Question

Research suggests that people who can switch off from work (Detachment) during off-hours are more satisfied with life and have fewer symptoms of psychological strain. Factors at work can affect your ability to detach when away from work. For example, a study looked at 1709 Swiss and German employees measured job stress in terms of time pressure (Time_Pressure) at work (no time pressure, low, medium, high and very high time pressure). Carry out a chi-square test to see if time pressure is associated with the ability to detach from work. Test the researcher’s hypothesis that there is an association between “Detachment” and “Time Pressure” following the four steps of hypothesis testing.

Time pressure	Detachment	Frequency
1	1	84
1	2	94
2	1	89
2	2	94
3	1	147
3	2	175
4	1	206
4	2	267
5	1	199
5	2	354

Answer 1

Step1:

H0: Null Hypothesis: There is no association between Detachment and Time Pressure

HA:Alternative Hypothesis: There is association between Detachment and Time Pressure

Step 2:
Observed Frequencies:

	Detachment =1	Detachment =2	Total
Time Pressure =1	84	94	178
Time Pressure =2	89	94	183
Time Pressure =3	147	175	322
Time Pressure =4	206	267	473
Time Pressure =5	199	354	553
Total	725	984	1703

Expected Frequencies:

	Detachment =1	Detachment =2	Total
Time Pressure =1	725X178/1703=75.51	102.49	178
Time Pressure =2	77.63	105.37	183
Time Pressure =3	136.60	185.40	322
Time Pressure =4	200.66	272.34	473
Time Pressure =5	234.60	318.40	553
Total	725	984	1703

The Test Statistic is calculated as follows:

Observed (O)	Expected (E)	(O - E)2/E
84	75.51	0.95
94	102.49	0.70
89	77.63	1.66
94	105.37	1.23
147	136.60	0.79
175	185.40	0.58
206	200.66	0.14
267	272.34	0.10
199	234.60	5.40
354	318.40	3.98
Total = =		15.55

The Test Statistic = 15.55

Step 3:

ndf = (r - 1) X (c -1)

    = (5 - 1)X (2 - 1) =5

By Technology, p -value = 0.0037

Since p - value = 0.0037 is less than = 0.05, the difference is significant. Reject null hypothesis.

Step 4:

Conclusion:
The data support the claim that there is association between Detachment and Time Pressure