Consider the model sometimes adopted for GVFs in (9.13). Consider the one-stage cluster design studied in Section 5.2.2, in which each psu has size M and an SRS of n psus is selected from the N psus in the population. Assume that N is large and n/N is small.
- For a binary response with p=yU, show that

- Show that the relative variance v=V (ṫ)/t2 can be written as v ≈ α + β/t, and give α and β. Consequently, if the intra class correlation coefficient is similar for responses in the survey, the GVF method should work well.