cfcfc809-e-about-the-association-between-being-a-healthcare-worker-and-vaccinati

Question

A contingency table shows 200 people: 80 are vaccinated (marginal P(vaccinated)=0.40). Among healthcare workers (50 people), 30 are vaccinated (P(vaccinated | healthcare)=0.60). Based on these probabilities, what can you conclude about the association between being a healthcare worker and vaccination status?

Accepted Answer

Being a healthcare worker is positively associated with being vaccinated because P(vaccinated | healthcare)=0.60 is greater than the marginal P(vaccinated)=0.40, indicating higher vaccination probability when conditioned on healthcare worker status.

Answer

The result is inconclusive because you must compare P(healthcare | vaccinated) to P(healthcare) instead of P(vaccinated | healthcare) to assess association.

Answer

There is no association because the marginal probability is a fixed population measure and conditional probabilities cannot be compared to indicate association.

Answer

There is a negative association because vaccination among healthcare workers should be less than the population rate due to workplace exemptions, so P(vaccinated | healthcare)=0.60 implies lower risk and thus negative correlation.