Very few testing procedures are absolutely perfect. This has become particularly apparent with the discussion of sensitivity and specificity of COVID-19 Rapid Antigen (RAT) tests recently. These have often been compared to the gold standard Polymerase Chain Reaction (PCR) test. The information booklet for a high quality RAT test provides details for sensitivity and specificity. RAT tests were applied to 101 subjects who where known to have COVID-19. Of those, 91 resulted in a positive RAT test. Another 305 subjects who were known not to be infected with COVID-19 were tested using the RAT test and 303 of them tested negative. Looking on the NSW Health Website, there are currently 166,957 active cases of COVID-19 in NSW out of a population of 8,160,000 people. Let C be the event that someone has COVID-19 and therefore Ccis the event that someone does not have COVID-19. Let P be the event that someone tests positive for COVID-19 and therefore P cis the event that someone tests negative for COVID-19. (b) Given someone has COVID-19, find the probability that a test will yield a positive result. (This probability represents the sensitivity of the test.) (c) Given someone does not have COVID-19, find the probability that the test will yield a negative result. (This probability represents the specificity of the test.) (d) Construct a tree diagram for the above scenario. Clearly label the arms representing sensitivity and specificity.
Very few testing procedures are absolutely perfect. This has become particularly apparent with the
discussion of sensitivity and specificity of COVID-19 Rapid Antigen (RAT) tests recently. These
have often been compared to the gold standard Polymerase Chain Reaction (PCR) test.
The information booklet for a high quality RAT test provides details for sensitivity and specificity.
RAT tests were applied to 101 subjects who where known to have COVID-19. Of those, 91 resulted
in a positive RAT test. Another 305 subjects who were known not to be infected with COVID-19
were tested using the RAT test and 303 of them tested negative.
Looking on the NSW Health Website, there are currently 166,957 active cases of COVID-19 in NSW
out of a population of 8,160,000 people.
Let C be the
not have COVID-19. Let P be the event that someone tests positive for COVID-19 and therefore
P cis the event that someone tests negative for COVID-19.
(b) Given someone has COVID-19, find the probability that a test will yield a positive
result. (This probability represents the sensitivity of the test.)
(c) Given someone does not have COVID-19, find the probability that the test will yield
a negative result. (This probability represents the specificity of the test.)
(d) Construct a tree diagram for the above scenario. Clearly label the arms representing
sensitivity and specificity.
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