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 94​% confidence. At least how many people were​ surveyed?

Answer 1

Answer: 915

Step-by-step explanation:

The formula to calculate the sample size is given by :-

$n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2$

Given : The proportion of people polled answered yes to the question​ : p=0.37

The margin of error : E=0.03

Significance level : $\alpha:\ 1-0.94=0.06$

Critical value : $z_{\alpha/2}=1.88$

Then ,

$n=(0.37)(0.63)(\dfrac{(1.88)}{0.03})^2\\\\\Rightarrow\ n=915.4096\approx915$

Hence, at-least 915 people were​ surveyed.