What Should the Sample Size be?

A chemist who has prepared a product designed to kill a particular type of insect wants to evaluate the kill rate of her preparation.

What sample size should she use if she wishes to be 95% confident that her experimental results fall within 0.02 of the true fraction of insects killed?

This is what I did to solve the problem. I am wondering if it is correct?

Let x be a true fraction.

alpha = 0.05

alpha/2 = 0.025

so, z = 1.96

sqrt(n) ≥ z / 0.02 = 98

n ≥ 9604

so, n = 9604

Re: What Should the Sample Size be?

Actually, I redid the problem above using the equation:

n = z^2 / (4*E^2)

So, z = 1.96, E = 0.02

Inserting those values into the equation, we'd get:

n = (1.96^2) / [4*(0.02^2)] = 2401

I was wondering if this was correct, not what I did previously.

Re: What Should the Sample Size be?

Yes the second attempt is correct as you remembered to include the standard deviation (or worst case of it)