Question

We have calculated a confidence interval based on a sample of size n = 100. Now we want to get a better estimate with a margin of error that is only one-fourth as large. How large does our new sample need to be?

Answer 1

25
50
200
400
Or 1600

Answer 2

I think it is 25
100 * 1/4

Answer 3

Let n = original sample size and n' be the new sample size


Now let's use the formula n = sigma*(z/E)^2 and replace E with E/4 and see what happens.


n = sigma*(z/E)^2


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


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


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


n' = sigma*16*(z/E)^2


n' = 16*sigma*(z/E)^2


n' = 16*n


So n' is 16 times larger than the original sample size.


Since the original sample size is n = 100, this means that


n' = 16*n


n' = 16*100


n' = 1600


So the new sample size needs to be 1600 to make the new margin of error be one-fourth of the original margin of error.