1
, , s 2, s ν : 408, 404, 399, 412, 420, 418, 400, 413, 416, 417, 396, 409, 401, 395, 398, 370
i | x i | : = 6476; = 2623490. (2.1): = = 404,75. (2.3): = (404+ 408) = 406. (2.5): s 2 = = = = 155,267. (2.6): s = = 12,4606. (2.8) 2.1: s 1 = 1,017 12,4606=12,6724. (2.7): ν = = = 0,03131. |
n = 2 m 1 :
= xm,
(2.3)
s 2 = , (2.4)
s 2 = . (2.5)
s = , (2.6)
ν = . (2.7)
< 50 .
2
, 2.1, x = lg N. N, :
i | N | x i = lgN | i | N | x i = lgN | i | N | x i = lgN | i | N | x i = lgN |
74133,6 | 4,8700 | 5,2085 | 5,4638 | 5,5922 | |||||||
83019,5 | 4,9192 | 5,2114 | 5,4654 | 5,5963 | |||||||
5,0238 | 5,2311 | 5,4712 | 5,6102 | ||||||||
5,0407 | 5,2621 | 5,4721 | 5,6476 | ||||||||
5,0447 | 5,3126 | 5,4850 | 5,6479 | ||||||||
5,0466 | 5,3321 | 5,4982 | 5,6744 | ||||||||
5,0665 | 5,3698 | 5,4991 | 5,8173 | ||||||||
5,0818 | 5,3756 | 5,5186 | 5,8652 | ||||||||
5,0840 | 5,3821 | 5,5208 | 5,8720 | ||||||||
5,1080 | 5,3839 | 5,5221 | 5,8980 | ||||||||
5,1100 | 5,3848 | 5,5231 | 5,9054 | ||||||||
5,1200 | 5,3927 | 5,5438 | 5,9112 | ||||||||
5,1203 | 5,3976 | 5,5471 | 5,9192 | ||||||||
5,1255 | 5,4085 | 5,5584 | 5,9302 | ||||||||
5,1621 | 5,4095 | 5,5609 | 5,9548 | ||||||||
5,1701 | 5,4103 | 5,5613 | 6,0826 | ||||||||
5,1761 | 5,4225 | 5,5660 | 6,1684 | ||||||||
5,1816 | 5,4336 | 5,5661 | 6,2604 | ||||||||
5,1907 | 5,4350 | 5,5799 | 6,2776 | ||||||||
5,1966 | 5,4628 | 5,5829 | 6,4587 |
|
|
:
R = 6,458679992 4,87001509= 1,5886649.
.
Δx ≈ = = 0,1765183
Δx = 0,18
2.3
e | x j | n j | ||
4,870 | 5,050 | 4,96 | ||
5,050 | 5,230 | 5,14 | ||
5,230 | 5,410 | 5,32 | ||
5,410 | 5,590 | 5,50 | ||
5,590 | 5,770 | 5,68 | ||
5,770 | 5,950 | 5,86 | ||
5,950 | 6,130 | 6,04 | ||
6,130 | 6,310 | 6,22 | ||
6,310 | 6,490 | 6,40 |
:
= 436,8; = 2393;
= 13156; = 72599.
(2.10):
= = 5,4595.
(2.3):
= (5,4627+ 5,4638) = 5,4633.
(2.12):
s 2 = = 0,1050.
(2.6) (2.7):
s = = 0,3240; ν = = 0,0593.
(2.13) :
h 1 = 5,4560; h 2 = 29,91;
h 3 = 164,45; h 4 = 907,49.
(2.14)
m 3 = 0,0227;
m 4 = 0,0347.
= = 0,6680722; = 3 = 0,1516.
3
2.2 , N = 0,5106 , .. x = lg N = 5,6990.
2.2 m = 66 (2.20) :
W = = 0,175.
(2.21)
y = = 0,6716.
2.5 W = 0,175 y = 0,6716 u = 0,984.
2.6
φ1(0,984) = 1,4456
(2.23) s = 0,2675
(2.22)
= = 5,69897 0,984 0,2675 = 5,4357.
4
2.1 90 %- , = 404,75; s = 12,4606.
2.6 k = 16 1 = 15 α = 0,1 t 0,1 = 1,7535.
|
|
(2.26)
404,75 1,7535 < a < 404,75 + 1,7535;
399,2876 < a < 410,2124
= 1 α
(2.27)
5
2.2 90 %- , = 5,4357; s = 0,2675; u = 0,9842 (. 2.3).
α = 0,1 2.7
z 0,05 = -1,282;
z 0,95 = 1,282.
2.3 u = 0,9842 2.6
φ2(0,9842) = 1,054.
(2.27)
5,4357 1,282 < a < 5,4357+ 1,282
5,3963< a < 5,4750
σ2 = 1 α
. (2.28)
1 = α/2 2 = 1 1 = 1 α/2.
σ .
6
2.1 90 %- , s 2 = 155,2667.
2.9 k = n 1 = 15
χ 0,052 = 25;
χ 0,952 = 7,26.
(2.28)
155,2667 < σ2 < 155,2667 ;
93,16< σ2 < 320,7989;
9,651943< σ < 17,91086.
< σ < . (2.29)
7
2.2 90 %- , s = 0,2675 u = 0,9842
α = 0,1 2.7
z 0,05 = -1,282
z 0,95 = 1,282
φ3(u) = φ3(0,9842) = 0,6707
(2.35)
< σ < ;
0,2394< σ < 0,3031
8
, α = 0,05 Δ a = 0,07. .
γ = 0,03. 2.7 p = 1-0,05/2=0,975 z 0,975 = 1,96 (2.31)
n = 1,962 ≈ 0, 71
n = 1
,
(1 + Δσ)2 = , (2.35)
Δσ () ; χ2α/2 χ20,5 = α/2 = 0,5 χ2 ( 2.9).
Δσ . Δσ = 0,4 0,5, Δσ = 0,25 0,35 Δσ = 0,1 0,2.
n ≥ 15 (2.35)
n = 1,5 + , (2.36)
9
, α = 0,05 Δσ = 0,6.
(2.36)
(1 + Δσ)2 = (1 + 0,6)2 = 2,56
2.10 k = n 1 χ20,05 χ20,5, k = n 1, (2.35).
k = 1
= = 7,648352
k = 3
= = 3,299578
k = 4
= = 2,824405
|
|
k = 5
= = 2,551724
n = k + 1 = 6
(2.36)
n = 1,5 + = 6, 84
, , n, (2.31) (2.33) (2.35) (2.36).
2.10 2.11.
1
2.1 , .
= 404,75
s = 12,4606
u n = = = 1,223857.
u n = 1,223857< u α=2,44
: , .. x 20 = 420 .
2
18 s 2 = 126,9. , , σ20 = 100 σ2 > σ20.
(3.3):
= =1,269
α = 0,05 2.10 k = n 1 = 17
χ20,05 = 27,6
(3.3)
= = 1,269
: (3.3) , , .
3
(3.5), α = 0,05; β = 0,07 Δσ = 0,3
2.8 z 1β = z 0,9 = 1,282; z 1α/2 = z 0,975 = 1,96.
(3.7)
n = 1,5 + 0,5 ≈ 75
. n 1 n 2 , s 21 > s 22. , , .. σ21 = σ22 = σ2 σ21 ≠ σ22. F - ( ),
F = s 21 > s 22. (3.8)
F 1α/2, 3.3
F = ≤ F 1α/2, (3.9)
, , .. σ21 = σ22 = σ2, .
(3.9) .
σ21 > σ22
F = ≤ F 1α, (3.10)
, . σ21 > σ22.
σ21 = σ22 = σ2 σ2:
s 2 =
4
30 20 . α = 0,1.
= 47; s 12 = 88.
= 45; s 22 = 105
σ21 ≠ σ22.
(3.10)
|
|
F = = 0,8381.
α = 0,1; k 1 = n 1 1 = 27 k 2 = n 2 1 = 29 3.3
F 1α/2 = F 0,95 = 1,8751
F = 0,8381< F 0,95 = 1,8751
: .