Chapter 9.2, Problem 57E

To determine

To find: The appropriate test statistic.

Answer to Problem 57E

The correct option is (e).

Explanation of Solution

Given:

  $\begin{array}{l}\text{Number of alumni}\left(n\right)=100\\ \text{Number of teens that were in favor of firing the coach}\left(x\right)=64\end{array}$

Formula used:

The formula to compute the test statistic is:

  $\begin{array}{l}z=\frac{\widehat{p}-p_0}{\sqrt{\frac{p_0\left(1-p_0\right)}{n}}}\\ Where,\\ \widehat{p}=\frac{x}{n}\end{array}$

Calculation:

Assume, $p_0$ to be 0.50.

The test statistic can be calculated as:

  $\begin{array}{c}z=\frac{\widehat{p}-p_0}{\sqrt{\frac{p_0\left(1-p_0\right)}{n}}}\\ =\frac{\frac{64}{100}-0.50}{\sqrt{\frac{0.50\left(1-0.50\right)}{100}}}\\ =\frac{0.64-0.50}{\sqrt{\frac{0.50\left(1-0.50\right)}{100}}}\end{array}$

Hence, the correct option is (e).