Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p
-Margin of error: $0.025$; confidence level: $96 \% ; \hat { \mathrm { p } }$ and $\hat { \mathrm { q } }$ are unknown
A) 1680
B) 21
C) 43
D) 1681

Question

Quizplus · Accepted Answer

The margin of error formula for a population proportion is $ E = Z \sqrt{\frac{\hat{p}\hat{q}}{n}} $. Given the margin of error and confidence level, we can find the critical value $ Z $ for 96% confidence, which is approximately 2.05. Solving for $ n $ using the formula $ n = \frac{Z^2 \cdot 0.25}{E^2} $ (assuming maximum variability with $\hat{p} = 0.5$), we find $ n \approx 1681 $.

Use the Given Degree of Confidence and Sample Data to Construct