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In: Statistics and Probability

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 338 of 2453 vaccinated children had ear​ infections, compared to 504 of 2455 unvaccinated children. Complete parts​ b) through​ c) below.

B.) 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 infections, p1 - p2 ​(Do not round until the final answer. Then round to one decimal place as​ needed.)

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

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