The sample size needed to estimate the difference between two population proportions to within a margin of errorEwith a significance level ofcan be found as follows. In the expressionE=zp1(1p1)/n1+p2(1p2)/n2

we replace bothn1

andn2byn(assuming that both samples have the same size) and replace each ofp1

andp2 by0.5(because their values are not known). Then we solve for n, and getn=(z)^2/2E^2

Finally, increase the value ofn

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

n=________