Question

A poll done for Newsweek 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 Newsweek poll? Use a 1% percent level of significance to test the claim of the contingent.

a)

State the parameter being tested:

State the hypotheses and identify the claim:

?0:

??:

b) Identify the test statistic:

c) State the statistical test to be used:

d) Calculate the p-value:

e) Interpret the p-value and compare to ?

f) Make a decision regarding ?0

g) State the conclusion

Answer 1

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, α = 0.01
from standard normal table, two tailed z α/2 =2.576
since our test is two-tailed
reject Ho, if zo < -2.576 OR if zo > 2.576
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 α| at los 0.01% is 2.576
we got |zo| =2.688 & | z α | =2.576
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -2.68775 ) = 0.00719
hence value of p0.01 > 0.0072,here we reject Ho
ANSWERS
---------------
a.
null, Ho:p=0.13
alternate, H1: p!=0.13
b.
test statistic: -2.6877
c.
critical value: -2.576 , 2.576
d.
p-value: 0.00719
e.
p value is less than alpha value
f.
decision: reject Ho
g.
we have enough evidence to support the claim that A poll done for Newsweek found that 13% of Americans have seen or sensed the presence of an angel.