I have a problem remembering the right maths to use for a technical problem I am trying to solve. Is there anyone here that can point me in the right direction please?

 

Here is the problem;

Lets say there is a population of 1,000,000 people

Within this population I want to know what percentage have a certain condition.

The proportion of people who have this condition is likely to be in the range of circa 1 in 75.

Lets assume that the people with the condition are distributed randomly distributed across the one million population

I would like to work out the number of people I would need to sample to know with a degree of certainty what proportion of people in the population had the particular condition.

In terms of the level of accuracy I think would be necessary, if the actual answer was 1 in 75 people, I would be happy to know if the range was between 1 in 70 to 1 in 80.

So I am not quite sure where to start to find how many people I need to sample in order to determine the proportion within the population.

Any ideas or suggestions on the right approach very much appreciated!

What you are after is a power calculation for proportions. Are you familiar with type 1 and 2 statistical errors: it's a good place to start. This website might help, but if you just want a quick estimate there are plenty of online power calculators. A population of a million should be enough to use calculations assuming an infinite population, but corrections for finite population sizes exist.