A random sample of 1000 people was taken. Seven hundred fifty of the people in the sample favored Candidate A. The 95% confidence interval for the true proportion of people who favor Candidate A is
A) .723 to .777.
B) .727 to .773.
C) .70 to .80.
D) .725 to .775.

Question

Quizplus · Accepted Answer

The 95% confidence interval for the proportion can be calculated using the formula for the confidence interval of a proportion: $p \pm z\sqrt{\frac{p(1-p)}{n}}$, where $p$ is the sample proportion, $z$ is the z-score corresponding to the confidence level (approximately 1.96 for 95%), and $n$ is the sample size. Here, $p = \frac{750}{1000} = 0.75$, $n = 1000$, and using the formula, the interval is approximately 0.723 to 0.777, which matches choice A.

A Random Sample of 1000 People Was Taken