Q.134 In a recent Zogby International ... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

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 鈥渓ikely鈥� or 鈥渧ery likely.鈥� Use the 鈥減lus-four鈥� 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 a $97 %$ confidence interval for the proportion of American adults who believe that a terrorist attack in their community is likely or very likely is between $8.9 %$ to $33.5 %$ .

Step by step solution

introduction

Given $x = 9$ and $n = 48$

$\overset{}{p'} = \frac{x}{n} = \frac{9}{48} = 0.1875$

Confidence interval = $97 %$

$伪 = 1 鈭� 0.97 = 0.03$

explanation

Now, $z_{\frac{a}{2}} = 2.17$

we have,

Error bound= $Z \frac{a}{2} \sqrt{\frac{p^{鈥�} q^{鈥�}}{n}}$

= 2.17 \sqrt{\frac{0.212 脳 0.788}{52}} = 0.123

Class interval = $p'$ $卤$ error bound

$鈬� (0.212 卤 0.123)$

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 between $8.9 % to 33.5 %$ .