Provide an appropriate response.
-Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded 2250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a $95 \%$ confidence interval.
A) $0.5625 \pm 0.0154$
B) $0.5625 \pm 0.4823$
C) $0.4375 \pm 0.0154$
D) $0.4375 \pm 0.4823$

Question

Quizplus · Accepted Answer

The proportion of the sample in favor of gun control legislation is $2250 / 4000 = 0.5625$. Using the formula for a $95\%$ confidence interval for a proportion, $p \pm z \sqrt{\frac{p(1-p)}{n}}$, where $p = 0.5625$, $n = 4000$, and $z$ is approximately $1.96$ for $95\%$ confidence, the margin of error is approximately $0.0154$. Therefore, the correct confidence interval is $0.5625 \pm 0.0154$.

Provide an Appropriate Response 95%95 \%95% Confidence Interval 0.5625±0.01540.5625 \pm 0.01540.5625±0.0154 B) 0.5625±0.48230.5625 \pm 0.48230.5625±0.4823

Provide an Appropriate Response $95 \%$ Confidence Interval $0.5625 \pm 0.0154$ B) $0.5625 \pm 0.4823$