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Chapter 11: Q.11 (page 480)

Justice in the Courts? In an issue of Parade Magazine, the editors reported on a national survey on law and order. One question asked of the 2512 U.S. adults who took part was whether the believed that juries "almost always" convict the guilty and free the innocent. Only 578 said that they did. At the 5% significance level do the data provide sufficient evidence to conclude that less than one in four Americans believe that juries "almost always" convict the guilty and free the innocent?

Short Answer

Expert verified

The data shows that less than one-quarter of all individuals in the United States believe juries "usually invariably" convict the guilty and exonerate the innocent.

Step by step solution

01

Given Information

Sample size is n=2512

Number of success is x=578.

Sample proportion would be p^=xn

=5782512

=0.1107

02

Explanation

A significance level of α,

To find zα/2using table II.

Significance level is 5%.

i.e. α=0.05.

Using table II,

zα/2=z0.05/2

=z0.025

=1.96

03

Explanation

The confidence interval for pis:

p^±zα/2·p^(1-p^)n

⇒CI=0.1107±1.960.1107(1-0.1107)2512

⇒CI=0.1107±0.0127

⇒CI=0.0980to0.1234

The highest limit of confidence is less than 0.25at a 5%significance level (one in four).

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