T 72 Determine the minimum sample size required in order to

(T. 72) Determine the minimum sample size required in order to estimate p, the population proportion, to within 0.05, with:

Solution

Using 50% planned proportion estimate,

Minimum sample size(N) = (Z_a/2/E)² *p*(1 - p)

using z-star calculator, (z-value = 1 - a/2 = 1 - 0.05/2 = qnorm(0.975))

part - a) N = (qnorm(0.975)/0.05)² * 0.5 * 0.5 = 384.16 = 385 (rounded tonext nearest integer)

part - b) N = (qnorm(0.975)/0.01)² * 0.5 * 0.5 = 9604 = 9604 (rounded to next nearest integer)