In the following table number of promoted officers in the la

In the following table: number of promoted officers in the last few years in the Philadelphia police department.
a. What percent of men were promoted
b. What percent of women were promoted
c. Is there statistical evidence of discrimination – dependency between gender and promotion> explain

Solution

Consider:

a)

P(promoted|men) = 75/110 = 0.681818182 or 68.18% [ANSWER]

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b)

P(promoted|women) = 20/30 = 0.666666667 or 66.67% [ANSWER]

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c)

Doing an Expected Value Chart,          
          
74.64285714   20.35714286  
35.35714286   9.642857143  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    0.024809498      
          
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    2      
b =    2      
          
df =    1      
          
Thus, the critical value is          
          
significance level =    0.05      
          
chi^2(critical) =    3.841458821      
              
          
Thus, comparing chi^2 < 3.8314, we   FAIL TO REJECT THE NULL HYPOTHESIS.      
          
Thus, there is no significant evidence that there is discrimination at 0.05 level. [CONCLUSION]