Chapter 8.2, Problem 38E

To determine

To find: The standard error of $\widehat{p}$

Answer to Problem 38E

The standard error is 0.0239.

Explanation of Solution

Given:

Number of trials ( n ) = 172

Number of events ( x ) = 19

Formula used:

The formula to compute the standard error is:

  $S{E}_{\widehat{p}}=\sqrt{\frac{\widehat{p}\left(1-\widehat{p}\right)}{n}}$

Calculation:

The sample proportion is:

  $\begin{array}{c}\widehat{p}=\frac{x}{n}\\ =\frac{19}{172}\\ =0.1105\end{array}$

The standard error can be calculated as:

  $\begin{array}{c}S{E}_{\widehat{p}}=\sqrt{\frac{\widehat{p}\left(1-\widehat{p}\right)}{n}}\\ =\sqrt{\frac{0.1105\left(1-0.1105\right)}{172}}\\ =0.0239\end{array}$

Thus, the required standard error is 0.0239.