margin of error - quick trick ?
hello , I have been reading a maths book about probability and there is a section about polls and surveys and finding the margin of error ,there is a quick formula in the book to find the margin of error , my question is does it work for any number of candidates here is my question. question . you survey a 1000 people , and you find that support for the 3 candidates are 60% 30% 10% , the margin of error will be , find the square root of the number of people surveyed 1000 people so the square root is 31.6 , divide by 98 , so 98 / 31.6 = 3 .1 % does this formula work for 3 , 4 , 5 ........... candidates?
Re: margin of error - quick trick ?
The margin of error is used to measure the variance of a mean or proportion (a proportion is a mean).
If you want the margin of error for one candidate, you can treat the problem as a binomial and if this is done then the margin of error of getting one candidate against another does have the margin according to sigma^2 / SQRT(N) where sigma^2 is the variance and N is the sample size.
The above situation applies when you treat a 1 as beloning to the candidate of interest (i.e. they voted for the candidate) and a 0 corresponds to voting for someone else.