.


:




:

































 

 

 

 


Goodness-of-Fit Tests for B.Col_1

( ).

- .

= 127,16, 20,978 ( 1).

:

= = = -0,4099+0,5 = 0,0901,

= = = - 0,2517 + 0,4099 = 0,1582,

= = = - 0,0040 + 0,2517= 0,2477,

= = = 0,2454 + 0,0040 = 0,2494,

= = = 0,4082- 0,2454 = 0,1628,

= = = 0,4772- 0,4082 = 0,069,

= = = 0,5 - 0,4772 = 0,0228.

 

2.2 c2 ,

-
(, 99]   0,0901 4,505 0,028
(99, 113]   0,1582 7,91
(113,127 ]   0,2477 12,385 0,155
(127, 141]   0,2494 12,47 0,999
(141, 155]   0,1628 12,73 0,586
(155, 169]   0,069
(169, )   0,0228
      1,768=

 

2.2

 

. c2 = = 3,841( ), a=0,05 , (4 , 2 ). . = 1,768 , = 3,841, .

 

2.2

 

X, ( ).

X .

1) , ( ) , .

 

2.3

/ , . , , .
  6,72 0,21
  8,2 0,4
  0,4 0,64
  12,9 0,69
  3,15 0,77
  34,5 0,93
  4,71 1,14
  1,14 1,51
  2,87 1,73
  3,07 1,86
  5,86  
  11,4 2,1
  3,12 2,32
  0,21 2,32
  1,51 2,4
  2,76 2,76
  0,93 2,87
  2,4 2,87
  3,5 2,99
  5,29 3,07
  1,86 3,12
  4,99 3,15
  8,77 3,5
  1,73 3,6
  0,77 4,59
  5,99 4,61
  7,95 4,71
  2,87 4,99
  0,64 5,29
  5,74 5,74
  0,69 5,86
  2,99 5,99
  4,59 6,72
  2,32 7,95
  2,32 8,2
    8,77
  2,1 11,4
  4,61 12,9
  30,1 30,1
  3,6 34,5
   

 

2) = 34,5- 0,21 = 34,29.

3) = = = 5,424.

4) :

= 0,21, =0,21+5,424 = 5,634, = 5,634 +5,424 = 11,058, = 11,058 +5,424= 16,482, = 16,482+ 5,424= 21,906, = 21,906+ 5,424 = 27,33, = 27,33+ 5,424 = 32,754, = 32,754+ 5,424 = 38,178 .

5) :

 

2.4

, .
[0.21; 5,634)  
[5,634; 11,058)  
[11,058; 16,482)  
[16,482; 21,906)  
[21,906; 27,33)  
[27,33; 32,754)  
[32,754; 38,178)  
 

 

6) .

) .

7) .

 

2.3

 

8) ( ):

( ) () .

9) .

10) pi : = .

.

- .

11) = = = 0,189358 = 0,189.

12) , . .

 

 

13) .

:

1- 0,344788 = 0,655212 =0,655.

14) , , , :

 

2.5-

      0,655212 0,655212
5,634 -1,06483 0,344788 0,221096 0,221096
11,058 -2,08996 0,123692 0,079318 0,079318
16,482 -3,1151 0,044374 0,028455 0,028455
21,906 -4,14023 0,015919 0,010208 0,010208
27,33 -5,16537 0,005711 0,003662 0,003662
32,754 -6,19051 0,002049 0,002049 0,002049
-   - -
- -    

 

2.6 c2 ,

- -
[0; 5,634)   0,655 26,21
[5,634; 11,058)   0,221 8,844
[11,058; 16,482)   0,079 3,173
[16,482; 21,906)   0,028 1,138
[21,906; 27,33)   0,01 0,408
[27,33; 32,754)   0,004 0,146
[32,754; )   0,002 0,082
      0,863 = c2

15) n = k r 1 = 3-1-1= 1, k = 3 2.6 , r =1 - ( ).

16) c2 = = 3,841 ( ), a=0,05 n = 1.

. = 0,863 , = 3,841, , , .

 

1 a.

2 1.

3 ( ):

;

npi, i = 1, 2, , k;

c2;

.

4 :

c2 ( , . 9);

(. , . 9).

5 .

 

1 ?

2 , ?

3 ?

4 ?

5 ?

6 ?

7 ?

8 c2?

9 .

10 ?

11 ?

 

()

                   
0.0 0.0000                  
0.1 0.0398                  
0.2 0.0793                  
0.3 0.1179                  
0.4 0.1554                  
0.5 0.1915                  
0.6 0.2257                  
0.7                    
0.8                    
0.9                    
1.0 0.3413                  
1.1                    
1.2                    
1.3                    
1.4                    
1.5                    
1.6                    
1.7                    
1.8                    
1.9                    
2.0 0.4772                  
2.1                    
2.2                    
2.3                    
2.4                    
2.5                    
2.6                    
2.7                    
2.8                    
2.9                    
3.0 0.49865                  
3.1 0.49903                  
3.2 0.49931                  
3.3 0.49952                  
3.4 0.49966                  
3.6 0.499841                  
3.8 0.499928                  
4.0 0.499968                  
4.5 0.499997                  
5.0 0.4999997                  
0.5                  

 


()
c2

n a
0.001 0.01 0.025 0.05 0.1 0.9 0.95 0.975 0.99
  10.827 6.635 5.024 3.841 2.706 0.016 0.0039 0.00098 0.00016
  13.815 9.210 7.378 5.991 4.605 0.211 0.103 0.051 0.020
  16.266 11.345 9.348 7.815 6.251 0.584 0.352 0.216 0.115
  18.466 13.277 11.143 9.488 7.779 1.064 0.711 0.484 0.297
  20.515 15.086 12.832 11.070 9.236 1.610 1.145 0.831 0.554
  22.457 16.812 14.449 12.592 10.645 2.204 1.635 1.237 0.872
  24.321 18.475 16.013 14.067 12.017 2.833 2.167 1.690 1.239
  26.124 20.090 17.535 15.507 13.362 3.490 2.733 2.180 1.647
  27.877 21.666 19.023 16.919 14.684 4.168 3.325 2.700 2.088
  29.588 23.209 20.483 18.307 15.987 4.865 3.940 3.247 2.558
  31.264 24.725 21.920 19.675 17.275 5.578 4.575 3.816 3.053
  32.909 26.217 23.337 21.026 18.549 6.304 5.226 4.404 3.571
  34.527 27.688 24.736 22.362 19.812 7.041 5.892 5.009 4.107
  36.124 29.141 26.119 23.685 21.064 7.790 6.571 5.629 4.660
  37.698 30.578 27.488 24.996 22.307 8.547 7.261 6.262 5.229
  39.252 32.000 28.845 26.296 23.542 9.312 7.962 6.908 5.812
  40.791 33.409 30.191 27.587 24.769 10.085 8.672 7.564 6.408
  42.312 34.805 31.526 28.869 25.989 10.865 9.390 8.231 7.015
  43.819 36.191 32.852 30.144 27.204 11.651 10.117 8.907 7.633
  45.314 37.566 34.170 31.410 28.412 12.443 10.851 9.591 8.260
  46.796 38.932 35.479 32.671 29.615 13.240 11.591 10.283 8.897
  48.268 40.289 36.781 33.924 30.813 14.041 12.338 10.982 9.542
  49.728 41.638 38.076 35.172 32.007 14.848 13.091 11.689 10.196
  51.179 42.980 39.364 36.415 33.196 15.659 13.848 12.401 10.856
  52.619 44.314 40.646 37.652 34.382 16.473 14.611 13.120 11.524
  54.051 45.642 41.923 38.885 35.563 17.292 15.379 13.844 12.198
  55.475 46.963 43.195 40.113 36.741 18.114 16.151 14.573 12.878
  56.892 48.278 44.461 41.337 37.916 18.939 16.928 15.308 13.565
  58.301 49.588 45.722 42.557 39.087 19.768 17.708 16.047 14.256
  59.702 50.892 46.979 43.773 40.256 20.599 18.493 16.791 14.953
  61.098 52.191 48.232 44.985 41.422 21.434 19.281 17.539 15.655
  62.487 53.486 49.480 46.194 42.585 22.271 20.072 18.291 16.362
  63.869 54.775 50.725 47.400 43.745 23.110 20.867 19.047 17.073
  65.247 56.061 51.966 48.602 44.903 23.952 21.664 19.806 17.789
  66.619 57.342 53.203 49.802 46.059 24.797 22.465 20.569 18.509
  67.985 58.619 54.437 50.998 47.212 25.643 23.269 21.336 19.233
  69.348 59.893 55.668 52.192 48.363 26.492 24.075 22.106 19.960
  70.704 61.162 56.895 53.384 49.513 27.343 24.884 22.878 20.691
  72.055 62.428 58.120 54.572 50.660 28.196 25.695 23.654 21.426
  73.403 63.691 59.342 55.758 51.805 29.051 26.509 24.433 22.164

 

 

Goodness-of-Fit Tests for B.Col_1

Chi-Squared Test

  Lower Upper Observed Expected  
  Limit Limit Frequency Frequency Chi-Squared
at or below   30,1429   9,05 0,46
  30,1429 30,7143   16,53 0,37
  30,7143 31,2857   16,12 0,00
above 31,2857     8,31 0,01

Chi-Squared = 0,845494 with 1 d.f. P-Value = 0,357829

 

The StatAdvisor

This pane shows the results of tests run to determine whether B.Col_1 can be adequately modeled by a normal distribution. The chi-squared test divides the range of B.Col_1 into nonoverlapping intervals and compares the number of observations in each class to the number expected based on the fitted distribution.

 

Since the smallest P-value amongst the tests performed is greater than or equal to 0,05, we can not reject the idea that B.Col_1 comes from a normal distribution with 95% confidence.

 



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