Brain Teaser: Algebra Why do we use 1/4 in place of p(12p) in formula (22) for sample

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Brain Teaser: Algebra Why do we use 1/4 in place of p(12p) in formula (22) for sample size when the probability of success p is unknown?

(a) Show that p(12p) 51/4 2(p 21/2)2.

(b) Why is p(12p) never greater than 1/4?

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