Question

In a survey of 1011 ​adults, a polling agency​ asked, "When you​ retire, do you think you will have enough money to live comfortably or not. Of the 1011 ​surveyed, 529 stated that they were worried about having enough money to live comfortably in retirement. Construct a 99​% confidence interval for the proportion of adults who are worried about having enough money to live comfortably in retirement.

Answer 1

(0.1533, 0.8932)

Explanation:

given that in a survey of 1011 ​adults, a polling agency​ asked, "When you​ retire, do you think you will have enough money to live comfortably or not.

Sample size = number of persons surveyed = n = 1011

X = persons who stated that they were worried about having enough money to live comfortably in retirement=529

Sample proportion p =
`(x)/(n) =0.5232`

`q=1-p = 0.4768`

Std error =
`=\sqrt{(pq)/(n) } \\=0.1439`

Margin of error for 99% = ±2.58*std error

= 0.3699

Confidence interval

= p±Marginof error

=
`(0.1533, 0.8932)`