In early 2010, 33% of subprime mortgages in a certain country were in distress,
ID: 3324369 • Letter: I
Question
In early 2010, 33%
of subprime mortgages in a certain country were in distress, meaning that their holders were either being foreclosed on or were at least 90 days delinquent on their payments. The federal government is hopeful that this percentage has declined due to mortgage aid programs that were initiated during the year. To test this hypothesis, a random sample of 200
subprime mortgages was selected later in 2010. From this sample it was found that 56
mortgages were in distress. Using =0.05,
answer parts a and b below. Determine the critical value(s) of the test statistic.
Explanation / Answer
Given that,
possibile chances (x)=56
sample size(n)=200
success rate ( p )= x/n = 0.28
success probability,( po )=0.33
failure probability,( qo) = 0.67
null, Ho:p=0.33
alternate, H1: p!=0.33
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.28-0.33/(sqrt(0.2211)/200)
zo =-1.5038
| zo | =1.5038
critical value
the value of |z | at los 0.05% is 1.96
we got |zo| =1.504 & | z | =1.96
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -1.5038 ) = 0.13263
hence value of p0.05 < 0.1326,here we do not reject Ho
ANSWERS
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null, Ho:p=0.33
alternate, H1: p!=0.33
test statistic: -1.5038
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.13263