Use the given data to find the minimum sample size required to estimate the population proportion.
-$\text { Margin of error: } 0.008 \text {; confidence level: } 99 \% ; \hat { \mathrm { p } } \text { and } \hat { \mathrm { q } } \text { unknown }$
A) 25,901
B) 15,900
C) 26,024
D) 25,894

Question

Quizplus · Accepted Answer

The sample size required to estimate the population proportion is given by the formula:$$n = \frac{z^2 \hat{p} \hat{q}}{e^2}$$where:* z is the z-score corresponding to the desired confidence level* p is the estimated population proportion* q is the estimated population proportion* e is the margin of errorIn this case, we have:* z = 2.576 (corresponding to a 99% confidence level)* p = 0.5 (since we don't know the population proportion, we use the most conservative estimate of 0.5)* q = 1 - p = 0.5* e = 0.008Plugging these values into the formula, we get:$$n = \frac{2.576^2 	imes 0.5 	imes 0.5}{0.008^2} = 25,901$$Therefore, the minimum sample size required is 25,901.