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Chapter 8: Q.134 (page 492)

In a recent Zogby International Poll, nine of 48 respondents rated the likelihood of a terrorist attack in their community as “likely” or “very likely.” Use the “plus-four” method to create a 97% confidence interval for the proportion of American adults who believe that a terrorist attack in their community is likely or very likely. Explain what this confidence interval means in the context of the problem.

Short Answer

Expert verified

The confidence interval in the context of the problem means that with a97%confidence interval for the proportion of American adults who believe that a terrorist attack in their community is likely or very likely is between 8.9%to33.5%.

Step by step solution

01

introduction

Given x=9and n=48

p'=xn=948=0.1875

Confidence interval =97%

α=1−0.97=0.03

02

explanation

Now,za2=2.17

we have,

Error bound= Za2p′q′n

=2.170.212×0.78852=0.123

Class interval = p'±error bound

⇒(0.212±0.123)

role="math" localid="1650888106268" =(0.089,0.335)

Hence, the proportion of American adults who believe that a terrorist attack in their community is likely or very likely is between8.9%to33.5%.

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