Question

A pollster wishes to estimate the true proportion of U.S. voters who oppose capital punishment. How many voters should be surveyed in order to be 95% confident that the true proportion is estimated to be within 5%?

Answer 1

To obtain the sample size,

$n=\frac{(z^*) ^2\hat p\hat q} {M.E^2}$

Where z* is the corresponding z score

P is the proportion of voters

q is the proportion of non-voters

M. E is the margin of error.

For 95%confidence interval, the z score is 1.96.

$n=\frac{(1.96)^2\hat p\hat q} {0.05^2}$

n=1536.64pq

Assuming that the proportion of voters is 0.5 then non-voters are 0.5.

n=1536.64pq

≈385 voters