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	88	77	79
	84	76	91
	85	66	97
2009	90	78	77
	82	76	77
	82	66	81
2011	88	85	98
	81	85	82
	89	78	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

(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)   31   52   25  samples in 100 would show an F statistic this large in the   (Click to select)   presence   absence  of interaction.

Answer 1

a)

b)

..............

Anova: Two-Factor With Replication
SUMMARY	Marketing	Engineering	Finance	Total
2007
Count	3	3	3	9
Sum	257	219	267	743
Average	85.66667	73	89	82.55556
Variance	4.333333	37	84	84.77778
2009
Count	3	3	3	9
Sum	254	220	235	709
Average	84.66667	73.33333	78.33333	78.77778
Variance	21.33333	41.33333	5.333333	41.19444
2011
Count	3	3	3	9
Sum	258	248	258	764
Average	86	82.66667	86	84.88889
Variance	19	16.33333	112	39.61111
Total
Count	9	9	9
Sum	769	687	760
Average	85.44444	76.33333	84.44444
Variance	11.52778	46.25	73.02778
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	171.1852	2	85.59259	2.261252	0.133016	3.554557
Columns	449.4074	2	224.7037	5.936399	0.010471	3.554557
Interaction	193.9259	4	48.48148	1.280822	0.314246	2.927744
Within	681.3333	18	37.85185
Total	1495.852	26

......................

THANKS

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