One of the tests for Covid-19 is a genetic test, the aim of which is to detect viral RNA. If this test is applied during Stage 1, it will not detect the virus since the virus is hidden away inside the patient’s cells. 2% of patients with respiratory symptoms whose test indicates the presence of the SARS-Cov2, do not in fact have the SARS-Cov2, due to errors in the way the test is conducted. If this test is applied during Stage 2, it should detect SARS-Cov2 but 3% of these tests fail to detect SARS-Cov2 also due to errors in the way the test is conducted.
One of the tests for Covid-19 is a genetic test, the aim of which is to detect viral RNA. If this test is applied during Stage 1, it will not detect the virus since the virus is hidden away inside the patient’s cells. 2% of patients with respiratory symptoms whose test indicates the presence of the SARS-Cov2, do not in fact have the SARS-Cov2, due to errors in the way the test is conducted. If this test is applied during Stage 2, it should detect SARS-Cov2 but 3% of these tests fail to detect SARS-Cov2 also due to errors in the way the test is conducted.
a) Write the 2% and 3% probabilities using conditional probability notation, e.g. P(X|Y)=0.02.
b) Are the 2% and 3% an example of a false positive rate or a false negative rate or neither?
c) Is it possible to estimate the false negative probability of the genetic test by applying the test to patients known to be in Stage 3 of Covid-19?
d) Is it possible to estimate the false positive probability by applying the test to patients known to be in Stage 3 of Covid-19?
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