16. Suppose that when sampling from a normal population having an unknown mean and unknown variance

16. Suppose that when sampling from a normal population having an unknown mean μ and unknown variance σ2, we wish to determine a sample size n so as to guarantee that the resulting 100(1 − α) percent confidence interval for μ

will be of size no greater than A, for given values α and A. Explain how we can approximately do this by a double sampling scheme that first takes a subsample of size 30 and then chooses the total sample size by using the results of the first subsample.