The sample size needed to estimate the difference between two population proportions to within a margin of errorE

E

with a significance level of

can be found as follows. In the expression

E=zsqrtp1(1p1)/n1+p2(1p2)/n2

n1andn2 byn(assuming that both samples have the same size) and replace each ofp1andp2by0.5

(because their values are not known). Then we solve for n, and getn=(z)2/2E2.Finally, increase the value ofnn

to the next larger integer number.Use the above formula and the rounded values for z* given in class to find the size of each sample needed to estimate the difference between the proportions of boys and girls under 10 years old who are afraid of spiders. Assume that we want a80

80

% confidence level and that the error is smaller than0.03.