Reply #125: here's the post:

[c-macdonald]

First of all, to assume the data is random and follows a normal distribution is a stretch and that assumption really wouldn't hold up after rigorous analysis. But let's say the data is random and we want to get a margin of error.

A sample size of 1000 yields a MOE of +/- 3.1% using the formula:

MOE = +/- 1.96* sqrt< (1-p)*p / n >

where p is our estimated probability of an event ocurring and n is our sample size.

Assuming n=1000, p=.5, we get 1.96* sqrt(.25/1000) = 0.0309 = +/- 3.1%

To get an accurate MOE for your data, you have to calculate each state using the sample size (n) and the percentage of voters for Kerry (p) and that would give you a margin of error at a 95% confidence level.

You can only use MOE = 1/sqrt(n) if the percentage you're measuring is unknown (i.e. you haven't gotten the results yet and want a ballpark figure). Since we have actual percentages for our samples, you have to use the formula I gave above.

With that said, it doesn't change the numbers too much but I'm not sure where you got the Std. Dev. = MOE/1.96 formula from. The MOE takes the Std. Dev. into consideration and, in the formula I gave, already factors in the Std. Dev.

So let's take Ohio. The MOE would be:

MOE = +/- 1.96*sqrt< (.521)(.479) /1963 > = +/- 2.21%

So that means his vote total should be between <49.89, 54.31>