Page 33 - Mechanical Engineers' Handbook (Volume 2)

22 Instrument Statics

ˆ y,x 0.05777, ˆ y,x 0.0173

ˆ ˆ / X 2 0.000550
y,x
b
ˆ tˆ y,x y tˆ y,x
y
y
1.0827 (1.833)(0.01737) 1.0827 0.0318
ˆ
b tˆ 0.0412 (1.833)(0.00055)
b
b
0.0412 0.00101
2
4. yi ˆ tˆ y tˆ 1/n X / X 2
yi
y,x
i
yi
0.9773 (1.833)(0.0325)
0.9773 0.0596
5. yi ˆ tˆ ˆy tˆ 1 1/n X / X 2
2
yi
yi
i
y,x
( 0.9773 4.9500) (1.833)(0.0715)
3.9727 0.1310
6. yi Line ˆ 2F(2, v)ˆ yi ; for any given point compare with 4 above
yi
ˆy (2)(3.01)ˆ yi
i
ˆy (2.46)ˆ yi
i
0.9773 0.0799; for point of 4 above
ˆ
7. ˆ tˆ y,x y t y,x
y
yi
n
y,x y,x / n
y,x
ˆ y,x 0.0577
y (1%)( ) (1%)(y) 0.010827
y
y
t/ n (1%)y/ˆ y,x 0.010827/0.05770 0.188
9
From the t table at t/ n 0.188 with n 2 for a straight line (two constraints).
t(0.10,v) t/ n
60 1.671 0.213
90 1.663 0.174
75 1.674 0.188
Therefore n 2 77 is the amount of data to obtain to assure the precision and
confidence level desired.

3.11 Inference and Comparison
Events are not only deterministic but probabilistic. Under certain specified conditions some
events will always happen. Some other events, however, may or may not happen. Under the
same specified conditions, the latter ones depend on chance and, therefore, the probability
of occurrence of such events is of concern. For example, it is quite certain that a tossed
unbiased die will fall down. However, it is not at all certain which face will appear on top