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...


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 Cc is the event that someone does


not have COVID-19. Let P be the event that someone tests positive for COVID-19 and therefore


Pc is the event that someone tests negative for COVID-19.


(e)  Given that a random individual tests positive for COVID-19 using a RAT test,


find the probability that the individual actually has the disease. (This probability represents the


positive predictive value of the test and is what we would actually care about if we were tested.)


(f) Comment on the relative size of your probability in part (e), taking into account the


fact that this is a high quality RAT test with very good sensitivity and specificity.


(g) Suppose you went to a family birthday party on the weekend and there were 10


individuals there. On Wednesday following the party, 6 out of 10 people at the party have tested


positive for COVID-19 using a PCR test. Now suppose that you test positive using a RAT test.


Estimate the probability of having COVID-19 given your positive RAT test taking into account


the information you received following the weekend’s party.

Jun 01, 2022
SOLUTION.PDF

Get Answer To This Question

Related Questions & Answers

More Questions »

Submit New Assignment

Copy and Paste Your Assignment Here