Answer: 978
Step-by-step explanation:
Given : Prior proportion of the people polled answered yes to the question "Are you in favor of the death penalty for a person convicted of murder? : p=0.53
Margin of error : [tex]E=0.03[/tex]
Significance level : [tex]\alpha: 1-0.94=0.06[/tex]
Critical value : [tex]z_{\alpha/2}=1.88[/tex]
The formula to find the sample size is given by :-
[tex]n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2[/tex]
i.e. [tex]n=(0.53)(0.53)(\dfrac{1.88}{0.03})^2[/tex]
[tex]978.243377778\approx978[/tex]
Hence, the minimum required sample size =978
