A random sample of 150 teachers in an inner-city school district found that 72% of them had volunteered time to a local charitable cause within the past 12 months. What is the standard error of the sample proportion?
A) 0.001
B) 0.016
C) 0.057
D) 0.069
E) 0.037

Question

Quizplus · Accepted Answer

The standard error of the sample proportion is calculated using the formula $\sqrt{\frac{p(1-p)}{n}}$, where $p$ is the sample proportion and $n$ is the sample size. Here, $p = 0.72$ and $n = 150$. Plugging these values into the formula gives $\sqrt{\frac{0.72(1-0.72)}{150}} = \sqrt{\frac{0.72(0.28)}{150}} = \sqrt{\frac{0.2016}{150}} = \sqrt{0.001344} = 0.0366$, which rounds to 0.037.

A Random Sample of 150 Teachers in an Inner-City School