In: Statistics and Probability
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 |
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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