A consumer protection agency is comparing the work of two electrical contractors. The agency plans to inspect residences in which each of these contractors has done the wiring in order to estimate the difference in the proportions of residences that are electrically deficient. Suppose the proportions of residences with deficient work are expected to be about 70% for both contractors. How many homes should be sampled in order to estimate the difference in proportions using a 95% confidence interval of width 3% ?
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