A recent poll of 120 adults who frequent the local farmer's market found that 54 have purchased reusable cloth bags for their groceries.The 95% confidence interval for the proportion of adults who have purchased reusable cloth bags is ________________________ .
A)0.361 to 0.539
B)0.4046 to 0.4954
C)0.4383 to 0.4617
D)0.205 to 0.525
E)0.3856 to 0.4896

Question

Quizplus · Accepted Answer

The 95% confidence interval for a proportion is calculated using the formula: $CI = \hat{p} \pm Z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$, where $\hat{p}$ is the sample proportion, $Z_{\alpha/2}$ is the Z-score for the desired confidence level (1.96 for 95%), and $n$ is the sample size. Here, $\hat{p} = \frac{54}{120} = 0.45$, $n = 120$, and using the formula, the confidence interval is approximately 0.361 to 0.539.

A Recent Poll of 120 Adults Who Frequent the Local