Question

According to the sixth annual survey of employees of advertising agencies, carried out by the company Altschuler, Melvoin & Glasser, these employees can wait another excellent year for their compensation (Adveertising Age, December 1, 1997). To investigate if there is any difference in the annual compensation of artistic directors, suppose you select a random sample of 10 of them from each of four regions: West, South, North and Northeast, and what you want to do the research with 10% of error range.

West	South	North	Northeast
60.9	50.8	49.5	65.9
45.9	39.6	42.3	58.6
62.1	44.2	35.5	49.3
66.6	40.0	49.1	52.9
68.0	53.9	56.7	48.5
65.0	45.4	41.4	52.9
49.4	61.1	51.3	52.4
62.3	42.3	49.4	48.1
62.6	38.4	42.1	13.2
57.2	38.3	55.7	45.9

Answer 1

Sol:

We shall do ANOVA single factor to check whether difference exists

In excel install analysis toolpak and then go to

Data>Data analysis >ANIOVA single factor

you get

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
West	10	600	60	52.09333
South	10	454	45.4	57.90667
North	10	473	47.3	45.94444
Northeast	10	487.7	48.77	190.1801
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	1294.227	3	431.4089	4.985592	0.005394	2.866266
Within Groups	3115.121	36	86.53114
Total	4409.348	39

Null hypothesis:

All the 4 group means are equal

Alternative hypothesi:

Atleast one of the group means are different.

alpha=0.10

From ANOVA table

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	1294.227	3	431.4089	4.985592	0.005394	2.866266
Within Groups	3115.121	36	86.53114
Total	4409.348	39				we get

we get

F=4.99

p=0.0054

p<0.01

Reject null Hypothesis

Accept alternative hypothesis.

Conclusion:

There is sufficient statistical evidence at 10% level of significance to conclude that there is difference in the annual compensation of artistic directors.