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Chapter 11: Q.8 (page 480)

Smallpox Vaccine. ABCNEWS.com published the results of a poll that asked U.S. adults whether they would get a smallpox shot if it were available. Sampling, data collection, and tabulation were done by TNS Intersearch of Horsham, Pennsylvania. When the risk of the vaccine was described in detail, 4 in 10 of those surveyed said they would take the smallpox shot. According to the article, "the results have a three-point margin of error" (for a 0.95 confidence level). Use the information provided to obtain a 95% confidence interval for the percentage of all U.S. adults who would take a smallpox shot, knowing the risk of the vaccine.

Short Answer

Expert verified

The confidence interval for the percentage of all adults who would take a smallpox vaccination may be 95%confidence, indicating a risk of 0.37to 0.43for the vaccine.

Step by step solution

01

Given Information

p=percentage of all adults who would take a smallpox shot indicates the risk of the vaccine.

Here x=4

and n=10.

02

Explanation

The confidence interval for p:

p^卤z伪/2p^(1-p^)n

Where

z伪/2p^(1-p^)n=Margin of error

p^=xn

=410

=0.40

The confidence interval for p:

=p^卤z伪/2p^(1-p^)n

=0.40卤0.03[margin of error is given as3-point]i.e,0.37and0.43

i.e,37%and43%

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Most popular questions from this chapter

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Margin of error=0.03

Confidence level=99%

Educated guess=0.5

(a) Obtain a sample size that will ensure a margin of error of at most the one specified (provided of course that the observed value of the sample proportion is further from 0.5that of the educated guess.

(b). Compare your answer to the corresponding one and explain the reason for the difference, if any.
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