Guided Example #4 - Chi-Square Test

Employers particularly want to know which days of the week employees are absent in a ﬁve day work week. Most employers would like to believe that employees are absent equally during the week. That is, the average number of times an employee is absent is the same on Monday, Tuesday, Wednesday, Thursday, or Friday. Suppose a sample of 20 absent days was taken and the days absent were distributed as follows:

	Monday	Tuesday	Wednesday	Thursday	Friday
Number of Absences	5	4	2	3	6

What is the value for $x^{2}$ test statistics?

A. $2.5$ B. $0$ C. $2$ D. $1.5$

Step 1

If the absent days occur with equal frequencies, then, out of 20 absent days, there would be 4 absences on Monday, 4 on Tuesday, 4 on Wednesday, 4 on Thursday, and 4 on Friday. These numbers are the expected (E) values. The values in the table are the observed (O) values or data.

Step 2

This time, calculate the χ2 test statistic by hand. Make a chart with the following headings:

Expected $(E)$ values
Observed $(O)$ values
$(O - E)$
${(0 - E)}^{2}$

Now add (sum) the last column. The sum is 10. Now divide this (10) sum by E (4). This is the $x^{2}$ test statistic.

O	E	O - E	(O-E)²
5	4	1	1
4	4	0	0
3	4	-2	4
2	4	-1	1
6	4	-2	4
			$\sum_{O - E}^{2} = 10$

All Steps

This time, calculate the χ2 test statistic by hand. Make a chart with the following headings:

Expected $(E)$ values
Observed $(O)$ values
$(O - E)$
${(0 - E)}^{2}$

Now add (sum) the last column. The sum is 10. Now divide this (10) sum by E (4). This is the $x^{2}$ test statistic.

O	E	O - E	(O-E)²
5	4	1	1
4	4	0	0
3	4	-2	4
2	4	-1	1
6	4	-2	4
			$\sum_{O - E}^{2} = 10$