A new vaccine was recently tested to see if it could prevent the painful and recurrent ear infections that many infants suffer from. The Lancet, a medical journal, reported a study in which babies about a year old were randomly divided into two groups. One group received vaccinations; the other did not. During the following year, only 325 of 2450 vaccinated children had ear infections, compared to 504 of 2457 unvaccinated children in the control group.

(a) Are the conditions for inference satisfied?

(b) Find a 95% confidence interval for the difference in rates of ear infection.

(c) Use your confidence interval to explain whether you think the vaccine is effective.