a. Construct a two-way (with interaction) ANOVA table for these data.  b. At the 5% significance level, can you conclude there is interaction between Ranks (Low, Medium, High) and Branch of Service?  c. Are you able to conduct tests on the main effects? If yes, conduct these tests at the 5% significance level.

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A Military Combat Strategist wants to understand how an accuracy rate (by bullets) for assault firearms shooting depends on Military Ranks and Branch of Service allowing for an interaction. The data are shown below:

Factor B Factor A Factor A Factor A
Branch of Service Low Ranks Medium Ranks High Ranks
Army 25 55 60
Army 40 60 65
Army 22 5 63
Army 30 100 60
Marines 70 75 100
Marines 85 50 115
Marines 74 54 108
Marines 100 45 160
Navy 75 75 75
Navy 55 70 60
Navy 41 55 79
Navy 40 70 65
Air Force 5 40 59
Air Force 10 25 30
Air Force 10 40 45
Air Force 5 35 40

a. Construct a two-way (with interaction) ANOVA table for these data. 

b. At the 5% significance level, can you conclude there is interaction between Ranks (Low, Medium, High) and Branch of Service? 

c. Are you able to conduct tests on the main effects? If yes, conduct these tests at the 5% significance level.

 

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