Chapter 9.2, Problem 37E

a.

To determine

To find: The test statistic.

Answer to Problem 37E

The test statistic is 1.23.

Explanation of Solution

Given:

Population proportion ( p ) = 12%

Number of students ( n ) = 100

Number of left-handed students ( x ) = 16

Formula used:

The formula to compute the test statistic is:

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

Calculation:

The hypotheses are:

  $\begin{array}{l}{H}_0:p=0.12\\ H_a:p\ne 0.12\end{array}$

The sample proportion is:

  $\begin{array}{c}\widehat{p}=\frac{x}{n}\\ =\frac{16}{100}\\ =0.16\end{array}$

The test statistic is calculated as:

  $\begin{array}{c}z=\frac{\widehat{p}-p_0}{\sqrt{\frac{p_0\left(1-p_0\right)}{n}}}\\ =\frac{0.16-0.12}{\sqrt{\frac{0.12\left(1-0.12\right)}{100}}}\\ =1.23\end{array}$

The test statistic is 1.23.

b.

To determine

To find: The p -value and show it in normal curve.

Answer to Problem 37E

The P -value is 0.2186.

Explanation of Solution

Calculation:

The P -value for two tailed test using table is computed as:

  $\begin{array}{c}P-value=2\times P\left(Z>\left|Z\right|\right)\\ =2\times P\left(Z>\left|1.23\right|\right)\\ =2\times 0.1093\\ =0.2186\end{array}$

Thus, the P - value is 0.2186.

Graph:

The figure is constructed as: