The following table shows the rank attained by male and female officers in the New York City Police Department (NYPD).
a)  Do these data indicate that men and women are equitably represented at all levels of the department? Test using a p-value approach.
                           

                           Male Female
Officer               21,900 4281
Detective             4058 806
Sergeant              3898 415
Lieutenant          1333 89
Captain                  359 12
Higher ranks         218 10

b) There are far more men than women in the police force in general. However, the NYC Police Commission has set itself certain goals with respect to the positions of the females among its ranks. Across the females they aim to target the same proportion by rank as
they do among the males. The target proportions by category are:
(1) Officer – 70% (2) Detectives – 15% (3) Sargent – 10%
(4) Lieutenant – 3% (5) Captain – 1% (6) Higher – 1%
Conduct a test to determine whether the proportions, by rank, among the female officers adhere to these targets. Use a 0.05 level of significance and a critical value approach.