The U.S. Department of Labor wants to estimate the percentage of females in the labor force to within ±5% with 90% confidence. As a planning value they use 46%, the
Reported percentage of females in the labor force of EU (European Union) countries.
How many employment records should be sampled?
A) 121
B) 269
C) 451
D) 382
E) 1000

Question

Quizplus · Accepted Answer

To estimate the sample size needed for a proportion with a specific margin of error and confidence level, the formula is: $n = \frac{Z^2 \times p(1-p)}{E^2}$, where $Z$ is the Z-score corresponding to the confidence level (for 90% confidence, $Z = 1.645$), $p$ is the estimated proportion (0.46 in this case), and $E$ is the margin of error (0.05 for ±5%). Plugging in the values: $n = \frac{1.645^2 \times 0.46 \times (1-0.46)}{0.05^2} \approx 269$. Therefore, 269 employment records should be sampled.

The US Department of Labor Wants to Estimate the Percentage of of Females