Question

In a survey of 1066 ​adults, a poll​ asked, "Are you worried or not worried about having enough money for​ retirement?" Of the 1066 ​surveyed, 566 stated that they were worried about having enough money for retirement. Construct a 95​% confidence interval for the proportion of adults who are worried about having enough money for retirement.

Answer 1

Solution :

Given that,

n = 1066

x = 566

Point estimate = sample proportion = = x / n = 0.531

1 - = 0.469

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

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

= 1.96 * (((0.531 * 0.469) / 1066)

= 0.030

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.531 - 0.030 < p < 0.531 + 0.030

0.501 < p < 0.561

( 0.501 , 0.561 )