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?
Accepted Solution
A:
Answer: 915Step-by-step explanation:The formula to calculate the sample size is given by :-[tex]n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2[/tex]Given : The proportion of people polled answered yes to the question : p=0.37The margin of error : E=0.03Significance level : [tex]\alpha:\ 1-0.94=0.06[/tex]Critical value : [tex]z_{\alpha/2}=1.88[/tex]Then ,[tex]n=(0.37)(0.63)(\dfrac{(1.88)}{0.03})^2\\\\\Rightarrow\ n=915.4096\approx915[/tex]Hence, at-least 915 people were surveyed.