Question

In a​ poll, 37​% 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 3​%, and the estimate was made with 95​% confidence. At least how many people were​ surveyed? The minimum number of surveyed people was nothing . ​(Round up to the nearest​ integer.)

Answer 1

Solution :

Given that,

= 37% = 0.37

1 - = 1 - 0.37 = 0.67

margin of error = E = 3% = 0.03

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (1.96 / 0.03)² * 0.37 * 0.67

= 1058.14

minimum number of surveyed people = 1058