2 Proportion of a certain characteristic in a population p i

2. Proportion of a certain characteristic in a population, p is estimated by sample proportion, A, where X is the number of sample units with that characteristic. n (Note that X is Binomial with parameters in and p)

Solution

as you can see p is the proportion and is estiamted by sample proportion of x/n

where x is the number of sample units with that characteristic

since is a binomila distribution , with only that we can say that the biases estimator for Var(X)

will be n(x/n) ( 1 - x/n)

why?

because x/n = p

(1 - x/n) = q

q = 1 - p

and n that is the number of the sample ( smaple size)