24
Chapter 1
finding the mean for an infinite sample size Eq. (1.30)
S
S
-~ -- t0.975 ~ < #I < -~ t0.975 N - 1
from Table E.2 d.f. = 755-1 = 754 t0.975 = t0.025 = 1.960
7 494
- 1.96~ < ~i < 176.703 Ksi ÷ 1.960
7.494
176.703
- -
754
176.684 Ksi _ The infinite standard deviation is Eq. (1.31)
X0.025
X0.025
with d.f. =N-1 for 150 and above [1.12]
x 2
N - 1 approaches 1 for 95 percentile
So
(1.84)
or
o’i ~ s ~ 7.494 Ksi
(1.85)
EXAMPLE 1.6. Three sets of radiator data (4.26) A, B, and C, with
nine samples each.
A
B
C
Mean
57,213 cycles
62,073
55,491
Standard
29,287 cycles
28,223
25,913
Deviation
Cv
51.19%
45.47%
46.7%
In small sampling theory [1.27] the means and standard deviations
may be checked for A and B also A and C so that it can be stated the samples
came from a larger Gaussian or near Gaussian distribution
Ho : JA = ~ No difference in the two group (Eq. (1.28))
Hi : ~A ¢ ~ and there is significant difference for Ho
1 "]
Chapter 1
finding the mean for an infinite sample size Eq. (1.30)
S
S
-~ -- t0.975 ~ < #I < -~ t0.975 N - 1
from Table E.2 d.f. = 755-1 = 754 t0.975 = t0.025 = 1.960
7 494
- 1.96~ < ~i < 176.703 Ksi ÷ 1.960
7.494
176.703
- -
754
176.684 Ksi _ The infinite standard deviation is Eq. (1.31)
X0.025
X0.025
with d.f. =N-1 for 150 and above [1.12]
x 2
N - 1 approaches 1 for 95 percentile
So
(1.84)
or
o’i ~ s ~ 7.494 Ksi
(1.85)
EXAMPLE 1.6. Three sets of radiator data (4.26) A, B, and C, with
nine samples each.
A
B
C
Mean
57,213 cycles
62,073
55,491
Standard
29,287 cycles
28,223
25,913
Deviation
Cv
51.19%
45.47%
46.7%
In small sampling theory [1.27] the means and standard deviations
may be checked for A and B also A and C so that it can be stated the samples
came from a larger Gaussian or near Gaussian distribution
Ho : JA = ~ No difference in the two group (Eq. (1.28))
Hi : ~A ¢ ~ and there is significant difference for Ho
1 "]