I am supposed to be finding the confidence interval for P(X=1) = EX = unemployment rate.
I have X = 1 if unemployed, 0 if employed. Y = 1 if no response, 0 if response.
I had to find unbiased estimators for theta1 = P(X=1,Y=0) and theta2 = P(Y=1). I also need to prove they are unbiased.
I am given n, number of questionnaires; n1 are collected back; Among the n1, m are unemployed.
I have theta1(hat) = m/n and theta2(hat) = 1 - n1/n.
I am not sure how to show these are unbiased and could use some direction.
Secondly, I need to find the variance of theta1(hat) and the 95% confidence interval for theta1(hat).
Any help is appreciated.