So I already know the answer to this problem I just need help with better understanding it. The question is:
A advisor wishes to construct 95% confidence interval for the percentage of all voters who favor a particular proposed law, to within 2 percentage points. From experience he thinks that the proportion is about 60%. The minimum size sample he should take, based on the initial estimate of 60%, is
a) 47 b)2305 c)1164 d)231 e)1576
I divided 1-.95 by 2 and I got .025, Then I used the invNorm(.025) and I got 1.96. So this is where I get confused

Question

So I already know the answer to this problem I just need help with better understanding it. The question is:
A advisor wishes to construct 95% confidence interval for the percentage of all voters who favor a particular proposed law, to within 2 percentage points. From experience he thinks that the proportion is about 60%. The minimum size sample he should take, based on the initial estimate of 60%, is
a) 47 b)2305 c)1164 d)231 e)1576
 I divided 1-.95 by 2 and I got .025, Then I used the invNorm(.025) and I got 1.96. So this is where I get confused

anonymous · Answer

My teacher broke down the problem using a specific formula. She did (1.96)^2*0.6*0.4 divided by 0.02^2 and the answer is b 2305. Where did she get the 0.4 from ?

jim_thompson5910 · Answer

She is using the formula on this page http://www.ltcconline.net/greenl/courses/201/estimation/ciprop.htm scroll all the way down and look for the formula in the last box this formula here $$\Large n = p(1-p)\left(\frac{z_{c}}{E}\right)^2$$

jim_thompson5910 · Answer

In this case, p = 0.6 so 1-p = 1-0.6 = 0.4