Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places.
-$95 \% \text { confidence; } n = 2015 , x = 1631$
A) 0.0231
B) 0.0192
C) 0.0145
D) 0.0171

Question

Quizplus · Accepted Answer

The margin of error E is calculated using the formula $ E = Z \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} $, where $\hat{p} = \frac{x}{n} = \frac{1631}{2015} \approx 0.8097$ and $Z$ is the Z-score for a 95% confidence level, which is approximately 1.96. Plugging in the values, $ E \approx 1.96 \times \sqrt{\frac{0.8097 \times 0.1903}{2015}} \approx 0.0171$.

Assume That a Sample Is Used to Estimate a Population 95% confidence; n=2015,x=163195 \% \text { confidence; } n = 2015 , x = 163195% confidence; n=2015,x=1631

Assume That a Sample Is Used to Estimate a Population $95 \% \text { confidence; } n = 2015 , x = 1631$