Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p .
n=56, x=30 ; 95% confidence
A) 0.405

Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion  p .
 n=56, x=30 ; 95%  confidence
A)  0.405<p<0.667
 
B)  0.425<p<0.647

C)  0.426<p<0.646

D)  0.404<p<0.668

Quizplus · Accepted Answer

To construct a 95% confidence interval for the population proportion $p$, we first calculate the sample proportion $\hat{p} = \frac{x}{n} = \frac{30}{56}$. Then, we use the formula for the confidence interval: $\hat{p} \pm Z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$, where $Z_{\alpha/2}$ is the Z-score for a 95% confidence level, which is approximately 1.96. Plugging in the values, we get the interval $0.405 < p < 0.667$.

Use the Given Degree of Confidence and Sample Data to Construct