In: Statistics and Probability
Area (rows) |
Female |
Male |
Manufacturing |
1016, 1007, 875, 968 |
978, 1056, 982, 748 |
Marketing |
1045, 895,848, 904 |
1154, 1091 878, 876 |
Research & Development |
770, 733, 844, 771 |
926, 1055, 1066, 1088 |
In the context of this problem (i.e. use the terms given, not a definition), list the 3 sets of hypothesis tests that can be conducted using this data.
First set: H0: ____________________________
H1: ____________________________
Second set: H0: ____________________________
H1: ____________________________
Third Set: H0: ____________________________
H1: ____________________________
With an alpha = .05 and the following ANOVA output (corresponding to the previous data abut salaries of males and females across 3 areas of a company.
Source of Variation |
SS |
Df |
MS |
F |
P-value |
F crit |
Area |
14070.58 |
2 |
7035.292 |
0.734418 |
0.49362 |
3.554557 |
Gender |
62220.17 |
1 |
62220.17 |
6.495194 |
0.02016 |
4.413873 |
Interaction |
80147.58 |
2 |
6.495194 |
4.183323 |
0.032208 |
3.554557 |
Error |
172429.5 |
18 |
9579.417 |
|||
Total |
328867.8 |
23 |
Are the salaries in manufacturing, marketing, research & development the same? ________________________________
Are the salaries of females and males the same? _______________________________
Is there a significant interaction effect between genders and areas of the company? _______________________________
Please provide as much detail and explanation as possible. Thank you
hypothesis for area :
H0 : There is no significant difference in average salaries in manufacturin, marketing, research & development.
Ha : There is significant difference in average salaries in manufacturin, marketing, research & development.
hypothesis for Gender :
H0 : There is no significant difference in average salaries between males and females.
Ha : There is significant difference in average salaries between males and females.
hypothesis for interaction :
H0 : There is no significant interaction effect of gender and area on the salaries..
Ha : There is significant interaction effect of gender and area on the salaries.
With an alpha = .05 and the following ANOVA output (corresponding to the previous data abut salaries of males and females across 3 areas of a company.
Source of Variation |
SS |
Df |
MS |
F |
P-value |
F crit |
Area |
14070.58 |
2 |
7035.292 |
0.734418 |
0.49362 |
3.554557 |
Gender |
62220.17 |
1 |
62220.17 |
6.495194 |
0.02016 |
4.413873 |
Interaction |
80147.58 |
2 |
6.495194 |
4.183323 |
0.032208 |
3.554557 |
Error |
172429.5 |
18 |
9579.417 |
|||
Total |
328867.8 |
23 |
Here for the area, the F - value (0.7347) < F(critical)(3.55) and p - value (0.4936)is greater than the significance value (0.05) so the salaries in manufacturing, marketing, research & development are same.
Here for the area, the F - value (6.4952) < F(critical)(4.4138) and p - value (0.0202)is greater than the significance value (0.05) so the salaries for males and females are different.
Here for the area, the F - value (4.1833) < F(critical)(3.55) and p - value (0.0202)is greater than the significance value (0.05) so the salaries for males and females are different.