Dr. Valerie R. Bencivenga
Economics 329
PRACTICE ASSIGNMENT #9A:
HYPOTHESIS TESTING I
1.
A statistician is hired by a government agency to analyze evidence of possible gender
discrimination in the hiring record of a small firm.
The firm recently hired twelve workers.
Of
these twelve hires, nine are men and three are women.
This is not due to the composition of
the applicant pool, which is half men and half women, and contains a large number of qualified
applicants of each gender.
The null hypothesis is no discrimination (the probability that a man
will be hired to fill an open position is no greater than .5, i.e.,
5
.
p
) and the alternative
hypothesis is discrimination (the probability that a man will be hired to fill a position is greater
than .5, i.e.,
5
.
p
).
Assume that each hire is a random trial, that the trials are independent,
and that the probability that a position will be filled by a man is constant from hire to hire.
a.
The rule that the agency has been using in these circumstances is to conclude that
there has been discrimination if more than 2/3 of employees are male.
In this case this
translates into the rejection region
8
X
(i.e., reject
0
H
if
9
X
), where
X
is a random
variable giving the number of employees who are male.
What is the maximum
probability of Type I error for this rejection region?
b.
If the true probability that a position will be filled by a man is .4, what is the probability
of Type I error for the test in part a?
c.
If the true probability is .6, what is the power of the test in part a?
What is the
probability of Type II error?
d.
If the true probability is .75, what is the power of the test in part a?
What is the
probability of Type II error?
e.
Plot the four points on the rejection probability curve that you have obtained in parts a
d.
What is the shape of the rejection probability curve?
f.
What rejection region should be used to control the maximum probability of Type I
error at 1%?
At 5%?
g.
If the statistician were called upon to testify in court, can it be said with certainty that
the firm is guilty of discrimination on the basis of the evidence of these twelve hires?
Explain in words how a judge should interpret the evidence.
2.
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 Spring '12
 BENCIVENGA
 Economics

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