Candidate A is facing two opposing candidates in a mayoral election. In a recent poll of 300 residents, 98 supported candidate B and 58 supported candidate C. Construct a 99% confidence interval on the population proportion for the support of candidate A in the following election.
A) [0.4057, 0.5543]
B) [0.4130, 0.5470]
C) [0.4779, 0.4821]
D) [0.4781, 0.4819]

Question

Quizplus · Accepted Answer

To find the confidence interval for the support of candidate A, we first calculate the proportion of support for A based on the poll. Since 98 people supported B and 58 supported C out of 300, the remaining people must support A, which is 300 - 98 - 58 = 144. The sample proportion for A is 144/300 = 0.48. To construct a 99% confidence interval, we use the formula for the confidence interval of a proportion: p ± z*sqrt[(p(1-p))/n], where p is the sample proportion, z is the z-score corresponding to the confidence level (for 99%, z ≈ 2.576), and n is the sample size. Plugging in the values: 0.48 ± 2.576*sqrt[(0.48*0.52)/300], we get the interval [0.4057, 0.5543].

Candidate a Is Facing Two Opposing Candidates in a Mayoral