Question

1. Consider the results of the following three sample designs, each based on n=3,600, drawn from the same population of N=1,800,000 elements:

Sample Design 1: SRS of n=3,600 with y=513 & se(y) =3.3

Sample Design 2: SRS of a=180 clusters from A=90,000 clusters, selecting b=B=20 elements with y=524 & se(y) =10.1

Sample Design 3: Random subsamples of b=4 from B=20 in each of a=900 clusters, selecting clusters at random from the population of A=90,000 clusters with y=509 & se(y)=5.4.

1. Compute the design effect d² and the intraclass correlation roh for Sample Designs 2 and 3. Discuss briefly the results from the two designs.
2. How can we reduce se(y) = 10.1 from Sample Design 2 to se(y)=5.4 (the standard error from Sample Design 3)?
3. For Sample Design 1, compute an estimate of the se(y) if n were to be reduced to 1,200.
4. Discuss whether any sample selected by the first design would have a mean closer to the population mean of the 1,800,000 elements than any mean from a sample selected by second design?

Answer 1