Question

In aâ poll, 51â% of the people polled answered yes to the questionâ "Are you in favor of the death penalty for a person convicted ofâ murder?" The margin of error in the poll was 33â%, and the estimate was made with 94â% confidence. At least how many people wereâ surveyed? The minimum number of surveyed people was:

Answer 1

Answer: 978

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 :
`E=0.03`

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

Critical value :
`z_(\alpha/2)=1.88`

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

`n=p(1-p)((z_(\alpha/2))/(E))^2`

i.e.
`n=(0.53)(0.53)((1.88)/(0.03))^2`

`978.243377778\approx978`

Hence, the minimum required sample size =978