A private opinion poll is conducted for a politician to determine what proportion of the population favorsadding more national parks. How large a sample is needed in order to be 90% confident that the sampleproportion will not differ from the true proportion by more than 5%?
A) 271
B) 164
C) 542
D) 9

Question

Quizplus · Accepted Answer

The sample size needed for a proportion can be calculated using the formula $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$, where $Z$ is the Z-score corresponding to the confidence level (1.645 for 90% confidence), $p$ is the estimated proportion (0.5 is used when the proportion is unknown for maximum sample size), and $E$ is the margin of error (0.05 for 5%). Plugging in the values, $n = \frac{1.645^2 \cdot 0.5 \cdot (1-0.5)}{0.05^2} \approx 271$.

A Private Opinion Poll Is Conducted for a Politician to Determine