2691 0.2700 0.0990

20.12.  

Използвайте следното име за променливата: Muscle_Cd и данните:

0.2682 0.6462 0.5985 0.1926 0.3555 0.7308 0.6786 0.3159 0.1089 0.2889 0.0999 0.0486 0.1908 0.3429 0.1899 0.1836 0.1089 0.3168 0.1422 0.0882 0.4689 0.5868 0.8622 0.1782 0.0198 0.0675 0.0594 0.0180 0.1143 0.1719 0.1620 0.1017 0.0747 0.0792 0.0459 0.0198 0.2331 0.2790 0.1557 0.1305 0.1134 0.1188 0.1008 0.0990 0.2097 0.2862 0.2520 0.2502 0.0504 0.0783 0.0396 0.0207 0.0747 0.0891 0.0522 0.0459 0.0099 0.0576 0.0126 0.0180 0.0108 0.0153 0.0144 0.0162 0.0252 0.0693 0.0405  0.0189 0.0963  0.1413 0.1179 0.1188

20.13.  

Използвайте следното име за променливата: Kidney_Zn и данните:

115.5681  614.3274  220.6143   95.8257  148.7511  123.1101  642.2976  224.3709 103.9734  186.8625  150.9390  102.2976  151.1118  399.9996  605.0871 370.0089  360.5769  626.6799  543.2832  103.7556  126.8838  153.7749  620.3799  182.0295   59.4450   65.9970  168.7500   59.0400  196.8750 1125.0000 270.0000  214.4070   97.1820  455.6250  179.2890  133.7400  298.4670  607.7970  316.9710  148.6890  416.9250 1008.9000 2390.400  476.3790 1094.5800 1350.2970  937.4400  874.8000   97.6950    141.3000   89.6850   93.6000  133.6500  208.7100  205.4880   81.5850  113.1840  121.7160   89.5230  108.432 73.9350   79.3170   78.5880   74.6280  134.5680   160.2270   114.5250  138.150 292.5000  450.0000   375.7500    253.9260

20.14.  

Използвайте следното име за променливата: Liver_Zn и данните:

74.7630 502.6959 153.8073  84.5307 136.8486 130.6476 486.2295 179.9073 105.3180 129.9627 126.2295  62.7282 111.6288 142.8867 181.0899 125.2143 123.3099 318.5865 152.1522  99.9189 127.4220 152.1342 635.2776 138.6747  63.8550  41.2290 132.3450  67.9590 117.3600 964.2780 177.6240 137.4300 68.2470  85.1670 115.1910  76.0500 135.2880 412.8300 149.3010 136.6290 189.1080 258.6150 302.7960 148.7700 175.5000 537.3720 414.2070 153.1710 80.4510  92.1060  80.4240  74.6010 113.5620  88.7130  87.4980  81.2250  89.2350 108.4140  86.0220 100.8720  76.5540  80.4780  72.3960  70.5870 97.7670 150.3540  81.7470  96.8490 227.2050 253.1250 230.9940 210.2760

20.15.  

Използвайте следното име за променливата: Gills_Zn  и данните:

51.7140  59.5080  51.7950  33.0750  60.8940  65.3310  65.7000  53.9910  73.9422  76.5099  74.7000  66.7872  74.7009  79.3917 107.5419 100.8999 134.1000 140.3289 134.2089 133.8426 106.5789 146.0889 149.2326 144.0189  40.8510  43.5780  42.6150  29.6550  47.2500  70.3620  50.4630  43.2000 45.5400  48.4380  50.0580  47.4480  63.1530  69.5970  64.4310  53.5500  37.2240  44.1450  57.8520  43.7940  82.3140 120.3030  91.7910  72.8280 60.3540  60.4170  51.0210  56.5830  62.6760  62.9010  56.8080  59.3370  50.6250  53.1810  46.9170  47.7900  63.0000  61.3080  57.2130  53.9100 69.7500  73.6560  64.7820  65.9700  85.6080  81.1170  70.9650  69.1290

20.16.  

Използвайте следното име за променливата: Skin_Zn и данните:

38.3040 41.4180 39.3975 42.8445 54.1710 63.1080 64.8189 62.4177 62.7444 66.2400 63.0198 63.0999 64.8999 71.2611 73.9179 67.6872 63.5445 74.7738 65.7288 67.8069 63.9468 76.5954 81.1368 70.3719 30.4020 33.2100 32.5890 21.7530 38.3760 41.5350 40.6260 31.5000 37.8090 40.6350 41.5440 29.9070 36.5400 61.4880 53.0640 45.8100 36.0900 43.8750 53.5140 40.2570 77.1750 88.1550 80.6580 70.3890 43.2000 45.1890 40.6530 45.0000 55.1070 56.8260 54.8910 54.0000 42.2370 44.9910 33.7500 39.5910 45.0900 46.1970 43.8390 42.2910  54.9990   62.9280   43.8390  54.0000  78.6870  80.1900   69.9120  65.9700

20.17.  

Използвайте следното име за променливата: Bones_Zn и данните:

49.2381 71.5230 35.5104 23.5377 24.5835 79.4673 72.5409 58.6557 24.1065 72.5409 27.2061 14.2083 16.0389 25.1847 77.0004 49.6305 31.0581 45.1323 40.3695 36.1089 42.3729 46.8279 56.4174 40.9608 21.3120 21.7530 24.2550 21.1140 27.2250 40.8060 30.2220 26.6310 17.3430 22.0950 23.8500 17.2800 27.0000 41.5170 34.8300 28.0170 20.7720 21.4740 28.3320 40.1760 45.2070  52.1460 46.0080 43.4700 20.5470 20.4480 18.4590 20.2860 23.2830 23.9490 21.5460 26.4510 17.1540 16.3620 12.7080 12.8880 12.7080 19.9260 11.9160 11.4750  16.7220   19.2780  17.7570  16.0650   27.4320  28.7190   22.5000  22.6710

20.18.  

Използвайте следното име за променливата: Muscle_Zn  и данните:

7.1073 20.9097 17.4249 13.3722 16.9029 18.0990 24.6573 13.8798 13.8798 15.3108 11.1969 10.4607 12.7368 16.4349 25.6356 11.3607  9.9342 5.9057 10.6848 10.5669 10.2429 10.8774 19.1529 11.7000 13.1850 16.3530 5.1650  9.1710 17.7480 24.7050 11.2500 12.5010 11.4570 10.3860  9.9540  9.0360  12.6360 26.0730 19.8000 10.8000 16.2720 17.1540 16.3800 15.9030 6.8750  37.0530 18.1800 14.8320  7.2270  9.6390    7.0290    8.2890  13.500  13.779 13.212 13.023 5.2560 8.2080    7.29       5.2110  13.5  14.1930  6.66 7.335 11.538 

 

ПРИЛОЖЕНИЕ 1

Стандартно нормално разпределение N (0, 1)

 

z

0.00

0.01

0.02

0.03

0.04

0.0

0.5

0.503989379

0.507978354

0.511966527

0.515953499

0.1

0.539827896

0.543795364

0.547758470

0.551716823

0.555670033

0.2

0.579259687

0.583166134

0.587064387

0.590954073

0.594834824

0.3

0.617911357

0.621719457

0.625515770

0.629299955

0.633071673

0.4

0.655421697

0.659096986

0.662757237

0.666402148

0.67003 J420

0.5

0.691462467

0.694974281

0.698468229

0.701944056

0.705401511

0.6

0.725746935

0.729069152

0.73237J166

0.735652770

0.738913765

0.7

0.758036422

0.761148006

0.764237576

0.767304982

0.770350076

0.8

0.788144666

0.791029974

0.793892006

0.796730665

0.799545861

0.9

0.815939908

0.818588775

0.821213646

0.823814480

0.826391238

1.0

0.841344740

0.843752345

0.846135756

0.848494980

0.850830029

1.1

0.864333898

0.866500443

0.868643073

0.870761839

0.872856799

1.2

0.884930268

0,886860491

0.888767499

0.890651383

0.892512238

1.3

0.903199451

0.904902018

0.906582427

0.908240802

0.909877266

1.4

0.919243289

0.920730109

0.922196112

0.923641445

0.925066257

1.5

0.933192771

0.934478263

0.935744490

0.936991617

0.938219807

16

0.945200711

0.946301077

0.947383870

0.948449263

0.949497431

1.7

0.955434568

0.956367097

0.957283815

0.958184901

0.959070532

1.8

0.964069734

0.964852162

0.965620555

0.966375089

0.967115942

1.9

0.971283507

0.971933461

0.972571119

0.973196650

0.973810224

2.0

0.977249938

0.977784475

0.978308376

0.978821799

0.979324905

2.1

0.982135643

0.982570884

0.982997038

0.983414253

0.983822675

2.2

0.986096601

0.986447466

0.986790661

0.987126322

0.987454580

2.3

0.989275919

0.989555950

0.989829586

0.990096947

0.990358150

2.4

0.991802471

0.992023745

0.992239749

0.992450589

0.992656367

2.5

0.993790320

0.993963425

0.994132240

0.994296853

0.994457354

2.6

0.995338778

0.995472853

0.995603474

0.995730718

0.995854658

2.7

0.996532977

0.996635789

0.996735852

0.996833231

0.996927987

2.8

0.997444809

0.997522864

0.997598756

0.997672537

0.997744260

2.9

0.998134120

0.998192789

0.998249775

0.998305122

0.998358871

3.0

0.998650033

0.998693692

0.998736057

0.998777162

0.998817040

3 1

0.999032329

0.999064496

0.999095677

0.999125901

0.999155194

3.2

0.999312798

0.999336262

0.999358984

0.999380986

0.999402289

3.3

0.999516517

0.999533462

0.999549856

0.999565714

0.999581052

3.4

0999663019

0.999675135

0.999686844

0.999698160

0.999709094

3.5

0.999767327

0.999775903

0.999784184

0.999792178

0.999799895

3.6

0.999840854

0.999846865

0.999852663

0.999858254

0.999863647

3.7

0.999892170

0.999896341

0.999900359

0.999904232

0.999907962

3.8

0.999927628

0.999930493

0.999933251

0.999935906

0.999938461

3.9

0.999951884

0.999953833

0.999955707

0.999957509

0.999959242

 

 

Стандартно нормално разпределение N(0,1)

 

z

0.05

0.06

0.07

0.08

0.09

0.0

0.519938873

0.523922253

0.527903240

0.531881440

0.535856456

0.1

0.559617712

0.563559473

0.567494933

0.571423709

0.575345420

0.2

0.598706274

0.602568057

0.606419814

0.610261186

0.614091818

0.3

0.636830590

0.640576374

0.644308699

0.648027240

0.651731677

0.4

0.673644759

0.677241874

0.680822481

0.684386299

0.687933051

0.5

0.708840345

0.712260318

0.715661192

0.719042736

0.722404724

0.6

0.742153956

0.745373154

0.748571176

0.751747842

0.754902979

0.7

0.773372720

0.776372779

0.779350124

0.782304631

0.785236183

0.8

0.802337508

0.805105527

0.807849842

0.810570386

0.813267094

0.9

0.828943888

0.831472403

0.833976760

0.836456943

0.838912939

1.0

0.853140919

0.855427672

0.857690314

0.859928875

0.862143390

1.1

0.874928011

0.876975542

0.878999459

0.880999834

0.882976744

1.2

0.894350161

0.896165253

0.897957619

0.899727366

0.901474606

1.3

0.911491948

0.913084979

0.914656492

0.916206622

0.917735507

1.4

0.926470700

0.927854925

0 929219087

0.930563344

0.931887852

1.5

0.939429229

0.940620050

0.941792438

0.942946563

0.944082597

1.6

0.950528549

0.951542794

0.952540341

0.953521368

0.954486051

1.7

0.959940886

0.960796142

0.961636477

0.962462069

0.963273096

1.8

0.967843287

0.968557300

0.969258155

0.969946026

0.970621086

1.9

0.974412010

0.975002175

0.975580885

0.976148306

0.976704602

2.0

0.979817852

0.980300797

0.980773894

0.981237299

0.981691164

2.1

0.984222449

0.984613720

0.984996631

0.985371321

0.985737932

2.2

0.987775567

0.988089412

0.988396244

0.988696189

0.988989373

2.3

0.990613313

0.990862548

0.991105971

0.991343692

0.991575823

2.4

0.992857185

0.993053143

0.993244339

0.993430871

0.993612833

2.5

0.994613830

0.994766365

0.994915046

0.995059954

0.995201171

2.6

0.995975369

0.996092924

0.996207393

0.996318845

0.996427351

2.7

0.997020181

0.997109875

0.997197128

0997281997

0.997364539

2.8

0.997813974

0.997881730

0.997947576

0.998011558

0.998073724

2.9

0.998411062

0.998461736

0.998510932

0.998558689

0.998605044

3.0

0.998855724

0.998893246

0.998929637

0.998964929

0.998999149

3.1

0.999183581

0.999211088

0.999237740

0.999263560

0.999288571

3.2

0.999422914

0.999442878

0.999462202

0.999480905

0.999499004

3.3

0.999595887

0.999610233

0.999624105

0.999637518

0.999650485

3.4

0.999719659

0.999729865

0.999739724

0.999749247

0.999758445

3.5

0.999807344

0.999814533

0.999821470

0.999828164

0.999834623

3.6

0:999868846

0.999873859

0.999878692

0.999883351

0.999887842

3.7

0.999911555

0.999915017

0 999918350

0.999921560

0.999924651

3.8

0.999940919

0.999943285

0.999945562

0.999947752

0.999949858

3.9

0.999960908

0.999962509

0.999964048

0.999965527

0.999966948

 

 

ПРИЛОЖЕНИЕ 2

Квантили tq(k)на симетричното t - разпределение на Стюдънт

k\q

0.60

0.75

0.90

0.95

0.975

I

0.324919256

1.000000793

3.077684596

6.313748599

12.706150301

2

0.288674755

0.816496595

1.885618985

2.919987310

4.302655725

3

0.276670562

0.764891865

1.637745299

2.353363016

3.182449291

4

0.270722467

0.740697033

1.533205705

2.131846486

2.776450856

5

0.267181122

0.726686835

1.475884801

2.015049176

2.570577635

6

0.264834625

0.717558351

1.439755124

1.943180905

2.446913641

7

0.263166839

0.711141865

1.414923645

1.894577508

2.364622560

8

0.261920832

0.706386345

1.396815605

1.859548320

2.306005626

9

0.260955630

0.702722218

1.383028803

1.833113856

2.262158887

10

0.260184834

0.699811835

1.372184215

1.812461505

2.228139238

11

0.259556145

0.697444875

1.363430329

1.795883691

2.200986273

12

0.259032618

0.695482640

1.356218036

1.782286745

2.178812792

13

0.258590944

0.693829634

1.350172170

1.770931704

2.160368240

14

0.258212367

0.692417075

1.345031251

1.761309250

2.144788596

15

0.257884949

0.691196647

1.340605422

1.753051038

2.131450856

16

0.257599027

0.690132538

1.336757123

1.745884219

2.119904821

17

0.257347210

0.689194621

1.333379487

1.739606432

2.109818524

18

0.257123247

0.688363571

1.330390660

1.734063062

2.100923666

19

0.256923158

0.687621196

1.327728114

1.729131327

2.093024705

20

0.256742396

0.686954422

1.325340691

1.724718004

2.085962478

21

0.256579824

0.686352450

1.323187462

1.720743512

2.079614205

22

0.256432031

0.685805048

1.321236596

1.717144187

2.073875294

23

0.256296744

0.685306532

1.319460807

1.713870006

2.068654794

24

0.256173394

0.684849510

1.317835086

1.710882316

2.063898137

25

0.256059707

0.684430006

1.316345788

1.708140189

2.059537110

26

0.255954546

0.684042902

1.314972451

1.705616341

2.055530786

27

0.255857913

0.683685357

1.313703706

1.703288035

2.051829142

28

0.255767532

0.683352823

1.312525910

1.701130259

2.048409442

29

0.255683972

0.683044163

1.311434517

1.699127097

2.045230758

30

0.255605528

0.682755399

1.310415882

1.697260359

2.042270353

31

0.255532200

0.682485961

1.309463187

1.695518677

2.039514584

32

0.255463419

0.682233576

1.308573019

1.693888407

2.036931619

33

0.255399186

0.681997108

1.307737421

1.692360456

2.034516910

34

0.255338364

0.681774281

1.306950708

1.690923455

2.032243174

35

0.255281520

0.681563961

1.306211743

1.689572855

2.030110409

40

0.255038799

0.680672656

1.303076260

1.683852133

2.021074579

45

0.254850079

0.679980872

1.300650183

1.679427442

2.014103302

50

0.254699444

0.679427785

1.298712959

1.675905423

2.008559932

55

0.254576094

0.678976448

1.297134986

1.673033694

2.004044291

60

0.254473207

0.678600713

1.295820766

1.670648544

2.000297172

120

0.253909320

0.676540139

1.288645990

1.657649591

1.979929038

0.253346570

0.674490366

1.281550794

1.644853000

1.959961082

Квантили tq(k)на симетричното t- разпределение на Стюдънт

 

k\q

0.99

0.995

0.9975

0.999

0.9995

1

31.820964068

63.655897975

127.321109176

318.288803101

636.577606201

2

6.964546628

9.924988262

14.089164324

22.328458726

31.599774957

3

4.540706868

5.840847734

7.453199942

10.214280337

12.924429029

4

3.746936272

4.604080459

5.597539712

7.172930054

8.610077202

5

3.364930308

4.032117431

4.773319233

5.893525667

6.868503988

6

3.142667993

3.707427823

4.316825652

5.207548384

5.958718248

7

2.997949196

3.499480954

4.029352567

4.785251804

5.408073775

8

2.896467777

3.355380613

3.832537914

4.500761861

5.041365512

9

2.821434464

3.249842848

3.689638106

4.296889529

4.780886229

10

2.763772500

3.169261618

3.581371857

4.143657861

4.586763680

11

2.718079486

3.105815267

3.496606951

4.024768714

4.436878953

12

2.680990292

3.054537956

3.428431228

3.929599188

4.317844287

13

2.650303941

3.012282832

3.372479114

3.852037480

4.220928531

14

2.624492481

2.976848918

3.325694706

3.787426976

4.140310921

15

2.602482709

2.946726454

3.286040737

3.732857294

4.072790034

16

2.583492460

2.920787665

3.251989256

3.686145646

4.014873412

17

2.566939656

2.898232196

3 222448868

3.645764082

3.965105861

18

2.552378646

2.878441592

3.196582838

3.610475687

3.921741154

19

2.539482011

2.860942914

3.173699952

3.579334589

3.883324098

20

2.527976903

2.845335985

3.153400030

3.551831469

3.849563655

21

2.517645044

2.831366146

3.135210136

3.527093213

3.81929567!

22

2.508322723

2.818760549

3 118839231

3.504974302

3 792229109

23

2.499873517

2.807337296

3.103996278

3.484965418

3.767636372

24

2.492161002

2.796950866

3.090535756

3.466775524

3.745371941

25

2.485103323

2.787437552

3.078203008

3.450186341

3.725144779

26

2.478627721

2.778724593

3.066888894

3.434979590

3.706663847

27

2.472661436

2.770684659

3.056520654

3.421009751

3.689492587

28

2.467140803

2.763263183

3.046952770

3.408204066

3.673922038

29

2.462020348

2.756387403

3.038039722

3.396271495

3.659515642

30

2.457263690

2.749984560

3.029781510

3.385212040

3.645982360

31

2.452825356

2.744036465

3.022105375

3.374880180

3.633467713

32

2.448678060

2.738488547

3.014938557

3.365275916

3 621826181

33

2.444794518

2.733286237

3.008244676

3.356326488

3.610912245

34

2.441147444

2.728393156

3.001950972

3.347959137

3.600725904

35

2.437718649

2.723809303

2.996057447

3.340028343

3.591121640

40

2.423257683

2.704455255

2.971173672

3.306922736

3.550958354

45

2.412116373

2.689594112

2.952074283

3.281456884

3.520253813

50

2.403266990

2.677788871

2936976671

3.261375241

3.495952114

55

2.396081982

2.668220986

2.924716682

3.245149856

3.476452548

60

2.390115696

2.660272003

2.914566721

3.231689334

3.460154403

120

2.357828635

2.617416612

2.859851520

3.15951 1834

3.373424988

2.326341928

2.575834515

2.807064448

3.090244718

3.290479071

ПРИЛОЖЕНИЕ  3

Квантили  χq2(k) на асиметричното  χ2- разпределение на Пирсън

 

k\q

0.005

0.010

0.025

0.050

0.100

0.500

1

3.927Е-05

0.0001571

0.0009821

0.0039322

0.0157907

0.4549362

2

0.0100247

0.0201004

0.0506357

0.1025862

0.2107208

1.3862936

3

0.0717235

0.1148316

0.2157949

0.351846

0.5843755

2.3659727

4

0.2069836

0.2971068

0.484419

0.7107241

1.0636243

3.3566947

5

0.4117508

0.5542969

0.8312089

1.1454773

1.6103091

4.3514587

6

0.6757334

0.8720833

1.2373419

1.6353805

2.2041303

5.348119

7

0.9892509

1.2390317

1.689864

2.1673492

2.8331052

6.3458093

8

1.3444027

1.6465062

2.1797247

2.7326326

3.4895374

7.3441201

9

1.7349114

2.0878894

2.7003887

3.3251151

4.1681557

8.342832

10

2.1558454

2.5581988

3.2469635

3.9402953

4.8651783

9.3418161

11

2.6032019

3.0534957

3.8157424

4.574809

5.5777883

10.340996

12

3.073785

3.5705513

4.4037775

5.2260277

6.3037959

11.340322

13

3.565042

4.1068996

5.0087376

5.8918606

7.0414997

12.339753

14

4.0746588

4.6604155

5.6287238

6.5706316

7.7895377

13.339272

15

4.6008741

5.2293559

6.2621229

7.2609348

8.5467531

14.338857

16

5.1421643

5.8121968

6.9076641

7.9616386

9.3122353

15.338497

17

5.6972737

6.407742

7.5641786

8.6717536

10.085183

16.338179

18

6.2647659

7.0149034

8.2307372

9.3904479

10.864937

17.337902

19

6.8439233

7.6326976

8.9065144

10.117006

11.650912

18.33765

20

7.4338114

8.2603684

9.5907725

10.850799

12.442601

19.33743

21

8.0336021

8.8971724

10.282907

11.591316

13.239596

20.337228

22

8.6426806

9.5424944

10.98233

12.338009

14.04149

21.337044

23

9.2603831

10.195689

1 1.688534

13.090505

14.847954

22.33688

24

9.8861987

10.856349

12.401146

13.848422

15.658679

23.33673

25

10.519647

11.523951

13.119707

14.611396

16.473405

24.336584

26

11.160218

12.198177

13.843881

15.379163

17.29188

25.336458

27

11.807655

12.878468

14.573373

16.151395

18.113889

26.336341

28

12.461281

13.564666

15.307854

16.927876

18.939235

27.336232

29

13.121067

14.256406

16.047051

17.708381

19.76774

28.33613

30

13.786682

14.953464

16.790756

18.492667

20.599245

29.336028

35

17.191729

18.50887

20.56938

22.465009

24.796648

34.335635

40

20.706577

22.164201

24.433058

26.509296

29.050516

39.335341

45

24.310982

25.9012

28.366177

30.612259

33.350378

44.335118

50

27.990825

29.706725

32.357385

34.764236

37.688637

49.334941

55

31.734894

33.570516

36.398113

38.958051

42.05962

54.334787

60

35.534397

37.484796

40.481707

43.187966

46.458885

59.334668

65

39.383227

41.443554

44.60297

47.449572

50.882935

64.334557

70

43.275305

45.4417

48.757536

51.739263

55.328945

69.334479

80

51.171933

53.539983

57.153152

60.391459

64.277842

79.334325

90

59.196327

61.754019

65.646592

69.126018

73.291079

89.334216

100

67.327533

70.064995

74.221882

77.929442

82.358127

99.33413

 

 

Квантили χq2 на асиметричното  χ2 - разпределение на Пирсън

 

k\q

0.900

0.950

0.975

0.990

0.995

1

2.7055406

3.8414553

5.0239026

6 6348913

7.8793998

2

4.6051761

5.9914764

7.3777791

9.210351

10.59653

3

6.2513945

7.8147247

9.348404

11.344882

12.838073

4

7.779434

9.4877285

11.143262

13.276699

14.860166

5

9.2363491

11.070483

12.832492

15.086317

16.749648

6

10.644637

12.591577

14.449355

16.811872

18.547513

7

12.017031

14.067127

16.012774

18.475324

20.277738

8

13.361562

15.507312

17.534545

20.090159

21.954861

9

14.683663

16.91896

19.022778

21.666048

23.589275

10

15.987175

18.307029

20.483201

23.209287

25.188055

11

17.275007

19.675153

21 920023

24.725022

26.756864

12

18.54934

21.026055

23.33666

26.216964

28.29966

13

19.811933

22.362027

24.735581

27.688184

29.819318

14

21.064141

23.684782

26.118935

29.141163

31.319425

15

22.307121

24.995797

27.488365

30.577951

32.801491

16

23.541821

26.296221

28.845325

31.999861

34.267053

17

24.769028

27.5871

30.190983

33.408717

35.718378

18

25.989418

28.869321

31.52641

34.805237

37.156386

19

27.203565

30.143505

32.852337

36.190775

38.582122

20

28.41197

31.41042

34.169581

37.566272

39.996856

21

29.615086

32.670558

35 478856

38.932232

41.400943

22

30.813285

33.92446

36.780678

40.289448

42.795664

23

32.00689

35.17246

38.075609

41.638334

44.181385

24

33.196235

36.415026

39.36406

42.979781

45.558363

25

34.381583

37.652489

40.646498

44.314014

46.927966

26

35.563164

38.88513

41.923138

45.641636

48.289777

27

36.741228

40.113266

43.194521

46.962837

49.645035

28

37.915907

41.337152

44.46079

48.278166

50.993559

29

39.087475

42.556948

45.722279

49.587829

52.335495

30

40.256017

43.772954

46.979218

50.892181

53.671868

35

46.058772

49.801832

53.203308

57.341988

60.274592

40

51.805044

55.758487

59.341679

63.690771

66.766047

45

57.505291

61.656219

65.410131

69.956901

73.166036

50

63.167113

67.504805

71.420194

76.153802

79.489839

55

68.796207

73.311479

77.380436

82.291977

85.749058

60

74.396999

79.081954

83.297706

88.37943

91.951806

65

79.97299

84.82064

89.177163

94.421996

98.104916

70

85.527036

90.531262

95.023149

100.42505

104.21477

80

96.578196

101.87947

106.62854

1 12.32879

116.32093

90

107.56501

113.14523

118.13591

124.1162

128.29868

100

118.498

124.3421

129.56125

135.80689

140.16971

 

 

4.3. Инсталиране на R.  

Системата за статистическа обработка на данните R се инсталира от http://cran.r-project.org/. Посочете използваната от вас операционна система, за да свалите (download) подходящата версия за R. Появяват се няколко web sites. Избираме по близък до България, за да се свали  R  по-бързо. Прочетете инструкциите за инсталиране на програмата. Освен ядрото можете да инсталирате и необходимите ви пакети.

 

  

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