An economist wants to examine the relationship between salary levels of managers

Question

An economist wants to examine the relationship between salary levels of managers from three branches of a medium size firm. He collects information from 18 randomly selected managers from the three branches, Branch A, Branch B and Branch C. He presented a summary of the information he collected in the table below:

Branches

Salary

Mean

Branch A

4.5

6.0

7.5

5.5

7.8

6.5

6.3

Branch B

6.6

6.4

8.5

6.0

7.0

4.8

6.55

Branch C

9.0

8.0

4.9

9.5

10.9

13.0

9.22

Note: The values in the table above are the monthly salaries of the selected managers in thousands of dollars

He decides to use the ANOVA test procedure for his study

Source of Variation

Sum of Squares

Degrees of Freedom

Mean Square

F-ratio

Treatment

SSF=?

2

MSF=15.681

F=???

Error

SSE=52.483

??

MSE=???

Total

SST=83.844

N-1=17

a. What are the hypothesis for the study above?

b. What are the main assumptions of this study?

c. Calculate the missing values in the ANOVA table above

d. Using a significance level of % derive a conclusion for the study

e. If necessary, use the Tukey-Kramer test procedure to find out which branches are different

Branches

Salary

Mean

Branch A

4.5

6.0

7.5

5.5

7.8

6.5

6.3

Branch B

6.6

6.4

8.5

6.0

7.0

4.8

6.55

Branch C

9.0

8.0

4.9

9.5

10.9

13.0

9.22

Explanation / Answer

a) H0: There is no significance difference between means of three groups

H1: There is a significance difference between means of three groups

alpha:5%

b)

c) ANOVA table

d)

At alpha=5%

P value=0.02979

P <0.05, we reject the H0.Hence claim is significant

ANOVA Source of Variation SS df MS F P-value F crit Between Groups 31.36111 2 15.68056 4.481581 0.029792 3.68232 Within Groups 52.48333 15 3.498889 Total 83.84444 17

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