Calculate 95% Confidence Interval in Public Opinion Polls

[Lobotomy]

hello
when doing a public opinion poll before an election in a country, they usually approximate the hypergeometric distribution with a binomial distribution and then using the normal approximation:

m +/-1.96*sqrt(m*(1-m)/n) to calculate a 95% confidence interval?
m= mean
n= number of people in the poll

is it as simple as that? assuming party A gets 30% of the votes, and 2000 voted we get a 95% statistically significant interval of:
30 +/-1.96*sqrt(0.30*(0.7)/2000)

is it as simple as that? i think this is what i learned in school a long time ago...

However if we make a poll within a defined population of let's say 5000 people. and the number of people in the poll is 3000. party A gets 30% of the votes in the poll. What can we say about the total population of 5000.
here we should use the hypergeometric distribution and can not use the binomialapproximation. I've only used the hypergeometric distribution in examples of sampling without replacement, where we want to calculate the probability of drawing a certain color ball. However this time, we draw som balls and we want to say something about the pot itself right (the balls are the votes and the pot is the total population vote). How do we do this?

 

[Valkarie]

Yes, you are correct in that the binomial approximation can be used to calculate the 95% confidence interval with the given parameters. However, in order to make an inference about the total population of 5000 people, you will need to use the hypergeometric distribution as you noted. The hypergeometric distribution is a probability distribution that describes the number of successes in a sample of size n from a population of size N, where each member of the population has a different probability of being chosen. In this case, the population size is 5000 and the sample size is 3000. The number of "successes" is 30%, which is the proportion of votes for party A. Using the hypergeometric distribution, you can then calculate the probability of obtaining a certain number of successes in the sample, given the population size and number of successes in the population. From this, you can make inferences about the total population of 5000 people.