The CEO of a company wants to estimate the percent of employees that use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. What is the estimate of the standard error of the proportion proportion $\sigma _ { \bar { p } }$ ?
A)0.039
B)0.050
C)0.350
D)0.455

Question

Quizplus · Accepted Answer

The standard error of the proportion is calculated using the formula $\sigma_{\bar{p}} = \sqrt{\frac{p(1-p)}{n}}$, where $p$ is the sample proportion and $n$ is the sample size. Here, $p = \frac{53}{150}$ and $n = 150$. Plugging these values into the formula gives $\sigma_{\bar{p}} = \sqrt{\frac{\frac{53}{150}(1-\frac{53}{150})}{150}} \approx 0.039$.

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The CEO of a Company Wants to Estimate the Percent $\sigma _ { \bar { p } }$