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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Male Female 2 Officer Detective 21900 4281 806 415 4058 3898 1333 359 ESergeant Lieutenant Captain Higher Ranks218 12 10