Question

In: Statistics and Probability

According to the sixth annual survey of advertising agency employees, conducted by the company Altschuler, Melvoin...

According to the sixth annual survey of advertising agency employees, conducted by the company Altschuler, Melvoin & Glasser, these employees can expect another excellent year for their compensation (Advertising Age, December 1, 1997). To investigate if there is any difference in annual art director compensation, suppose you select a random sample of 10 from each of four regions: West, South, North, and Northeast, and what you want the research to do with 10% error range. Use all the tools learned in the course, carry out the analysis required for the study.
The base salary (in thousands of dollars) for each of the individuals:

West South North Northeast

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	46.5
57.2	38.3	55.7	45.9

Expert Solution

Answer:

H0:Null Hypothesis: ( there is no significant difference in the annual compensation of artistic directors)

HA: Alternative Hypothesis: (At least one mean is different from other 3 means) ( there is a significant difference in the annual compensation of artistic directors) (Claim)

From the given data, the following Table is calculated:

	West	South	North	Northeast	Total
N	10	10	10	10	40
	600	454	473	521	2048
Mean	600/10=60	454/10=45.4	473/10=47.3	521/10=52.1	2048/40=51.2
	36468.84	21132.76	22786.4	27484.76	107872.76
Std. Dev.	7.2176	7.6096	6.7782	6.1523	8.7927

From the above Table, ANOVA Table is calculated as follows:

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F - Stat
Between treatments	1271	3	1271/3=423.6667	423.6667/48.4489=8.7446
Within treatments	1744.16	36	1744.16/36=48.4489
Total	3015.16	39

F - Stat = 423.6667/48.4489=8.7446

Degrees of Freedom of numerator = 3

Degrees of Freedom of numerator = 36

By Technology, p - value =0.0002

Since p - value = 0.0002 is less than = 0.10, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that there is a significant difference in the annual compensation of artistic directors.

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orchestra answered 1 year ago

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