Chapter 11, Problem 2CRE

To determine

To explain: The invalidness of the result.

Explanation of Solution

Given information:

The observed number of counts in four tries is as follows

	Correct answers
	$0$	$1$	$2$	$3$	$4$
Knowledgeable teacher	$5$	$1$	$6$	$3$	$9$
Ignorant teacher	$20$	$0$	$3$	$0$	$1$

  $\begin{array}{l}{\chi }^2=20.24\\ P<0.05\end{array}$

Concept used:

For chi square test to be used, in each cell the expected count should be more than or equal to $5$ .

Formula used:

Expected count = $\frac{\text{row total }\times \text{ column total}}{\text{total of all rown or columns}}$

Calculation:

The expected count will be

	Correct answers
	$0$	$1$	$2$	$3$	$4$	Total
Knowledgeable teacher	$\frac{24\times 25}{48}=12.5$	$\frac{24\times 1}{48}=0.5$	$\frac{24\times 9}{48}=4.5$	$\frac{24\times 3}{48}=1.5$	$\frac{24\times 10}{48}=5$	$24$
Ignorant teacher	$\frac{24\times 25}{48}=12.5$	$\frac{24\times 1}{48}=0.5$	$\frac{24\times 9}{48}=4.5$	$\frac{24\times 3}{48}=1.5$	$\frac{24\times 10}{48}=5$	$24$
Total	$25$	$1$	$9$	$3$	$10$	$48$

Using the concept aforementioned, there are $6$ cells which have expected count less than $5$ .

Hence, the result isn’t valid because chi square can’t be used.