There are 2,000 eligible voters in a precinct. Despite protests from knowledgeable persons that a sample size of 500 was too large in relation to the total, the 500 selected at random were asked to indicate whether they planned to vote for the Liberal incumbent or the Conservative challenger. Of the 500 surveyed, 350 said they were going to vote for the Liberal incumbent. Using the 0.99 confidence coefficient, what are the confidence limits for the proportion that plan to vote for the Liberal incumbent?
A) 0.060 and 0.700
B) 0.612 and 0.712
C) 0.397 and 0.797
D) 0.826 and 0.926
E) 0.6542 and 0.7458

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] = 0.02049. The margin of error is 2.576 * 0.02049 = 0.052. Thus, the confidence interval is 0.7 ± 0.052, which is approximately 0.6542 to 0.7458.

There Are 2,000 Eligible Voters in a Precinct