Use the given data to find the minimum sample size required to estimate the population proportion.
-$$\text { Margin of error: } 0.018 \text {; confidence level: } 99 \% ; \hat { \mathrm { p } } \text { and } \hat { \mathrm { q } } \text { unknown }$$
A) 7116
B) 4966
C) 5117
D) 4114

Question

Quizplus · Accepted Answer

To find the minimum sample size, we need to use the formula:
n = $\frac{	ext{Z}^2	ext{pq}}{	ext{E}^2}$
where Z is the z-score for the given confidence level and is 2.576, p and q are unknown and hence we take them as 0.5 each and E is the given margin of error, which is 0.018.
Thus, plugging in the values we get:
n = $\frac{(2.576)^2(0.5)(0.5)}{(0.018)^2}$ = 5117.47.
Rounding up to the nearest whole number, the minimum sample size required is 5117. Hence, the best choice is C.