Solve the problem.
-A newspaper article about the results of a poll states: "In theory, the results of such a poll, in 99 cases out of 100 should differ by no more than 6 percentage points in either direction from what would have been obtained by interviewing all voters in the United States." Find the sample size suggested by this statement.
A)268
B)19
C)461
D)378

Question

Quizplus · Accepted Answer

The statement suggests a confidence level of 99% and a margin of error of 6 percentage points. Using the formula for sample size in estimating proportions, $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$, where $Z$ is the Z-score corresponding to the confidence level (2.576 for 99%), $p$ is the estimated proportion (0.5 for maximum variability), and $E$ is the margin of error (0.06). Substituting these values, we get $n = \frac{(2.576)^2 \cdot 0.5 \cdot (1-0.5)}{(0.06)^2} \approx 461$.

Solve the Problem. -A Newspaper Article About the Results of a Poll States