A recent poll of 120 adults who frequent the local farmer's market found that 54 have purchased reusable cloth bags for their groceries.Based on these data, what is the margin of error for a 95% confidence interval of the proportion of adults who have purchased reusable cloth bags?
A)0.0454
B)0.0117
C)0.089
D)0.075
E)0.0432

Question

Quizplus · Accepted Answer

The margin of error for a 95% confidence interval can be calculated using the formula for the margin of error of a proportion: $ME = Z * \sqrt{\frac{p(1-p)}{n}}$, where $Z$ is the Z-score for the confidence level (approximately 1.96 for 95%), $p$ is the sample proportion, and $n$ is the sample size. Here, $p = \frac{54}{120} = 0.45$ and $n = 120$. Plugging these values into the formula gives $ME = 1.96 * \sqrt{\frac{0.45(1-0.45)}{120}} \approx 0.089$.

A Recent Poll of 120 Adults Who Frequent the Local