Page 369 - Fundamentals of Probability and Statistics for Engineers

352 Fundamentals of Probability and Statistics for Engineers

140

120
(x)
l 2
(g/cm 2 ) 100 ^ α + β ^ x
Young’s modulus, y 80 l 1 (x)

60

40

20

0
10 20

Stress, x (g/cm 2 )
f
Figure 11.5 The 95% confidence band for E Y g, for Example 11.4

f T (t)

1– γ

γ /2 γ /2
t
γ
γ
–t n, /2 t n, /2
n
1/2
2 1
^

c 2
Figure 11.6 Probability density function of T ˆ "B 0 ) [ P "x i x) ]

iˆ1
Using B ^ as the test statistic, we have shown in Section 11.1.4 that the random
variable defined by Equation (11.36) has a t-distribution with n 2 degrees of

freedom. Suppose we wish to achieve a Type-I error probability of . We would
^
reject H 0 if j 0 j exceeds (see Figure 11.6)
TLFeBOOK