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 within 2%?

Answer 1

Answer:

To determine the sample size i.e., number of voters

Given,

margin of error = 2% = 0.02

confidence interval = 95%

Here for the 95% confidence interval , Z value = 1.96

Now let us consider,

n = p^ * (1 - p^) * (Z / E)^2

substitute all values in the above formula

n = 0.5*0.5*(1.96/0.02)^2

n = 2401

So here number of voters i.e., n = 2401