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Why were sample sizes of 400 for smaller counties and 800 for larger counties used?

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Why were sample sizes of 400 for smaller counties and 800 for larger counties used?

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The sample sizes were selected to obtain acceptable margin of errors for the prevalence estimates at an affordable cost. An 800-sample size was used in Jackson, St. Louis counties and City of St. Louis to obtain prevalence for both African American and white, and in Boone, Buchanan, Cole, Greene, and Jasper to obtain prevalence for both urban and rural populations.

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