Provide an appropriate response.
-A senator wishes to estimate the proportion of United States voters who favor abolishing the Electoral College. How large a sample is needed in order to be $98 \%$ confident that the sample proportion will not differ from the true proportion by more than $5 \%$ ?
A) 543
B) 385
C) 12
D) 1086

Question

Quizplus · Accepted Answer

The sample size needed for estimating a proportion with a specific margin of error (E) at a certain confidence level can be calculated using the formula: $n = \left(\frac{Z^2 \cdot p \cdot (1-p)}{E^2}\right)$, where $Z$ is the Z-score corresponding to the confidence level, $p$ is the estimated proportion (when unknown, $p = 0.5$ is used for maximum sample size), and $E$ is the margin of error. For a $98\%$ confidence level, the Z-score is approximately $2.33$ (from Z-tables). Assuming $p = 0.5$ for maximum variability, and $E = 0.05$ (5%), the calculation is $n = \left(\frac{(2.33)^2 \cdot 0.5 \cdot (1-0.5)}{(0.05)^2}\right)$, which simplifies to approximately $543$.

Provide an Appropriate Response 98%98 \%98% Confident That the Sample Proportion Will Not Differ from the Proportion

Provide an Appropriate Response $98 \%$ Confident That the Sample Proportion Will Not Differ from the Proportion