Question

There are 2,000 eligible voters in a precinct. 548 of the voters are randomly selected and asked whether they planned to vote for the democratic incumbent or the republican challenger. of the 548 surveyed, 474 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?

Answer 1

Sample size, n = 548
Point estimate, p = 474/548 = 0.865 or 86.5%
Z at 0.99 confidence coefficient = 2.58

Confidence limits = p +/- Z*Sqrt [p(1-p)/n] = 0.865 +/- 2.58 Sqrt [0.865(1-0865)/548] = 0.865 +/- 0.0378 = (0.8272,0.9028) or (82.72%,90.28)