Candidate A is facing two opposing candidates in a mayoral election. In a recent poll of 300 residents, she has garnered 51% support. Construct a 95% confidence interval on the population proportion for the support of candidate A in the following election.
A) [0.4534, 0.5666]
B) [0.4625, 0.5575]
C) [0.5084, 0.5116]
D) [0.5086, 0.5114]

Question

Quizplus · Accepted Answer

The 95% confidence interval for a population proportion is calculated using the formula: $$CI = \hat{p} \pm Z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$, where $\hat{p}$ is the sample proportion (0.51), $Z_{\alpha/2}$ is the Z-score for a 95% confidence level (approximately 1.96), and $n$ is the sample size (300). Plugging these values into the formula gives the confidence interval $[0.4534, 0.5666]$.

Candidate a Is Facing Two Opposing Candidates in a Mayoral