A rare condition
A test has sensitivity 0.98 and specificity 0.90. The prevalence is 0.02. Compute the positive predictive value and the proportion of positive tests that are false alarms.
Worked answer
Sensitivity 0.98 and specificity 0.90 mean 1-\beta=0.98 and \alpha=0.10. With prevalence 0.02,
\mathrm{PPV}=\frac{0.02\times 0.98}{0.02\times 0.98+0.98\times 0.10}=\frac{0.0196}{0.1176}\approx 0.167.
About 83\% of the positive tests are false alarms.