Question

In a survey of 1002 ​adults, a polling agency​ asked, "When you​ retire, do you think you will have enough money to live comfortably or not. Of the 1002 ​surveyed, 524 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.

Select the correct choice below and fill in the answer boxes to complete your choice.

​(Use ascending order. Round to three decimal places as​ needed.)

A. 99% of the population lies in the interval between nothing and nothing.

B.There is a 99% probability that the true proportion of worried adults is between nothing and nothing.

C.There is 99% confidence that the true proportion of worried adults is between __ and __

Answer 1

Solution :

Given that,

n = 1002

x = 524

Point estimate = sample proportion = = x / n = 524 /1002 =0.523

1 - = 1 -0.523= 0.477

At 99% confidence level

= 1-0.99% =1-0.99 =0.01

/2 =0.01/ 2= 0.005

Z/2 = Z0.005 = 2.576

Z/2 = 2.576

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 2.576 * ((0.523*(0.477) /1002 )

= 0.041

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.523 - 0.01 < p < 0.523 + 0.041

0.482 < p < 0.564

(0.482 ,0.564 )

C.There is 99% confidence that the true proportion of worried adults is between 0.482 and 0.564.