A human resources manager at a large company wants to estimate the proportion of employees that would be interested in reimbursement for college courses. If she wishes
To be 95% confident that her estimate is within 5% of the true proportion, how many
Employees would need to be sampled?
A) 271
B) 385
C) 543
D) 646
E) 1234

Question

Quizplus · Accepted Answer

To achieve a 95% confidence level with a 5% margin of error when the population proportion is unknown, the formula to calculate the sample size is $n = \frac{Z^2 \times p(1-p)}{E^2}$, where $Z$ is the Z-score corresponding to the confidence level (1.96 for 95%), $p$ is the estimated proportion (0.5 is used when the proportion is unknown for maximum sample size), and $E$ is the margin of error (0.05 for 5%). Substituting these values gives $n = \frac{(1.96)^2 \times 0.5(1-0.5)}{(0.05)^2} = 384.16$. Rounding up to the nearest whole number gives 385.

A Human Resources Manager at a Large Company Wants to Estimate