I have to show that the mean of the sampling distribution is = to pi (the proportion of ___ in a population), and that the standard error of the sampling distribution is = to sqrt(pi(1-pi)/n)
This is how my professor wrote the problem:
Let p, the sample proportion, be written as p = ng/n, where n = sample size and ng = the number of girls in the sample. Show that E(p) = pi and V(p) = pi(1-pi)/n, where pi = proportion of girls in the population.
His hint was to "use the binomial" and "do not use sums of 0s and 1s".
Thank you in advance for any help you can offer.
This is how my professor wrote the problem:
Let p, the sample proportion, be written as p = ng/n, where n = sample size and ng = the number of girls in the sample. Show that E(p) = pi and V(p) = pi(1-pi)/n, where pi = proportion of girls in the population.
His hint was to "use the binomial" and "do not use sums of 0s and 1s".
Thank you in advance for any help you can offer.