qi, :
, (2.11)
k , 1,1 P = 0,95 1,4 P = 0,99. m £ 4, k (. 1.1).
qi, Pi, :
, (2.12)
ki , 1,1 P = 0,95 1,4 P = 0,99. m £ 4, ki (. 1.1).
, (2.13)
,
. (2.14)
, (2.15)
,
. (2.16)
(2.13) (2.15) , :
, (2.17)
K , (. 2.1).
2.1
K P
P | ||||||||||
0,5 | 0,75 | |||||||||
0,95 | 0,81 | 0,77 | 0,74 | 0,71 | 0,73 | 0,76 | 0,78 | 0,79 | 0,80 | 0,81 |
0,99 | 0,87 | 0,85 | 0,82 | 0,80 | 0,81 | 0,82 | 0,83 | 0,83 | 0,84 | 0,85 |
:
, P. (2.18)
, . .
. (2.1) zi.
, .
2 2 0,5. . 1.2.
|
|
-, :
, (2.19)
, /(2K4);
e ;
F , 2;
T , K.
C, (2.19) :
, (2.20)
t , C.
(2.4).
(2.4) :
,
.
1. (2.7):
.
2. (2.8):
;
.
3. (1.19):
;
p = 0,95;
p = 0,99.
4. , (2.11):
.
5. , (2.13) (2.15), . , , (2.17) p:
p = 0,95;
p = 0,99.
6. :
p = 0,95;
p = 0,99.
( ). : , Microsoft Office Excel MathCAD. Excel MathCAD, , . 2.2.
2.2
Excel MathCAD
Excel | MathCAD | |
(2.5) | corr |
1) , () ?
2) f (2.1) ?
3) , ?
1. 8.207-76. . . .
2. 2083-90. . .
3. . . / . . , . . . .: - , 1985, 256 .
4. . . / . . . .: , 1978, 262 .
5. . . , / . . , . . . .: , 2011, 820 .
6. . . MATHCAD: . . / . . , . . . : , 2006, 34 .
.1
c2 .
k P
k | P | |||||||
0,02 | 0,05 | 0,10 | 0,20 | 0,80 | 0,90 | 0,95 | 0,98 | |
0,000628 | 0,00393 | 0,0158 | 0,0642 | 1,642 | 2,706 | 3,841 | 5,412 | |
0,0404 | 0,103 | 0,211 | 0,446 | 3,219 | 4,605 | 5,991 | 7,824 | |
0,185 | 0,352 | 0,584 | 1,005 | 4,642 | 6,251 | 7,815 | 9,837 | |
0,429 | 0,711 | 1,064 | 1,649 | 5,989 | 7,779 | 9,488 | 11,668 | |
0,752 | 1,145 | 1,610 | 2,343 | 7,289 | 9,236 | 11,070 | 13,388 | |
1,134 | 1,635 | 2,204 | 3,070 | 8,558 | 10,645 | 12,592 | 15,033 | |
1,564 | 2,167 | 2,833 | 3,822 | 9,803 | 12,017 | 14,067 | 16,622 | |
2,032 | 2,733 | 3,490 | 4,594 | 11,030 | 13,362 | 15,507 | 18,168 | |
2,532 | 3,325 | 4,168 | 5,380 | 12,242 | 14,684 | 16,919 | 19,679 | |
3,059 | 3,940 | 4,865 | 6,179 | 13,442 | 15,987 | 18,307 | 21,161 | |
3,609 | 4,575 | 5,578 | 6,989 | 14,631 | 17,275 | 19,675 | 22,618 | |
4,178 | 5,226 | 6,304 | 7,807 | 15,812 | 18,549 | 21,026 | 24,054 | |
4,765 | 5,892 | 7,042 | 8,634 | 16,985 | 19,812 | 22,632 | 25,472 | |
5,368 | 6,571 | 7,790 | 9,467 | 18,151 | 21,064 | 23,685 | 26,873 | |
5,685 | 7,261 | 8,517 | 10,307 | 19,311 | 22,307 | 24,996 | 28,259 | |
6,614 | 7,962 | 9,312 | 11,152 | 20,465 | 23,542 | 26,296 | 29,633 | |
7,255 | 8,672 | 10,085 | 12,002 | 21,615 | 24,769 | 27,587 | 30,995 | |
7,906 | 9,390 | 10,865 | 12,857 | 22,760 | 25,989 | 28,869 | 32,346 | |
8,567 | 10,117 | 11,651 | 13,716 | 23,900 | 27,204 | 30,144 | 33,687 | |
9,237 | 10,851 | 12,444 | 14,578 | 25,038 | 28,412 | 31,410 | 35,020 |
.2
|
|
d
n | ||||
0,01 | 0,05 | 0,95 | 0,99 | |
0,9137 | 0,8884 | 0,7236 | 0,6829 | |
0,9001 | 0,8768 | 0,7304 | 0,6950 | |
0,8901 | 0,8686 | 0,7360 | 0,7040 | |
0,8826 | 0,8625 | 0,7404 | 0,7110 | |
0,8769 | 0,8578 | 0,7440 | 0,7167 | |
0,8722 | 0,8540 | 0,7470 | 0,7216 | |
0,8682 | 0,8508 | 0,7496 | 0,7256 | |
0,8648 | 0,8481 | 0,7518 | 0,7291 |
.3
m a, n q
n | m | q2 | ||
0,01 | 0,02 | 0,05 | ||
0,98 | 0,98 | 0,96 | ||
11 14 | 0,99 | 0,98 | 0,97 | |
15 20 | 0,99 | 0,99 | 0,98 | |
21 22 | 0,98 | 0,97 | 0,96 | |
0,98 | 0,98 | 0,96 | ||
24 27 | 0,98 | 0,98 | 0,97 | |
28 32 | 0,99 | 0,98 | 0,97 | |
33 35 | 0,99 | 0,98 | 0,98 | |
36 49 | 0,99 | 0,99 | 0,98 |
.4
k | P | k | P | ||
0,95 | 0,99 | 0,95 | 0,99 | ||
4,303 | 9,925 | 2,110 | 2,898 | ||
3,182 | 5,841 | 2,101 | 2,878 | ||
2,776 | 4,604 | 2,093 | 2,861 | ||
2,571 | 4,032 | 2,086 | 2,845 | ||
2,447 | 3,707 | 2,080 | 2,831 | ||
2,365 | 3,499 | 2,074 | 2,819 | ||
2,306 | 3,355 | 2,069 | 2,807 | ||
2,262 | 3,250 | 2,064 | 2,797 | ||
2,228 | 3,169 | 2,060 | 2,787 | ||
2,201 | 3,106 | 2,056 | 2,779 | ||
2,179 | 3,055 | 2,052 | 2,771 | ||
2,160 | 3,012 | 2,048 | 2,763 | ||
2,145 | 2,977 | 2,045 | 2,756 | ||
2,131 | 2,947 | 2,042 | 2,750 | ||
2,120 | 2,921 | ¥ | 1,95996 | 2,57582 |
.6
.
z F(z)
F(z) | z | F(z) | z | F(z) | z | F(z) | z |
0,0005 | 3,2905 | 0,25 | 0,6745 | 0,50 | +0,0000 | 0,80 | +0,8416 |
0,005 | 2,5750 | 0,30 | 0,5244 | 0,55 | +0,1257 | 0,85 | +1,0364 |
0,01 | 2,3267 | 0,35 | 0,3853 | 0,60 | +0,2533 | 0,90 | +1,2816 |
0,05 | 1,6449 | 0,40 | 0,2533 | 0,65 | +0,3853 | 0,95 | +1,6449 |
0,10 | 1,2816 | 0,45 | 0,1257 | 0,70 | +0,5244 | 0,99 | +2,3267 |
0,15 | 1,0364 | 0,50 | 0,0000 | 0,75 | +0,6745 | 0,995 | +2,5750 |
0,20 | 0,8416 | 0,9995 | +3,2905 |
.7
n n
n | q | n | q | ||
0,05 | 0,01 | 0,05 | 0,01 | ||
1,414 | 1,414 | 2,929 | 3,258 | ||
1,710 | 1,728 | 2,944 | 3,275 | ||
1,917 | 1,972 | 2,958 | 3,291 | ||
2,067 | 2,161 | 2,972 | 3,307 | ||
2,182 | 2,310 | 2,985 | 3,322 | ||
2,273 | 2,431 | 2,998 | 3,337 | ||
2,349 | 2,532 | 3,010 | 3,351 | ||
2,414 | 2,616 | 3,022 | 3,364 | ||
2,470 | 2,689 | 3,033 | 3,377 | ||
2,519 | 2,753 | 3,044 | 3,389 | ||
2,563 | 2,809 | 3,055 | 3,401 | ||
2,602 | 2,859 | 3,065 | 3,413 | ||
2,638 | 2,905 | 3,075 | 3,424 | ||
2,670 | 2,946 | 3,084 | 3,435 | ||
2,701 | 2,983 | 3,094 | 3,445 | ||
2,728 | 3,017 | 3,103 | 3,455 | ||
2,754 | 3,049 | 3,112 | 3,465 | ||
2,779 | 3,079 | 3,120 | 3,474 | ||
2,801 | 3,106 | 3,129 | 3,483 | ||
2,823 | 3,132 | 3,137 | 3,492 | ||
2,843 | 3,156 | 3,145 | 3,501 | ||
2,862 | 3,179 | 3,152 | 3,510 | ||
2,880 | 3,200 | 3,160 | 3,518 | ||
2,897 | 3,220 | 3,167 | 3,526 | ||
2,913 | 3,239 | 3,175 | 3,534 |
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