The mayor of a town believes that 78% of the residents favor annexation of a new...

The mayor of a town believes that 78% of the residents favor annexation of a new bridge. Is there sufficient evidence at the 0.02 level to dispute the mayor's claim?

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Expert Solution

Given that,
possibile chances (x)=78
sample size(n)=100
success rate ( p )= x/n = 0.78
success probability,( po )=0.5
failure probability,( qo) = 0.5
null, Ho:p=0.5
alternate, H1: p!=0.5
level of significance, α = 0.02
from standard normal table, two tailed z α/2 =2.326
since our test is two-tailed
reject Ho, if zo < -2.326 OR if zo > 2.326
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.78-0.5/(sqrt(0.25)/100)
zo =5.6
| zo | =5.6
critical value
the value of |z α| at los 0.02% is 2.326
we got |zo| =5.6 & | z α | =2.326
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 5.6 ) = 0
hence value of p0.02 > 0,here we reject Ho
ANSWERS
---------------
null, Ho:p=0.5
alternate, H1: p!=0.5
test statistic: 5.6
critical value: -2.326 , 2.326
decision: reject Ho
p-value: 0
we have enough evidence to support the claim that dispute the mayor's claim

orchestra answered 1 year ago

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