The National AIDS Behavioral Surveys interviewed a sample of adults in the citie
ID: 3182202 • Letter: T
Question
The National AIDS Behavioral Surveys interviewed a sample of adults in the cities where AIDS is most common. This sample included 810 heterosexuals who reported having more than one sexual partner in the past year. We can consider this an SRS of size 810 from the population of all heterosexuals in high-risk cities who have multiple partners. These people risk infection with the AIDS virus. Yet 291 of the respondents said they never use condoms. Is this strong evidence that more than one-third of this population never use condoms? (Use = 0.05.)
Ho: p =
Ha: p >
z =
Explanation / Answer
Given that,
possibile chances (x)=291
sample size(n)=810
success rate ( p )= x/n = 0.3593
success probability,( po )=0.3333
failure probability,( qo) = 0.6667
null, Ho:p=0.3333
alternate, H1: p>0.3333
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.64
since our test is right-tailed
reject Ho, if zo > 1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.35926-0.3333/(sqrt(0.22221111)/810)
zo =1.5673
| zo | =1.5673
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =1.567 & | z | =1.64
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: right tail - Ha : ( p > 1.5673 ) = 0.05852
hence value of p0.05 < 0.05852,here we do not reject Ho
ANSWERS
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null, Ho:p=0.3333
alternate, H1: p>0.3333
test statistic: 1.5673
critical value: 1.64
decision: do not reject Ho
p-value: 0.05852