Simultaneous Intervals by Bonferroni
A pollster estimates a proportion in each of five independent subgroups, using the same sample size n in each, and wants the five confidence intervals to be simultaneously valid with overall confidence at least 95%. Using the Bonferroni correction, each interval is built at confidence 99% (z = 2.576), and the worst-case variance p(1-p) = 1/4 is assumed. What is the smallest n per subgroup that makes each interval's half-width at most 0.02? Give an integer.
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Source: Standard Bonferroni simultaneous-confidence-interval construction in survey design. Statement written for AxiomIQ.