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

Question

Quizplus · Accepted Answer

To find the minimum sample size, we use the formula 
$$n=\frac{z^2\cdot \frac{1}{2}\cdot \frac{1}{2}}{E^2}$$
where 
- $z$ is the z-score corresponding to the confidence level (in this case, $z=2.576$ for a 99% confidence level)
- $E$ is the margin of error
- $\frac{1}{2}$ is used as an estimate for $\hat{p}$ and $\hat{q}$ when they are unknown (which gives the largest possible sample size needed)

Plugging in the given values, we get
$$n=\frac{(2.576)^2\cdot \frac{1}{2}\cdot \frac{1}{2}}{(0.008)^2}\approx25901$$
Therefore, the minimum sample size required is 25,901, which is answer choice B.

Use the Given Data to Find the Minimum Sample Size 0.0080.0080.008

Use the Given Data to Find the Minimum Sample Size $0.008$