p.hat <- 0.82; p.hat
SE <- sqrt(p.hat * (1 - p.hat) / 800); SE # est. SE
p.hat - 1.96 * SE # lower end of CI
p.hat + 1.96 * SE # upper end of CI
confint(prop.test(656, 800)) # 656 = 0.82 * 800
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