Question

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	82	65	95
	84	83	93
	86	68	91
2009	88	74	85
	87	66	80
	80	84	95
2011	83	70	95
	90	71	85
	81	73	78

(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

(c) Using α = 0.05, choose the correct statement.

• The main effects of department and year are significant, but there is not a significant interaction effect.

• The main effect of department is significant; however, there is no significant effect from year or interaction between department and year.

• The main effect of year is significant; however, there is no significant effect from department or interaction between department and year.

(d) Interpret the p-values carefully.

The p-values range from highly significant (Department) to insignificant (Year). The interaction effect, if any, is  (Click to select)  weak  strong  since about  (Click to select)  71  90  39  samples in 100 would show an F statistic this large in the  (Click to select)  presence  absence  of interaction.

Answer 1

(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.)

			Factor 2
	Means:
		Marketing	Engineering	Finance
	2007	84.0	72.0	93.0	83.0
Factor 1	2009	85.0	74.7	86.7	82.1
	2011	84.7	71.3	86.0	80.7
		84.6	72.7	88.6	81.9
ANOVA table
Source	SS	df	MS	F	p-value
Factor 1	24.96	2	12.481	0.31	.7342
Factor 2	1,229.41	2	614.704	15.48	.0001
Interaction	84.81	4	21.204	0.53	.7125
Error	714.67	18	39.704
Total	2,053.85	26

  

(c) Using α = 0.05, choose the correct statement.

• The main effects of department and year are significant, but there is not a significant interaction effect.

• The main effect of department is significant; however, there is no significant effect from year or interaction between department and year.

• The main effect of year is significant; however, there is no significant effect from department or interaction between department and year.

(d) Interpret the p-values carefully.

The p-values range from highly significant (Department) to insignificant (Year). The interaction effect, if any, is  (Click to select)  weak  since about  (Click to select)  71   samples in 100 would show an F statistic this large in the  (Click to select)  presence   of interaction.