An organization published an article stating that in any one-year period, approx
ID: 3313542 • Letter: A
Question
An organization published an article stating that in any one-year period, approximately 11.8 percent of adults in a country suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, nine of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult population in the country. Find the P-value? An organization published an article stating that in any one-year period, approximately 11.8 percent of adults in a country suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, nine of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult population in the country. Find the P-value?Explanation / Answer
Given that,
possibile chances (x)=9
sample size(n)=100
success rate ( p )= x/n = 0.09
success probability,( po )=0.118
failure probability,( qo) = 0.882
null, Ho:p=0.118
alternate, H1: p<0.118
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=0.09-0.118/(sqrt(0.104076)/100)
zo =-0.8679
| zo | =0.8679
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =0.868 & | z | =1.64
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: left tail - Ha : ( p < -0.86793 ) = 0.19272
hence value of p0.05 < 0.19272,here we do not reject Ho
ANSWERS
---------------
null, Ho:p=0.118
alternate, H1: p<0.118
test statistic: -0.8679
critical value: -1.64
decision: do not reject Ho
p-value: 0.19272
no evidence to support suffering from depression or a depressive illness is lower than the percent in the general adult population
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