Question

Justice in the Courts?

In a n issue of Parade Magazine, the editors reported on a national survey on law and order. One question asked of 2512 U.S. adults who took part was whether they believed that juries “almost always” convict the guilty and free the innocent Only 578 said they did. At the 5% significance level, do the data provide sufficient evidence to conclude that less than one in four Americans (25%) believe that juries “almost always” convict the guilty and free the innocent?

Answer 1

Given that,
possibile chances (x)=578
sample size(n)=2512
success rate ( p )= x/n = 0.23
success probability,( po )=0.25
failure probability,( qo) = 0.75
null, Ho:p=0.25
alternate, H1: p<0.25
level of significance, α = 0.05
from standard normal table,left tailed z α/2 =1.64
since our test is left-tailed
reject Ho, if zo < -1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.2301-0.25/(sqrt(0.1875)/2512)
zo =-2.304
| zo | =2.304
critical value
the value of |z α| at los 0.05% is 1.64
we got |zo| =2.304 & | z α | =1.64
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value: left tail - Ha : ( p < -2.30388 ) = 0.01061
hence value of p0.05 > 0.01061,here we reject Ho
ANSWERS
---------------
null, Ho:p=0.25
alternate, H1: p<0.25
test statistic: -2.304
critical value: -1.64
decision: reject Ho
p-value: 0.01061
we have enough evidence to support the claim that less than one in four Americans (25%) believe that juries “almost always” convict the guilty and free the innocent.