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 333 of 2455 vaccinated children had ear infections, compared to 499 of 2452 unvaccinated children in the control group.

a.State the null hypothesis and the alternative hypotheses for this situation. Also explain in words what each hypothesis is claiming.

b. Conduct the appropriate significance test and state your conclusion.

c. Construct a 95% confidence interval for the difference in rates of ear infections.