Question

A researcher would like to estimate p, the proportion of U.S. adults who support recognizing civil unions between gay or lesbian couples. If the researcher would like to be 95% sure that the obtained sample proportion would be within 1.5% of p (the proportion in the entire population of U.S. adults), what sample size should be used?

(a) 17,778(b) 4,445(c) 1,112(d) 67(e) 45

Answer 1

(b) 4,445

Explanation:

If the researcher would like to be 95% sure that the obtained sample proportion would be within 1.5% of p (the proportion in the entire population of U.S. adults), what sample size should be used?

Given a=0.05, |Z(0.025)|=1.96 (check standard normal table)

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

=(1.96/0.015)^2*0.5*0.5

=4268.444

Take n=4269

Answer:(b) 4,445