Isn't that the virus test, not the anti-body test? Maybe a fairly low percentage have the virus but a high percentage have been exposed and have the anti-body.

The optimistic take on this is: that means soon enough will be exposed that their immunity will stop the spread.

The pessimistic take on this is: we also don't have strong evidence that the previously exposed are immune, ie, have a strong enough immune response to stop the virus.

Those 30% numbers are still very high, the similar rate in Italy has dropped bellow 10% for 2 weeks now (it's the line-chart on this page [1] bellow "Tamponi giornalieri e contagiati"), with the latest week's figures somewhere between 5% and 7%.

[1] https://lab24.ilsole24ore.com/coronavirus/

Norway's number of positive tests was 5% at the current peak of the epidemic, for reference. Testing and isolation measures have been very effective here, so we have not had an overwhelming wave of infections (yet, knock on wood).

You are conflating a test for active virus versus an antibody test. my suspicion is that a very large percentage of people in certain neighborhoods of New York City are going to show up having been exposed and never presented symptoms. I just don't compute how else you can explain this with a virus that is so transmissible. we should also keep in mind that the number of deaths isn't necessarily indicative by itself of number of infections since deaths can be caused by hospitals being overrun.

This only tells if you are sick not if you were sick