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 is needed in order to be

92%

confident that the sample proportion will not differ from the true proportion by more than

5%

?

Answer 1

Solution,

Given that,

=  1 - = 0.5

margin of error = E = 0.05

At 92% confidence level

= 1 - 92%  

= 1 - 0.92 =0.08

/2 = 0.04

Z/2 = Z0.04  = 1.751

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.751 / 0.05)2 * 0.5 * 0.5

= 306.60

sample size = n = 307