Concept explainers
(a)
To explain: whether or not the conditions for inference are fulfilled.
(a)
Answer to Problem 13E
Yes
Explanation of Solution
It is told that samples are split into two classes on a random basis. The total
The assumptions and conditions required for inference are met.
(b)
To find: a confidence interval of 95 percent for the difference in ear rates of infection.
(b)
Answer to Problem 13E
(0.0470, 0.0888)
Explanation of Solution
Given:
Formula used:
Calculation:
the observed proportions are
Estimating the standard deviation
For a 95% confidence level,
Therefore, the 95% confidence interval is
A 95 % confidence interval is (0.0470, 0.0888) for the difference in the proportion of unvaccinated and vaccinated children who have ear infections.
(c)
To explain: whether the vaccine uses a confidence interval to be successful or not.
(c)
Explanation of Solution
There are 95 percent sure, based on these samples, that the real difference in the proportion of ear infections among unvaccinated and vaccinated children is between 4.7 percent and 8.88 percent. Since 0 is not in interval and both values are positive, it can infer that the percentage of ear infections among unvaccinated children is 4.7 to 8.88 percent higher than that of vaccinated children. it may assume, then, that the vaccine is effective.
Chapter 22 Solutions
Stats: Modeling the World Nasta Edition Grades 9-12
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