A city planner wants to construct a confidence interval for the proportion of workers who would take public transportation to work if it were available. What sample size should he use to estimate the proportion to within 4 percentage points at a 90% level of confidence?
A) 30
B) 423
C) 218
D) 842
E) 601

Question

Quizplus · Accepted Answer

The sample size for estimating a proportion with a specific margin of error (E) at a certain confidence level (Z) can be calculated using the formula: $n = \left(\frac{Z^2 \cdot p \cdot (1-p)}{E^2}\right)$, where $p$ is the estimated proportion (if unknown, 0.5 is used for maximum sample size), and $E$ is the margin of error in decimal form. For a 90% confidence level, $Z$ value is approximately 1.645. Assuming $p = 0.5$ for maximum variability, and $E = 0.04$ (4%), the calculation is $n = \left(\frac{1.645^2 \cdot 0.5 \cdot (1-0.5)}{0.04^2}\right)$, which is approximately 423. Thus, the correct sample size to meet the criteria is 423.

A City Planner Wants to Construct a Confidence Interval for the Proportion