A survey estimates the unemployment rate by computing: $\text{Rate} = \frac{\text{Number Unemployed}}{\text{Labor Force}} = \frac{5,200}{65,000} = 0.08$

From survey data:

• Number unemployed: $\hat{U} = 5,200$ (SE = 180)
• Labor force: $\hat{L} = 65,000$ (SE = 600)

Using the delta method (Taylor series) to estimate SE(unemployment rate): $SE(\hat{p}) \approx \sqrt{\left(\frac{\partial f}{\partial U}\right)^2 SE(U)^2 + \left(\frac{\partial f}{\partial L}\right)^2 SE(L)^2}$ where $f(U, L) = U / L$.

The approximate standard error of the unemployment rate is: