Question 1162709: If you wanted to estimate the true percentage of all voters in Ghana who are in favour of abolition of the Senate, and if you wanted your maximum error of estimate to be 6% with a confidence level of 95%,what would the required sample size be?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! half mineral is z*sqrt(p*(1-p)/n)
let that equal 0.06
z will be 1.96 for 95% CI
z^2=3.8416
z^2*p(1-p)/n=0.0036, squaring both sides
3.8416*0.25=0.0036*n. I use 0.5 for p and 1-p as the most conservative estimate. The largest value of the product p and 1-p occurs when they are both the same. [Just like the largest product of two numbers that add to a constant occurs when each number is half the constant. Try it with 100 as the constant. Also might want to notice the pattern of difference as one gets further from the constant.]
n=266.78 or 267.
If you want a smaller sample size see if there is an approximate value of the parameter that is not 50%. For example, if the parameter were 30%, then p(1-p) would be 0.21, not 0.25, and the sample size would be 16% fewer people.
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