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Data Collectionhard
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A school district estimates average test scores using two alternative designs:

Design A: Simple random sample of 400 students from 80,000

Design B: Cluster sample of 8 schools, then 50 students per school (400 total)

The intraclass correlation for test scores within schools is ρ=0.015\rho = 0.015ρ=0.015. Using the design effect formula DEFF=1+(m−1)ρ\text{DEFF} = 1 + (m-1)\rhoDEFF=1+(m−1)ρ where mmm is cluster size, what is the ratio SEB/SEA\text{SE}_B / \text{SE}_ASEB​/SEA​?