Sample size = Z2/2 * p ( 1 - p) / E2
a)
When prior estimate for proportion is not specified then p = 0.50
Sample size = 2.57582 * 0.5 * 0.5 / 0.052
= 663.5
n = 664 (Rounded up to nearest integer)
b)
Sample size = 2.57582 * 0.38 * (1 - 0.38) / 0.052
= 625.26
n = 626 (Rounded up to nearest integer)
c)
With known estimate of proportion in part b) dramatically reduces the sample size.
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