Promotion discrimination? The table shows the rank attained by male and female officers in the New York City Police Department (NYPD). Do these data indicate that men and women are equitably represented at all levels of the department? (All possible ranks in the NYPD are shown.)

a) What’s the probability that a person selected at random from the NYPD is a female?

b) What’s the probability that a person selected at random from the NYPD is a detective?

c) Assuming no bias in promotions, how many female detectives would you expect the NYPD to have?

d) To see if there is evidence of differences in ranks attained by males and females, will you test goodness-of-fit, homogeneity, or independence?

e) State the hypotheses.

f) Test the conditions.
g) How many degrees of freedom are there?
h) Find the chi-square value and the associated P-value.
i) State your conclusion.
j) If you concluded that the distributions are not the same, analyze the differences using the standardized residuals of your calculations.

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