Your state is considering raising the legal age for consumption of alcoholic beverages to 21 years old.How large a sample size must be taken to make an estimate of the true proportion of citizens who favor this move.The error should be no more than 0.01 with 99% confidence.
A) 167
B) 16641
C) 6450
D) 65
E) 1670

Question

Quizplus · Accepted Answer

To estimate the sample size needed for a proportion with a specified margin of error and confidence level, the formula is $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$, where $Z$ is the Z-score corresponding to the confidence level, $p$ is the estimated proportion (0.5 if unknown, to maximize sample size), and $E$ is the margin of error. For a 99% confidence level, $Z \approx 2.576$, $p = 0.5$ (assuming maximum variability), and $E = 0.01$. Plugging these values in gives $n = \frac{(2.576)^2 \cdot 0.5 \cdot (1-0.5)}{(0.01)^2} \approx 16640.64$, which rounds up to 16641.

Your State Is Considering Raising the Legal Age for Consumption