Answer :
Answer:
1770
Step-by-step explanation:
We need to estimate number of households to be sampled to construct a 99% confidence interval.
Number of households to be sampled=n=?
[tex]n=\frac{(z_{\frac{\alpha}{2} })^2 pq }{E^{2} }[/tex]
[tex]z_{\frac{\alpha}{2} } =z_{\frac{\0.01}{2} }=z_{0.005 }=2.576[/tex]
The proportion can be estimated as
p=x/n.
We know that 24 out of 40 households owns their home.
so, x=24 and n=40.
p=24/40
p=0.6
q=1-p=1-0.6=0.4
pq=0.6*0.4=0.24
E=0.03
[tex]n=\frac{(z_{\frac{\alpha}{2} })^2 pq }{E^{2} }[/tex]
[tex]n=\frac{2.576^2(0.24)}{0.03^2}[/tex]
[tex]n=\frac{1.5926}{0.0009}[/tex]
n=1769.56.
n=1770.
Thus, the number of households that need to be sampled are 1770.