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STAT 496, Spring 2011
Homework Assignment #6, Due by Thursday, March 24
1.
An engineer is interested in the effects of cutting speed (A), tool geometry (B), and
cutting angle (C) on the life (in hours) of a machine tool.
Because the hardness of the
raw material being tooled may vary, heats of raw material are used as blocks.
The
eight treatment combinations are run in a random order within each block (heat). The
levels of each of the 3 factors are given below along with the data.
Low (–1)
High (+1)
A: Cutting Speed
50 rpm
100 rpm
B: Tool Geometry
Type 1
Type 2
C: Cutting Angle
5
o
10
o
XA
XB
XC
Heat I
Heat II
Heat III
–1
–1
–1
22
31
25
+1
–1
–1
32
43
30
–1
+1
–1
35
50
35
+1
+1
–1
45
55
47
–1
–1
+1
43
45
38
+1
–1
+1
36
38
40
–1
+1
+1
50
61
54
+1
+1
+1
47
43
39
a)
Compute means for the low and high levels of each of the three factors.
Display
these graphically and comment on the apparent effects of each of the factors.
b)
Construct an interaction plot for factors A and C using the data from Type 1 tool
geometry.
Construct a second interaction lot for factors A and C using the data
from the Type 2 tool geometry.
Comment on the plots.
What do they indicate
about the possible interaction between factors A and C? What do they indicate
about the 3way interaction?
c)
Compute the overall sample mean and estimate the full effects for each factor, 2
way and 3way interaction.
d)
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This note was uploaded on 02/11/2012 for the course STAT 496 taught by Professor Staff during the Spring '08 term at Iowa State.
 Spring '08
 Staff

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