A factorial experiment was designed to determine factors in a high-energy electron beam process that affect hardness in metals. Results for two factors, each with three levels, are presented in the following ANOVA table. Factor A is the travel speed in mm/s, and factor B is accelerating voltage in volts. The outcome is Vickers hardness. There were six replications for each treatment.

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7.
A factorial experiment was designed to determine factors in a high-energy
electron beam process that affect hardness in metals. Results for two factors, each with three
levels, are presented in the following ANOVA table. Factor A is the travel speed in mm/s,
and factor B is accelerating voltage in volts. The outcome is Vickers hardness. There were
six replications for each treatment.
Source
DF
MS
F
P
Travel Speed
2
106912.1
53456.1
8.740
0.0006
Acceleration
2
150390.3
75195.2
12.294
0.000
Interaction
4
11408.8
2852.2
0.466
0.76
Error
45
275228
6116.2
Total
53
543939.3
a) The appropriate statistical analysis to test would be:
a. One-way ANOVA
b. Two-way ANOVA
c. Three-way ANOVA
d. Two-Sample t-test
b) Does there appear to be an interaction between travel speed and accelerating voltage
at the .01 level? What does this say about the additive model?
c) Can the effect of travel speed on hardness in metals be described by interpreting the
main effects of travel speed? If so, interpret the main effects at the .01 level,
including the appropriate test statistic and p-value. If not, explain why not.
d) Can the effect of accelerating voltage on hardness in metals be described by
interpreting the main effects of accelerating voltage? If so, interpret the main effects
at the .01 level, including the appropriate test statistic and p-value. If not, explain
why not.
Transcribed Image Text:7. A factorial experiment was designed to determine factors in a high-energy electron beam process that affect hardness in metals. Results for two factors, each with three levels, are presented in the following ANOVA table. Factor A is the travel speed in mm/s, and factor B is accelerating voltage in volts. The outcome is Vickers hardness. There were six replications for each treatment. Source DF MS F P Travel Speed 2 106912.1 53456.1 8.740 0.0006 Acceleration 2 150390.3 75195.2 12.294 0.000 Interaction 4 11408.8 2852.2 0.466 0.76 Error 45 275228 6116.2 Total 53 543939.3 a) The appropriate statistical analysis to test would be: a. One-way ANOVA b. Two-way ANOVA c. Three-way ANOVA d. Two-Sample t-test b) Does there appear to be an interaction between travel speed and accelerating voltage at the .01 level? What does this say about the additive model? c) Can the effect of travel speed on hardness in metals be described by interpreting the main effects of travel speed? If so, interpret the main effects at the .01 level, including the appropriate test statistic and p-value. If not, explain why not. d) Can the effect of accelerating voltage on hardness in metals be described by interpreting the main effects of accelerating voltage? If so, interpret the main effects at the .01 level, including the appropriate test statistic and p-value. If not, explain why not.
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