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 5​%, and the estimate was made with 94​% confidence. At least how many people were​ surveyed?

Answer 1

solution:

= 69%=0.69

1 - = 1 - 0.69 = 0.31

margin of error = E = 5% = 0.05

At 94% confidence level the z is ,

= 1 - 94% = 1 - 0.94 = 0.06

/ 2 = 0.06 / 2 = 0.03

Z_/2 = Z_0.03 = 1.881

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

= (1.881 / 0.05)² * 0.69 * 0.31

= 302.7250 = 303

Sample size = 303