Question

A large corporation was interested in determining whether an association exists between commuting time of their employees and the level of stress-related problems observed on the job. A study of 116 assembly-line workers revealed the following:

Commuting Time		Stress
		High	Moderate	Low
	Under 15 min.	15	6	21
	15 min. to 45 min.	9	9	32
	Over 45 min.	21	7	5

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

1. H0:____________________________      HA: __________________________

2. Find the Chi Square c2 test:

3. Conclusion:

Answer 1

a)

The null and alternate hypothesis are:

H0: There is no association between the two variables.

Ha: There is association between the two variables.

b)

Observed frequencies (Oi):

	High	Mod	Low	TOTAL
Under 15	15	6	21	42
15 to 45	9	9	32	50
Over 45	21	7	5	33
TOTAL	45	22	58	125

Now, Expected frequency = [(Row total) x (Column total)] / Table total

Expected frequencies (Ei):

	High	Mod	Low	TOTAL
Under 15		7.392	19.488	42
15 to 45	18	8.8	23.2	50
Over 45	11.88	5.808	15.312	33
TOTAL	45	22	58	125

Test statistic value =

c)

The critical value is given by:

Since the test statistic value is greater than the critical value, so we have sufficient evidence to reject null hypothesis H0. Thus, we can say that there is association between the two variables.