We know the clustering structure for the data in Example 10.7. Use results from Chapter 5 (assume one-stage cluster sampling) to estimate the proportion for each cell and margin in the 2×2 table, and find the variance for each estimated proportion. Now use estimated design effects to perform a hypothesis test of independence using X2F. How do the results compare to the model-based test?

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S N Male 43 15 58 Female 32 52 lof 85 75 67 142