Question

A private opinion poll is conducted for a politician to determine what proportion of the population favors decriminalizing marijuana possession. How large a sample isneeded in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 5%?

Answer 1

α=0.02

t_α/2s/√n=0.05xbar

n=(t_α/2s/0.05xbar)²

Answer 2

a=0.02, |Z(0.01)|=2.33 (check standard normal table)

SO n=(Z/E)^2*p*(1-p)
=(2.33/0.05)^2*0.5*0.5
=542.89

Take n=543