Fundamentals of Probability and Statistics for Engineers

Using 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 exceeds (see F igure 11.6)

0

10 20

20

40

60

80

100

120

140

+^x

l 2 (x)

l 1 (x)

Young’s modulus,

y

(g/cm

2 )

Stress,x (g/cm^2 )

^

Figure 11. 5 The 95% confidence band for E Y for Example 11.4

1–

/2 /2

• tn,/2 tn,/2

fT(t)

t

Figure 11. 6 Probability density function of T

352 Fundamentals of Probability and Statistics for Engineers

B^



j ^ 0 j

α β

f g

γ

γ γ

γ γ

ˆ"B^ 0 ) c^2 [

Pn

iˆ 1

"xix)^2 ]^1

1/2

,