Answer:
90% confidence interval for the proportion p of adult residents who are parents in this county is [0.433 , 0.527].
Step-by-step explanation:
We are given that we wish to estimate what percent of adult residents in a certain county are parents. Out of 300 adult residents sampled, 144 had kids.
Firstly, the pivotal quantity for 90% confidence interval for the proportion p of adult residents who are parents in this county is given by;
P.Q. =
~ N(0,1)
where,
= proportion of adults residents who are parents in this county in a sample of 300 adults =
= 48%
n = sample of adults residents = 300
p = population proportion of adults
<em>Here for constructing 90% confidence interval we have used One-sample z proportion statistics.</em>
So, 90% confidence interval for the population proportion, p is ;
P(-1.6449 < N(0,1) < 1.6449) = 0.90 {As the critical value of z at 5%
significance level are -1.6449 & 1.6449}
P(-1.6449 <
< 1.6449) = 0.90
P(
<
<
) = 0.90
P(
< p <
) = 0.90
<u>90% confidence interval for p </u>= [
,
]
= [
,
]
= [0.433 , 0.527]
Therefore, 90% confidence interval for the proportion p of adult residents who are parents in this county is [0.433 , 0.527].