Problem 3: 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 following year, only 333 of 2455 vaccinated children had ear infections, compared to 499 of 2452 unvaccinated children in the control group. a) Do we have some evidence to suggest that the vaccine helped reduce the chance of ear infections in babies? Is this statistically significant? b) Perform a hypothesis test at alpha level: a = 0.01. Assume all conditions are met. c) What type of error could we have made with part b)? Explain.

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Chapter1: Combinatorial Analysis
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Problem 3: 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 following year, only 333 of 2455 vaccinated
children had ear infections, compared to 499 of 2452 unvaccinated children in the control group.
a) Do we have some evidence to suggest that the vaccine helped reduce the chance of ear
infections in babies? Is this statistically significant?
b) Perform a hypothesis test at alpha level: a = 0.01. Assume all conditions are met.
c) What type of error could we have made with part b)? Explain.
Transcribed Image Text:Problem 3: 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 following year, only 333 of 2455 vaccinated children had ear infections, compared to 499 of 2452 unvaccinated children in the control group. a) Do we have some evidence to suggest that the vaccine helped reduce the chance of ear infections in babies? Is this statistically significant? b) Perform a hypothesis test at alpha level: a = 0.01. Assume all conditions are met. c) What type of error could we have made with part b)? Explain.
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