Question

Write expressions for first phase and second phase sample sizes for estimating mean using ratio, product and regression estimators.

Answer 1

In case when population mean of Auxiliary character is unknown we selected a large first phase sample of size n" of population of size N, by using a random sampling without replacement.

Exponential type ratio and product estimators of population mean in two phase sampling can be used here.

Shri venkatnaramana was first to introduce ratio method for mean

And in second phase use sample size n where n< n" by using random sampling without replacement and a variable 'y' is measured n1 responding and n2 as not responding.

Again a sub sample of size r (n2/k , k> 1) is drawn from n2 not responding.

Hence the estimator y dash is given by

Y° = n1/n y dash + n2/n y dash

And in