An exit poll is conducted to estimate the proportion of voters who chose candidate A over candidate B.Out of 40 people surveyed, 12 indicated that they had voted for candidate A.What is a 95% confidence interval for the proportion of voters who chose candidate A?
A) (0.158, 0.442)
B) (0.181, 0.419)
C) (0.132, 0.469)
D) (0.154, 0.446)

Question

Quizplus · Accepted Answer

The proportion of voters who chose candidate A is $ p = \frac{12}{40} = 0.3 $. The standard error (SE) for a proportion is calculated using the formula $ SE = \sqrt{\frac{p(1-p)}{n}} $, where $ p $ is the sample proportion and $ n $ is the sample size. Here, $ SE = \sqrt{\frac{0.3(1-0.3)}{40}} = 0.0725 $. For a 95% confidence interval, we use a Z-score of approximately 1.96 for the normal distribution. The margin of error (ME) is $ ME = Z \times SE = 1.96 \times 0.0725 \approx 0.142 $. The confidence interval is $ p \pm ME = 0.3 \pm 0.142 = (0.158, 0.442) $.

An Exit Poll Is Conducted to Estimate the Proportion of Voters