Chapter 8.2, Problem 37E

To determine

To find: The standard error of $\widehat{p}$ and interpret it.

Answer to Problem 37E

The standard error is 0.0059.

Explanation of Solution

Given:

Number of trials ( n ) = 4579

Number of events ( x ) = 914

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:

  $\begin{array}{c}\widehat{p}=\frac{x}{n}\\ =\frac{914}{4579}\\ =0.1996\end{array}$

The standard error can be calculated as:

  $\begin{array}{c}S{E}_{\widehat{p}}=\sqrt{\frac{\widehat{p}\left(1-\widehat{p}\right)}{n}}\\ =\sqrt{\frac{0.1996\left(1-0.1996\right)}{4579}}\\ =0.0059\end{array}$