There are 2,000 eligible voters in a precinct. 500 of the voters are randomly selected and asked whether they planned 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 sample proportion is 350/500 = 0.7. Using a 0.99 confidence level, the z-score is approximately 2.576. The standard error is sqrt[(0.7)(0.3)/500]. The confidence interval is 0.7 ± 2.576 * standard error, which gives limits approximately 0.647 and 0.753.

There Are 2,000 Eligible Voters in a Precinct