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 correct confidence interval can be calculated using the formula for a confidence interval for a proportion: $$CI = \hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$, where $\hat{p}$ is the sample proportion, $Z$ 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, we get the confidence interval approximately as $0.45 \pm 1.96 \sqrt{\frac{0.45(1-0.45)}{120}}$, which calculates to the interval (0.361, 0.539).

A Recent Poll of 120 Adults Who Frequent the Local