Ear infections A new vaccine was recently tested to seeif it could prevent the painful and recurrent ear infectionsthat many infants suffer from. The Lancet, a medicaljournal, reported a study in which babies about a yearold were randomly divided into two groups. One group received vaccinations; the other did not. During the fol-lowing year, only 333 of 2455 vaccinated children had ear infections, compared to 499 of 2452 unvaccinatedchildren in the control group.a) Are the conditions for inference satisfied?b) Find a 95% confidence interval for the difference inrates of ear infection.c) Use your confidence interval to explain whether youthink the vaccine is effective.

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Ear infections 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 fol-
lowing year, only 333 of 2455 vaccinated children had
ear infections, compared to 499 of 2452 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.
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