NYPD and sex discrimination The table below showsthe rank attained by male and female officers in the NewYork City Police Department (NYPD). Do these datasummaries indicate that men and women are equitablyrepresented at all levels of the department? a) What’s the probability that a person selected atrandom from the NYPD is a female?b) What’s the probability that a person selected atrandom from the NYPD is a detective?c) Assuming no bias in promotions, how many femaledetectives would you expect the NYPD to have? d) To see if there is evidence of differences in ranks at-tained 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) The chi-square value for the table is 290.1 and theP-value is less than 0.0001. State your conclusionabout the hypotheses. SexMale Female RankOfficer 21,900 4,281Detective 4,058 806Sergeant 3,898 415Lieutenant 1,333 89Captain 359 12Higher ranks 218 10
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
NYPD and sex discrimination The table below shows
the rank attained by male and female officers in the New
York City Police Department (NYPD). Do these data
summaries indicate that men and women are equitably
represented at all levels of the department?
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?
tained by males and females, will you test goodness-
of-fit, homogeneity, or independence?
f) Test the conditions.
g) How many degrees of freedom are there?
h) The chi-square value for the table is 290.1 and the
P-value is less than 0.0001. State your conclusion
about the hypotheses.
Male Female
Officer 21,900 4,281
Detective 4,058 806
Sergeant 3,898 415
Lieutenant 1,333 89
Captain 359 12
Higher ranks 218 10
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