SOLUTION: After calculating the sample size needed to estimate a population proportion to within .04, your statistics professor told you the maximum allowable error must be reduced to just .

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Question 1089638: After calculating the sample size needed to estimate a population proportion to within .04, your statistics professor told you the maximum allowable error must be reduced to just .01. If the original calculation led t a sample size of 800, the sample size will now have to be:
I know the answer but do not know how to get it. Can someone please help me?!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We will use the formula
n+=+p%281-p%29%28z%2FE%29%5E2
as shown on this page (scroll down to the section titled "Finding n to Estimate a Proportion")

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Initially we're told that an error of E = 0.04 will lead to a sample size of n = 800. We don't know z and we don't know p. We don't need to know p. If p is unknown, then we assume that p = 0.5. The goal here is to find z given n = 800 and E = 0.04. Let's do that

n+=+p%281-p%29%28z%2FE%29%5E2

800+=+0.5%281-0.5%29%28z%2F0.04%29%5E2

800+=+0.25%28z%2F0.04%29%5E2

800%2F0.25+=+%28z%2F0.04%29%5E2

3200+=+%28z%2F0.04%29%5E2

%28z%2F0.04%29%5E2+=+3200

z%2F0.04+=+sqrt%283200%29

z%2F0.04+=+56.5685424949239

z+=+0.04%2A56.5685424949239

z+=+2.26274169979696

So the z critical value is roughly z = 2.2627

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We'll use z = 2.2627 and the new error threshold of E = 0.01 to find n to be...

n+=+p%281-p%29%28z%2FE%29%5E2

n+=+0.5%281-0.5%29%282.2627%2F0.01%29%5E2

n+=+0.25%28226.27%29%5E2

n+=+0.25%2A51198.1129

n+=+12799.528225

n+=+12800 (round up to the nearest whole number)

The new sample size needed is approximately 12800