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A new vaccine was tested to see if it could prevent the ear infections that many...

A new vaccine was tested to see if it could prevent the ear infections that many infants suffer from. Babies about a year old were randomly divided into two groups. One group received​vaccinations, and the other did not. The following​ year, only 331 of 2456 vaccinated children had ear​ infections, compared to 499 of 2448 unvaccinated children.

Let ^p1  be the sample proportion of success in the unvaccinated​ group, and let ^p2 be the sample proportion of success in the vaccinated group. Find the​ 95% confidence interval for the difference in rates of ear​infection,

p1−p2.

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