Respuesta :
Answer:
98% confidence interval estimate of the proportion of Mississippi mortgages that are delinquent lie between ( 0.0529 , 0.1731 ) or 5.29% to 17.31%
Step-by-step explanation:
Given -
A random sample of 150 mortgages in the state of Mississippi was randomly selected. From this sample, 17 were found to be delinquent on their current payment.
Sample size n = 150
Let x be the no of people delinquent on their current payment
Proportion of sucess [tex](\widehat{p})[/tex] = [tex]\frac{x}{n}[/tex] = [tex]\frac{17}{150}[/tex] = 0.113
confidence interval = 99%
[tex]\alpha = 1- \frac{98}{100}[/tex] = .02
[tex]z_{\frac{\alpha }{2}}[/tex] = [tex]z_{\frac{.02}{2}}[/tex] = 2.326
98% confidence interval estimate of the proportion of Mississippi mortgages that are delinquent = [tex]\widehat{p}\pm z_{\frac{\alpha }{2}}\frac{\sqrt{\widehat{p} (1 - \widehat{p})}}{n}[/tex]
= [tex]0.113\pm z_{\frac{.02 }{2}}\frac{\sqrt{0.113 (1 - 0.113)}}{150}[/tex]
= [tex]0.113\pm 2.326\times.02584[/tex]
= [tex]0.113\pm .06010[/tex]
= [tex](0.113 - .06010) , (0.113 + .06010)[/tex]
= ( 0.0529 , 0.1731 )
