Candidate A is facing two opposing candidates in a mayoral election. In a recent poll of 300 residents, 153 supported her. Construct a 90% 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) [0.5086, 0.5114]
D) [0.5090, 0.5110]

Question

Quizplus · Accepted Answer

To construct a confidence interval, we need to use the formula:
sample proportion +/- z-score*(standard error)
Where z-score is based on the desired level of confidence (90%), which gives us a z-score of 1.645. The standard error can be calculated as:
sqrt((sample proportion*(1-sample proportion))/sample size)
Plugging in the values, we get:
0.51 +/- 1.645*sqrt((0.51*0.49)/300)
Simplifying, we get:
0.51 +/- 0.03
Which gives us the interval of [0.48, 0.54]. Among the answer choices, only choice B matches this interval.

Candidate a Is Facing Two Opposing Candidates in a Mayoral