Question

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. Calculate the 98% confidence interval estimate of the proportion of Mississippi mortgages that are delinquent. 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. Calculate the 98% confidence interval estimate of the proportion of Mississippi mortgages that are delinquent.

Answer 1

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%

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
`(\widehat{p})` =
`(x)/(n)` =
`(17)/(150)` = 0.113

confidence interval = 99%

`\alpha = 1- (98)/(100)` = .02

`z_{(\alpha )/(2)}` =
`z_{(.02)/(2)}` = 2.326

98% confidence interval estimate of the proportion of Mississippi mortgages that are delinquent =
`\widehat{p}\pm z_{(\alpha )/(2)}\frac{\sqrt{\widehat{p} (1 - \widehat{p})}}{n}`

=
`0.113\pm z_{(.02 )/(2)}(√(0.113 (1 - 0.113)))/(150)`

=
`0.113\pm 2.326*.02584`

=
`0.113\pm .06010`

=
`(0.113 - .06010) , (0.113 + .06010)`

= ( 0.0529 , 0.1731 )