Question

The manager of a telemarketing call centre wishes to determine whether an association exists between the communicating time of its employees and the level of stress-related problems observed on the job. A study of 100 employees reveals the following:

	stress	stress	stress
Commuting time	(High)	(Moderate)	(low)
20 mins and under	15	12	33
over 20 mins	25	8	7

At the 5% level of significance, is there evidence of a significant relationship between commuting time and stress?

Answer 1

We are provided with data on commuting time and the level of stress. We are to determine if there is a relation between the two. For this, we can perform a Chi-square test.

The given data is:

Commuting time	Stress (High)	Stress (Moderate)	Stress (low)
20 mins and under	15	12	33
over 20 mins	25	8	7

First, we compute the total for each row and each column. Doing so, we get:

Commuting time	Stress (High)	Stress (Moderate)	Stress (low)	TOTAL
20 mins and under	15	12	33	60
over 20 mins	25	8	7	40
TOTAL	40	20	40	100

Next, we determine the expected values for each cell. This is done multiplying the row total and column total for that cell and then dividing the product by the grand total.

Doing so, we get:

Commuting time	Stress (High)	Stress (Moderate)	Stress (low)	TOTAL
20 mins and under	24	12	24	60
over 20 mins	16	8	16	40
TOTAL	40	20	40	100

Now, we compute:

Doing so, we get:

Commuting time	Stress (High)	Stress (Moderate)	Stress (low)
20 mins and under	3.375	0	3.375
over 20 mins	5.0625	0	5.0625

The chi-square statistic is computed using the formula:

Substituting the values in the formula, we get:

The number of rows = n1 = 2. The number of columns = n2 = 3.

Hence, the degrees of freedom becomes: (n1 - 1) + (n2 - 1) = (2 - 1) + (3 - 1) = 1 + 2 = 3.

We set the significance level at 5%. Using the Chi-square table, the critical value is 7.815.

Thus, the chi-square statistic is greater than 7.815. Hence, we can reject the null hypothesis.

Therefore, the alternate hypothesis can be accepted and we conclude that there is a significant relationship between commuting time and stress.