Question

In a​ poll, 69​% of the people polled answered yes to the question​ "Are you in favor of the death penalty for a person convicted of​ murder?" The margin of error in the poll was 22​%, and the estimate was made with 96​% confidence. At least how many people were​ surveyed?

The minimum number of surveyed people was __

​(Round up to the nearest​ integer.)

Answer 1

Solution :

Given that,

$\hat p$= 69%=0.69

1 - $\hat p$ = 1 - 0.69= 0.31

margin of error = E = 22% = 0.22

At 96% confidence level the z is ,

$\alpha$ = 1 - 96% = 1 - 0.96 = 0.04

$\alpha$ / 2 = 0.04 / 2 = 0.02

Z$\alpha$/2 = Z0.02= 2.054 ( Using z table )

Sample size = n = (Z$\alpha$/2 / E)2 * $\hat p$ * (1 - $\hat p$ )

= (2.054 / 0.25)2 * 0.69 * 0.31

= 14.43

Sample size =15