Statistics sample / popoualtion question. CoNFuSeD!?

[AmyMS]

Imagine a total population of T people, made up a total of M men and F women. T = M + F

Now imagine I draw a sample of R people from this population. This sample is found to be made up of B men and G women (R = B + G).

How would I go about proving or disproving that the sample population is representative (in terms of gender) of the whole population at the 95% confidence limit?

Also, how could I work out the minimum sample size (R) needed to give a representative sample of the population, with 95% confidence?

[JohnM]

You could compare two proportions, M/T against B/R using a z-test (normal approximation to the binomial). If the difference between them is not significant, then you would also be able to conclude that the difference between F/T and G/R is not significant. Therefore, your sample is representative of the population since the sample percentages (proportions) are not significantly different from the known population proportions.

[AmyMS]

You could compare two proportions, M/T against B/R using a z-test (normal approximation to the binomial). If the difference between them is not significant, then you would also be able to conclude that the difference between F/T and G/R is not significant. Therefore, your sample is representative of the population since the sample percentages (proportions) are not significantly different from the known population proportions.

Thanks for the quick response!

I'm still confused how to do this because surely you need a standard deviation to use the z-test? If all I have are the population proportion M/T, and the sample proportion B/R how can I use the z-test?

Sorry, don't want to be pain, but I don't understand.