Use the given degree of confidence and sample data to construct a confidence interval for the population proportion $p$.
$n = 130 , x = 69 ; 90 \%$ confidence
A) $0.458

Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion $p$.
$n = 130 , x = 69 ; 90 \%$ confidence
A) $0.458 < p < 0.604$
B) $0.461 < p < 0.601$
C) $0.459 < p < 0.603$
D) $0.463 < p < 0.599$

Quizplus · Accepted Answer

The sample proportion $\hat{p} = \frac{x}{n} = \frac{69}{130} = 0.5308$. Using the formula for the confidence interval for a population proportion $\hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$ with a 90% confidence level (Z ≈ 1.645), the interval is approximately $0.459 < p < 0.603$.

Use the Given Degree of Confidence and Sample Data to Construct