
,1
~
ffltn
E.r";;~
1. (75 pts.) A balanced 22 factorial design was used
to see how the factors Temperature
(A) and Copper
content (B) effect the warping of metallic plates 1. The high level of temperature was 100° C and the low
level of temperature was 50° C. The high level of copper content was 80% and the low level was 40%.
The response variable was a measure of the amount of warping (larger values correspond
to greater
warping).
A
B
AB
Temperature
Copper
Observations
Total
Mean
SD
Content
(Warping)
(1)
1
1
+1
17
20
37
18.5
2.1
~I
a
+1
1
1
16
12
28
14.0
2.8
'L
b
1
+1
1
24
22
46
23.0
1.4
$3
ab
+1
+1
+1
25
23
48
24.0
1.4
7,
a. Estimate
the (main) effect A
~~_.i.~=
~~~
~
=
~~
~2
,

4
b 4
.11
=
 J.
7
.5
n
2
k"\
1
b. Estimate
the (main) effect B
 ~
,)

~
h
~
4;
~
::.

~~=~~~.!~.
.:_!~
.:=
7 .
'l .s
~ 2.k~\
4
c. Estimate
the (interaction) effect AB
~ ~
b
.J
41
::
~=~3 
'1
,",.f
1~
=
2.75
!I12.k'"
1
d. Estimate 0", the assumed
common standard deviation of ~
measurement
of warping.
~l.

5,'2.
..,.
..
5;
~.5~""'"
5,'1.

(211)'t.,.f (z.S)'Z.+ Q.1)1
(,,'1)'
vp


.q.
4
~
~p
C; 2.o(
e. Estimate
the standard
deviation
of ~
~.
(\

r
 .J.
..
)
0
0"'"
51) (~I,
=

=

~
~
:::
1.4'2'2.
~~
Vi:
This is a subset of the data displayed
in Johnson and Leone (1977), Statistics and Experimental Design
in Engineering
and the Physical Sciences,
John Wiley, New York, NY.
2
~"~,.,,.,.
.,
y~~~,c""".,,.
,.,