In a national survey of 2026 adults, 1580 responded that lack of respect and cou
ID: 3218383 • Letter: I
Question
In a national survey of 2026 adults, 1580 responded that lack of respect and courtesy in American society is a serious problem, and 1257 indicated that they believe that rudeness is a more serious problem than in past years. Is there convincing evidence that more than three-quarters of U.S. adults believe that rudeness is a worsening problem? Test the relevant hypotheses using a significance level of 0.05. (For z give the answer to two decimal places. For P give the answer to four decimal places.)
You may need to use the appropriate table in Appendix A to answer this question.
z = P =Explanation / Answer
Given that,
possibile chances (x)=1257
sample size(n)=2026
success rate ( p )= x/n = 0.6204
success probability,( po )=0.75
failure probability,( qo) = 0.25
null, Ho:p>0.75
alternate, H1: p<0.75
level of significance, = 0.05
from standard normal table,left tailed z /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=0.62043-0.75/(sqrt(0.1875)/2026)
zo =-13.4682
| zo | =13.4682
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =13.468 & | z | =1.64
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: left tail - Ha : ( p < -13.46818 ) = 0
hence value of p0.05 > 0,here we reject Ho
ANSWERS
---------------
null, Ho:p=0.75
alternate, H1: p<0.75
test statistic: -13.4682
critical value: -1.64
decision: reject Ho
p-value: 0
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