Answered: A new vaccine was tested to see if it…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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

329

2453

vaccinated children had ear infections, compared to

497

2448

unvaccinated children. Complete parts a) through c) below.

a) Are the conditions for inference satisfied?

Yes. The data were generated by a randomized experiment, less than 10% of the population was sampled, the groups were independent, and there were more than 10 successes and failures in each group.

Your answer is correct.

No. It was not a random sample.

No. The groups were not independent.

No. More than 10% of the population was sampled.

b) Let

be the sample proportion of success in the unvaccinated group, and let

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.

The confidence interval is

4.84.8%,9.09.0%.

(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. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.

No. No conclusion can be made based on the confidence interval.

No. We are 95% confident that the rate of infection of vaccinated babies could be as much as

nothing%

higher compared to unvaccinated babies.

(Do not round until the final answer. Then round to one decimal place as needed.)

Yes. We are 95% confident that about

nothing%

of unvaccinated babies will get an ear infection, while only

nothing%

of vaccinated babies will. This is a meaningful reduction.

(Do not round until the final answer. Then round to one decimal place as needed.)

Your answer is not correct.

Yes. We are 95% confident that the rate of infection is lower by an amount from

4.84.8%

9.09.0%.

This is a meaningful reduction, considering the 20% infection rate among unvaccinated babies.

(Use ascending order. Do not round until the final answer. Then round to one decimal place as needed.)

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