A poll done for an organization found that 13% of Americans have seen or sensed
ID: 3228601 • Letter: A
Question
A poll done for an organization found that 13% of Americans have seen or sensed the presence of an angel. A contingent doubts that the percent is really that high. It conducts its own survey. Out of 76 Americans surveyed, only two had seen or sensed the presence of an angel. As a result of the contingent's survey, would you agree with the organization's poll? Conduct a hypothesis test at the 5% level. Note: If you are using a Student's t distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) El Part (a) State the null hypothesis. O Ho: p 0.13 Ho: p s 0.13 Ho: p 20.13 O Ho: p 0.13 E Part (b) State the alternative hypothesis. Hap 0.13 Hat p 0.13 O Ha: p> 0.13 Ha: p 0.13Explanation / Answer
Given that,
possibile chances (x)=2
sample size(n)=76
success rate ( p )= x/n = 0.0263
success probability,( po )=0.13
failure probability,( qo) = 0.87
null, Ho:p=0.13
alternate, H1: p<0.13
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=0.02632-0.13/(sqrt(0.1131)/76)
zo =-2.6877
| zo | =2.6877
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =2.688 & | z | =1.64
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: left tail - Ha : ( p < -2.68775 ) = 0.0036
hence value of p0.05 > 0.0036,here we reject Ho
ANSWERS
---------------
a.
null, Ho:p>=0.13
b.
alternate, H1: p<0.13
c.
P' repoesents the proportiofi of Aniencans who have not seen or sensed angels.
d.
test statistic: -2.6877
critical value: -1.64
decision: reject Ho
p-value: 0.0036
we have evidence that it is not that high
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