Chapter 11, Problem R11.2RE

To determine

To explain why chi-square test is not appropriate for this setting.

Answer to Problem R11.2RE

The condition of large counts is not satisfied so, could not use Chi-square test.

Explanation of Solution

Given:

		Count of correct answers
		Zero	one	Two	Three	Four
Knowledge of teacher	Knowledgeable	5	1	6	3	9
	Ignorant	25	0	3	0	1

  ${\chi }^2=20.4,P<0.05$

The expected values are:

		Zero	one	Two	Three	Four	Total
Knowledgeable	Observed	5	1	6	3	9	24
	Expected	13.58	0.45	4.08	1.36	4.53	24.00
Ignorant	Observed	25	0	3	0	1	29
	Expected	16.42	0.55	4.92	1.64	5.47	29.00
Total	Observed	30	1	9	3	10	53
	Expected	30.00	1.00	9.00	3.00	10.00	53.00

The expected values of some categories less than 5. Therefore, the condition of large counts is not satisfied. Hence, could not use Chi-square test.