Question

Consider a simple poll that is measuring the proportion of citizens that hold a particular political belief. What is a conservative, "worst case scenario" sample size if you want the margin of error to be 2.6%? Sample Size =

Answer 1

Answer:

Given that,

Consider a simple poll that is measuring the proportion of citizens that hold a particular political belief.

What is a conservative, "worst-case scenario" sample size if you want the margin of error to be 2.6%:

i.e,

Margin of error (E) =2.6% = 0.26

Consider,

= 0.05

Now,

The sample size (n):

p = 0.5

q = 1 - p

= 1 - 0.5

= 0.5

Here at 95% CI, z value is 1.96.

substitute values

= 0.5 0.5 (1.96/0.26)^2

= 0.5 0.5 (7.5385)^2

= 0.5 0.5 56.829

=14.2073

n=14 (Approximately)