Respuesta :
Answer:
Interval estimate for the proportion of all homeowners in the United States that hold a home equity loan lie between (.17033 , .22967 ) or 17% to 22.9%
Step-by-step explanation:
Given -
In a recent poll of 1,200 homeowners in the United States, one in five homeowners reports having a home equity loan that he or she is currently paying off.
If one in five homeowners reports having a home equity loan then for 1200 homeowners = [tex]\frac{1200}{5}[/tex] = 240 homeowners reports having a home equity loan.
Sample proportion [tex](\widehat{p})[/tex] = [tex]\frac{240}{ 1200}[/tex] = 0.2
confidence coefficient = 0.99
[tex](\alpha)[/tex] = 1 - confidence coefficient = 1 - 0.99 = .01
[tex]z_{\frac{\alpha}{2}} = z_{\frac{.01}{2}}[/tex] = 2.58
interval estimate for the proportion of all homeowners in the United States that hold a home equity loan
= [tex]\widehat{p}\pm z_{\frac{\alpha}{2}}\sqrt\frac{{\widehat{p}( 1 - \widehat{p})}}{n}[/tex]
= [tex]0.2\pm z_{\frac{.01}{2}}\sqrt\frac{{0.2( 1 - 0.2)}}{1200}[/tex]
= [tex]0.2\pm 2.58\times \sqrt\frac{{0.2( 0.8)}}{1200}[/tex]
= [tex]0.2\pm .02967[/tex]
= [tex](0.2 - .02967 ) , (0.2 + .02967)[/tex]
= (.17033 , .22967 )
