A particular magazine identified the top accounting firms in 15 geographic regions across a certain country. Even though all 15 regions reported growth in the past year, region A and region B reported the highest combined growths, with 23 % and 19%, respectively. A characteristic description of the accounting firms in these regions included the number of partners in the firm. The accompanying table contains data on the number of partners.
Number of partners data
Region |
Number of Partners |
||
---|---|---|---|
A |
123123 |
||
A |
5959 |
||
A |
4444 |
||
A |
4444 |
||
A |
4040 |
||
A |
1010 |
||
A |
4444 |
||
A |
5454 |
||
A |
4545 |
||
A |
2020 |
||
A |
1313 |
||
A |
2020 |
||
A |
3030 |
||
B |
7878 |
||
B |
6060 |
||
B |
1717 |
||
B |
3030 |
||
B |
3636 |
||
B |
1010 |
||
B |
2323 |
||
B |
2727 |
||
B |
1010 |
||
B |
66 |
||
B |
1414 |
||
B |
88 |
||
B |
88 |
||
B |
1111 |
||
B |
1515 |
a) What is the F stat test statistic?
b) What is the critical value?
c) What is the P - Value?
Solution:
In excel install analysis tool pack then go to
Data>Data analysis>ANOVA-single factor
You will get
you will get
below output
Anova: Single Factor | |||||||
SUMMARY | |||||||
Groups | Count | Sum | Average | Variance | |||
A | 13 | 165846 | 12757.38 | 1102089960 | |||
B | 15 | 33673 | 2244.867 | 4926172.695 | |||
ANOVA | |||||||
Source of Variation | SS | df | MS | F | P-value | F crit | |
Between Groups | 769644341.3 | 1 | 7.7E+08 | 1.505241743 | 0.230861 | 4.225201 | |
Within Groups | 13294045937 | 26 | 5.11E+08 | ||||
Total | 14063690278 | 27 |
COMING TO ANSWERS:
solutionA:
F=1.505241743
solutionB:
F critical value=4.225201273
solutionC:
p=0.230860973
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