Looking for some statistics help

[Iconoclastic]

1. If I want to find out what % of the local population (say, 10 million total people) consider themselves to be music lovers, how many people do I need to poll before I can achieve, say 95% confidence level with, say a confidence interval of +-2.5% (for example 30-35%)? Or +-5% (for example 30-40%)?

2. Similarly, if I want to ask X number of people in the local population what THEY think the true % of the local population is who consider themselves to be music lovers, how many people would I need to ask before I can achieve 95% confidence level that the mean answer I get from that X number of people is +-2.5 or +-5% of the true mean (the mean that I would have had I asked every single person in the local population)?

Anything would be appreciated.

[Siegmund]

In the first case, you will need about 9000/k^2 people to get 95% confidence your estimate is within +/- k% of being right. (So, around 400 for 5% and around 1500 for 2.5%) Unless the size of the population is very small (less than a few thousand) it makes almost no difference how many are in the population.

In the second case, the answer will depend on how widely divergent people's guesses are, but will tend to be modestly lower than for part 1.

I'm sure you already realize that these two methods may yield quite different numbers . If you are going to actually administer such a survey, I would also suggest you come up with a firmer idea of what "consider to be a music lover" means (some people will just run with the question, but many will ask you to clarify - and whether they ask or not... people interpreting the question differently does add some unneeded noise to the survey.)