(Solution) - Consider the model sometimes adopted for GVFs in 9 13 Consider -(2025 Original AI-Free Solution)

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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 (?)/t2 can be written as v ? ? + ?/t, and give ? and ?. Consequently, if the intra class correlation coefficient is similar for responses in the survey, the GVF method should work well.