There are 2,000 eligible voters in a precinct. A total of 500 voters are randomly selected and asked whether they plan to vote for the Democratic incumbent or the Republican challenger. Of the 500 surveyed,350 said they would vote for the Democratic incumbent. Using the 0.99 confidence coefficient,what are the confidence limits for the proportion that plan to vote for the Democratic incumbent?
A)0.647 and 0.753
B)0.612 and 0.712
C)0.397 and 0.797
D)0.826 and 0.926

Question

Quizplus · Accepted Answer

The proportion of sampled voters planning to vote for the Democratic incumbent is 350/500 = 0.7. Using the 0.99 confidence coefficient (Z-score approximately 2.576 for 99% confidence) and the formula for the confidence interval of a proportion: $p \pm Z \sqrt{\frac{p(1-p)}{n}}$, where $p = 0.7$ and $n = 500$, we calculate the confidence limits. Plugging in the values: $0.7 \pm 2.576 \sqrt{\frac{0.7(0.3)}{500}}$, we get the confidence interval approximately between 0.647 and 0.753.

There Are 2,000 Eligible Voters in a Precinct