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Econ3500f11-test1-6oct11
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I.
A diagnostic test for a certain disease is said to be 90% accurate in that, if a person has
the disease, the test will detect it with probability 0.9. Also, if a person does not have the
disease, the test will report that he or she does not have it with probability 0.9. Only 1 %
of the population has the disease in question. If a person is chosen at random from the
population and the diagnostic test indicates that she has the disease, what is the
conditional probability that she does, in fact, have the disease?
B1= person has the disease
B2= person does not have the disease
A = test is positive
P(B1) = 0.01
P(B2) = 0.99
P(A/B1) = 0.90
P(A/B2) = 0.10
P(B1/A) = P(B1 and A) / P(A)
P(B1 and A) = P(A/B1) P(B1) = 0.90*0.01 = 0.009
P(A) = P(B1 and A) + P(B2 and A)
= P(A/B1) P(B1) + P(A/B2) P(B2)
= 0.90*0.01 + 0.10*0.99 = 0.108
P(B1/A) = P(B1 and A) / P(A) = 0.009/0.108 = 1/12 = 0.0833
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II
A multiple choice test has 3 questions, each with 4 possible answers, 1 of which is
correct. Let X denote the number of correct answers. If pure guesswork were used in
taking the test, what would be the probability distribution of X?
Let A=correct guess P(A)=1/4
B=wrong guess P(B)=3/4
P(X=0) = (3/4)^3
P(X=1) = 3*(1/4)*(3/4)^2
P(X=2) = 3*(1/4)^2*(3/4)
P(X=3) = (1/4)^3
X
p(X)
---------0
27/64
1
27/64
2
9/64
3
1/64
3
III The following are the sorted final exam grades data (N=72) discussed in Ramsey’s
textbook:
The sorted data set is:
32
60
66
70
78
42
60
66
72
78
46
60
66
74
80
46
60
66
74
80
48
60
66
74
80
48
60
66
74
82
52
60
68
74
82
52
62
68
74
86
56
62
68
76
86
56
62
68
76
86
58
64
70
76
90
58
64
70
78
92
58
64
70
78
58
66
70
78
60
66
70
78
Find the five numbers summary for these data and indicate where each of them is located
by writing the numbers on their approximate locations in the following boxplot.
Min.
(…60…….)
Median
3rd Qu.
Max.
(…67….)
(..76….)
(…92…)
30
40
50
60
70
80
90
(..32..)
1st Qu.
lower whisker = 60-1.5*(76-60) = 36 which is not a data value [text pg 45]
max=upper whisker=92; min=32; Q1=60; median=67; Q3=76