Question

A new test for diabetes was carried out. Of the 80 people who tested positive, it was found that actually 40 had diabetes. Of the 9920 people who tested negative, only 9840 did not have the disease actually. The sensitivity of this new test is:

• A. 33%
• B. 50%
• C. 65%
• D. 99%

Hint:

Sensitivity equals true positives over all who truly have the disease, including the missed negatives.

Answer 1

The Correct Option is A

Start by sorting all 10000 people into the four cells of a diagnostic table. The 80 who tested positive split into 40 genuine cases (true positives) and 40 wrongly flagged (false positives). The 9920 who tested negative split into 9840 correctly cleared (true negatives) and the remaining $9920-9840=80$ who actually had diabetes but slipped through (false negatives). Sensitivity asks what fraction of all true diabetics the test managed to catch. The total number of true diabetics is the true positives plus the false negatives, $40+80=120$. The test caught 40 of them, so sensitivity is $\frac{40}{120}\times100$, which equals roughly 33.3%. The distractors come from mixing up the denominator, for example using only the test positives. The intended value is about a third. $$\boxed{33\%}$$