Here we return to the controversy about the HPV vaccine. Recall that we assumed that 3 in 100,000 serious health problems occur after the vaccine. We also assumed that the health problems are not due to the vaccine. So we also expect 3 in 100,000 similar serious health problems in girls who are not vaccinated. Suppose that the CDC tracks 400,000 vaccinated girls and 500,000 un-vaccinated girls.

Can they conduct inference procedures for a treatment effect using a normal probability model?