# What Should the Sample Size be?

• Apr 9th 2014, 03:19 PM
AwesomeHedgehog
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
• Apr 12th 2014, 12:09 PM
AwesomeHedgehog
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.
• Apr 12th 2014, 12:53 PM
Shakarri
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)