Chapter 11.1, Problem 4E

To determine

To find: The chi-square test statistic

Answer to Problem 4E

The test statistic is 4.0389.

Explanation of Solution

Given:

The table is:

85

99

16

Formula used:

The formula to compute the test statistic is

  ${\chi }^2={\displaystyle \sum {\left(O-E\right)}^2/E}$

Calculation:

Here,

  $\begin{array}{l}{p}_1=\frac{18}{38}=0.4737\\ p_2=\frac{18}{38}=0.4737\\ p_3=\frac{2}{38}=0.0526\end{array}$

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:p_1=p_2=p_3\\ H_a:\text{ At least one of }{p}_i\text{ is different}\end{array}$

The calculation for test statistic is done as:

Observed value	Expected value	$\left(O-E\right)$	${\left(O-E\right)}^2$	${\left(O-E\right)}^2/E$
0.4737	85	-9.7368	94.8061	1.0007
0.4737	99	4.2632	18.1745	0.1918
16	10.5263	5.4737	29.9612	2.8463
				${\displaystyle \sum {\left(O-E\right)}^2/E}=4.0389$

The test statistic is:

  $\begin{array}{c}{\chi }^2={\displaystyle \sum {\left(O-E\right)}^2/E}\\ =4.0389\end{array}$

Thus, the test statistic is 4.0389.