Suppose there are k groups each consisting of N boys. We want to estimate the mean age μ of these kN boys. Fix 1<n<N and consider the follow

Suppose there are k groups each consisting of N boys. We want to estimate the mean age µ of these kN boys. Fix 1<n<N and consider the following two sampling schemes.

I. Draw a simple random sample without replacement of size nk out of all Nk boys.

II. From each of the k groups draw a simple random sample with replacement of size n .

Let (Ybar) and (Ybar_G) be the respective sample mean ages for the two schemes. Which of the following are true?

3. Var(Ybar)may be less than Var(Ybar_G) in some cases.

if all the group means are same.

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