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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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.