Chapter 9.2, Problem 38E

a.

To determine

To find: The test statistic

Answer to Problem 38E

The test statistic is -2.18.

Explanation of Solution

Given:

Number of trials ( n ) = 150

Population proportion ( p ) = 0.72

Number of success ( p ) = 96

Formula used:

The test statistic is:

  $z=\frac{\widehat{p}-p_0}{\sqrt{\frac{p_0\left(1-p_0\right)}{n}}}$

Calculation:

The test statistic can be calculated as:

  $\begin{array}{c}z=\frac{\widehat{p}-p_0}{\sqrt{\frac{p_0\left(1-p_0\right)}{n}}}\\ =\frac{0.64-0.72}{\sqrt{\frac{0.72\left(1-0.72\right)}{150}}}\\ =-2.18\end{array}$

Hence, the value is -2.18.

b.

To determine

To find: The P -value.

Answer to Problem 38E

The P -value is 0.0101.

Explanation of Solution

Calculation:

The P -value is calculated as:

  $\begin{array}{c}P-value=2\times P\left(Z>|-2.18|\right)\\ =0.0292\end{array}$

The P -value is 0.0292.

Graph:

The figure could be constructed as: