Question

In: Statistics and Probability

A large company is organized into 3 different functional areas: manufacturing, marketing, and research & development....

  1. A large company is organized into 3 different functional areas: manufacturing, marketing, and research & development. The employees claim that the company pays women less than men for similar jobs. The company randomly selected 4 females and 4 males from each area and recorded their weekly salaries in dollars.

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

Solutions

Expert Solution

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.


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