1) A diagnostic test for Cat Scratch Fever has been developed, and administered
ID: 3274775 • Letter: 1
Question
1) A diagnostic test for Cat Scratch Fever has been developed, and administered to a random sample of 1000 people, with the following outcomes:
a) What is the positive predictive value (PPV), PPV = Pr(infectedl+)? (Show all work!)
b) In the test results above, what is the false negative rate, Pr(infectedl-)? (Show all work!)
2) The white cells of 31% of the Caucasian population react positively with HLA anti-A1, and those of 21% react positively with HLA anti-B8. If these two traits are independent. In addition, 17% of the people in the population are both Al positive and B8 positive.
a) Are the events A1+ and B8+ independent?
b) What proportion of the Caucasian population has a reaction to either anti-A1 or anti-B8?
test result infected clear total positive (+) 147 2 149 negative (-) 3 848 851 total 150 850 1000Explanation / Answer
a)
Out of 149 results that are positive, 147 are infected so the positive predictive value (PPV) is,
PPV = Pr(infected | +) = 147 / 149 = 0.9866
b)
Out of 851 results that are negative, 3 are infected so the false negative rate is,
Pr(infected | -) = 3 / 851 = 0.0035
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2)
From the given information:
P(anti-A1) = 0.31, P(anti-B8) = 0.21, P(anti-B8 and anti-A1) = 0.17
a)
Since P(anti-B8 and anti-A1) is not equal to P(anti-A1)*P(anti-B8) so the events A1+ and B8+ are not independent.
b)
P(anti-B8 or anti-A1) =P(anti-B8)+P(anti-A1)-P(anti-B8 and anti-A1) = 0.31+0.21 -0.17 = 0.35
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