Estimate a 95% confidence interval for the proportion of children experiencing at least one incident of AOM in the group that received the Influenza Vaccine. Estimate a 95% confidence interval for the proportion of children experiencing at least one incident of AOM in the group that received the Placebo (c). How do these 95% CIs compare? (Similar range of values? or are they overlapping?)

College Algebra
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Chapter9: Sequences, Probability And Counting Theory
Section9.7: Probability
Problem 3SE: What is an experiment?
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An article in the Journal of the American Medical Association documents the results of a randomized clinical trial designed to evaluate whether the influenza vaccine is effective in reducing the occurrence of acute Otitis media (AOM) in young children. Acute otitis media is an infection that causes inflammation of the middle ear canal. In the study, children were randomized to receive either the influenza vaccine or a placebo. The children were followed for one year after randomization, and monitored for AOM during this period. 262 children were randomized to the vaccine group, and 150 of these children experienced at least one incident of AOM during the follow-up period. 134 children were randomized to the placebo group, and 83 of these children experience at least one incident of AOM during the follow-up period.

Estimate a 95% confidence interval for the proportion of children experiencing at least one incident of AOM in the group that received the Influenza Vaccine.
Estimate a 95% confidence interval for the proportion of children experiencing at least one incident of AOM in the group that received the Placebo
(c). How do these 95% CIs compare? (Similar range of values? or are they overlapping?) 

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