In: Statistics and Probability
Oxnard Petro, Ltd., has three interdisciplinary project
development teams that function on an ongoing basis. Team members
rotate from time to time. Every 4 months (three times a year) each
department head rates the performance of each project team (using a
0 to 100 scale, where 100 is the best rating). Are the main effects
significant? Is there an interaction?
Year | Marketing | Engineering | Finance |
2007 | 90 | 69 | 96 |
84 | 72 | 86 | |
80 | 78 | 86 | |
2009 | 72 | 73 | 89 |
83 | 77 | 87 | |
82 | 81 | 93 | |
2011 | 92 | 84 | 91 |
87 | 75 | 85 | |
87 | 80 | 78 | |
Click here for the Excel Data File
(a-1) Choose the correct row-effect hypotheses.
a. | H0: A1 ≠ A2 ≠ A3 ≠ 0 | ⇐⇐ year means differ |
H1: All the Aj are equal to zero | ⇐⇐ year means are the same | |
b. | H0: A1 = A2 = A3 = 0 | ⇐⇐ year means are the same |
H1: Not all the Aj are equal to zero | ⇐⇐ year means differ |
a
b
(a-2) Choose the correct column-effect
hypotheses.
a. | H0: B1 ≠ B2 ≠ B3 ≠ 0 | ⇐⇐ department means differ |
H1: All the Bj are equal to zero | ⇐⇐ department type means are the same | |
b. | H0: B1 = B2 = B3 = 0 | ⇐⇐ department means are the same |
H1: Not all the Bj are equal to zero | ⇐⇐ department type means differ |
a
b
(a-3) Choose the correct interaction-effect
hypotheses.
a. | H0: Not all the ABjk are equal to zero | ⇐⇐ there is an interaction effect |
H1: All the ABjk are equal to zero | ⇐⇐ there is no interaction effect | |
b. | H0: All the ABjk are equal to zero | ⇐⇐ there is no interaction effect |
H1: Not all the ABjk are equal to zero | ⇐⇐ there is an interaction effect |
a
b
(b) Fill in the missing data. (Round your Table of
Means values to 1 decimal place, SS and F values
to 2 decimal places, MS values to 3 decimal places, and
p-values to 4 decimal places.)
Table of Means | ||||
Factor 2 (Department) | ||||
Factor 1 (Year) | Marketing | Engineering | Finance | Average |
2007 | ||||
2009 | ||||
2011 | ||||
Total | ||||
Source | SS | df | MS | F | p-value |
Factor 1 (Year) | |||||
Factor 2 (Department) | |||||
Interaction | |||||
Error | |||||
Total | |||||