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 2​%, and the estimate was made with 95​% confidence. At least how many people were​ surveyed?

Answer 1

Answer:

2239

Step-by-step explanation:

Given-

Percent of peopl polling yes to the question​ "Are you in favor of the death penalty for a person convicted of​ murder?" $= 37$%

Margin error in the poll  $= 2$%

Confidence Interval $= 95$%

The alpha value is $1 -0.95 =0.05$

The $z_\frac{\alpha }{2}$ for Confidence Interval of $95$% $= 0.196$

The sample size is given by

$n = p*q*(\frac{z}{e} )^2$

Where,

$p = \frac{37}{100} = 0.37 q = 100-0.37 = 0.63 e =2/100 = 0.02 z = 1.96 (critical value)n = p*q*(\frac{z}{e} )^2 = 0.37 * 0.63(\frac{1.96}{0.02} )^2 \\n = 2238.69\\n= 2239$