Question

in a​ poll, 51​% 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 5​%, and the estimate was made with 95​% confidence. At least how many people were​ surveyed?

The minimum number of surveyed people was? (Round to the nearest integer)

Answer 1

Solution :

Given that,

= 0.51

1 - = 1 - 0.51 = 0.49

margin of error = E = 5% = 0.05

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

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.96 / 0.05)2 * 0.51 * 0.49

= 384.00

Sample size =384