A population proportion is to be estimated from the sample described. Approximate the 95% confidence interval. Round your answer to four decimal places, if necessary.
-A poll of 1300 voters in one district showed that $55 \%$ of them would favor stricter gun control laws. Find the $95 \%$ confidence interval for the population proportion favoring stricter gun control laws.
A) $0.5223

Question

A population proportion is to be estimated from the sample described. Approximate the 95% confidence interval. Round your answer to four decimal places, if necessary.
-A poll of 1300 voters in one district showed that $55 \%$ of them would favor stricter gun control laws. Find the $95 \%$ confidence interval for the population proportion favoring stricter gun control laws.
A) $0.5223 < \mathrm { p } < 0.5777$
B) $0.5224 < \mathrm { p } < 0.5776$
C) $0.5492 < \mathrm { p } < 0.5508$
D) $0.5305 < \mathrm { p } < 0.5695$

Quizplus · Accepted Answer

The sample proportion is 0.55. The standard error is calculated as $\sqrt{\frac{0.55 \times (1-0.55)}{1300}}$. Using a Z-score of 1.96 for a 95% confidence interval, the margin of error is $1.96 \times \text{standard error}$. Adding and subtracting this margin from the sample proportion gives the interval $0.5224 < p < 0.5776$.

A Population Proportion Is to Be Estimated from the Sample 55%55 \%55%

A Population Proportion Is to Be Estimated from the Sample $55 \%$