[EMAIL PROTECTED] (Xiao Li) wrote in message news:<[EMAIL PROTECTED]>... > Let N be the population size. Let p denote the proportion of this > population with a certain characteristic (ie. has diabetes, divorced, > homosexual, etc.) Let's say we are trying to estimate p using a > sample of size n. So we collect our sample and calculate p^ to be the > proportion of elements in our sample with our characteristic of > interest. Then we calculate the standard of deviation of p^ (also > known as the standard error) because it gives us an idea of how close > our sample proportion is to the real proportion. > > Now, my statistics textbook says the standard of deviation is given by > SD(p^) = root[(p^(1-p^))/n] when sampling with replacement or when > the sample size is significantly smaller than the population size. > > My question is why isn't there a N variable in our equation for > SD(p^)? According to this formula, if we are trying to figure out the > proportion of people with diabetes in Berkeley, California with sample > size n, we would get the same standard of error as if we are trying to > figure out the proportion of people with diabetes in the world with > sample size n. (In the former, the N is a lot smaller than in the > later).
For a sample of size n, drawn without replacement from a population of size N in which the variance is V, the sampling variance of the sample mean is (V/n)(N-n)/(N-1). If N >> n then V/n is often close enough. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
