Statistics Worksheet With Answers - Stat 200 Page 4
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63.
The table below gives the results of a study of 452 individuals enrolled in a methadone
treatment program. The number of positive HIV tests and negative HIV tests are provides separately for
people with different durations of intravenous drug use. Row and column totals are also provided.
HIV Test Result
Intravenous Drug
Total
Use
Tested Positive
Tested Negative
Never
23
53
76
Less than 4 years
77
141
218
At least 4 years
78
80
158
Total
178
274
452
a.
What
i s
t he
p robability
t hat
a
r andomly
s elected
s ubject
i n
t he
p rogram
w ill
t est
p ositively
f or
H IV?
P(HIV)
=
1 78/452
=
. 3938
b.
What is the probability that a randomly selected subject in the program will have had at least 4
years of drug use and test positively for HIV?
P(least 4 years and HIV) = 78/452 = .1726
c.
Given that a randomly selected subject has had at least 4 years of drug use, what is the probability
that he/she will have a positive HIV test?
P(HIV|at least 4 years) = 78/158 = .4937
d.
Are the events “test positively for HIV” and “at least 4 years of drug use” mutually exclusive?
Explain.
No, they both can ocurr at the same time.
e. Are the events “test positively for HIV” and “at least 4 years of drug use” independent? Why?
If they are independent, it means that that P(HIV and at least 4 years) = P(HIV) * P(at least 4 years)
P(HIV) = 178/452 = .3938
P(at least 4 years) = 158/452 = .3496
P(HIV and at least 4 years) = 78/452 = .1726
.1726 does not equal P(HIV) * P(at least 4 years)= .3938*.3496 = .1376
So they are dependent
f. Calculate the following odds and odds ratio for testing positive for HIV.
(1.) Odds of testing positive versus negative for persons with at least 4 years of intravenous drug
use.
4 years of intravenous drug use. 78/80 = .975
(2.) Odds of testing positive versus negative for persons with no intravenous drug use.
no intravenous drug use. 23/53 = .434
(3.) Odds ratio of (1) versus (2). Explain this in words.
.975/.434 = 2.247, those with 4 or more years of drug use were 2.2 times more likely to contract HIV
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