Question

A study regarding the relationship between age and the amount of pressure sales personnel feel in relation to their jobs revealed the following sample information. At the 0.02 significance level, is there a relationship between job pressure and age?

	Degree of Job Pressure
Age (years)	Low	Medium	High
Less than 25	92	85	56
25 up to 40	86	63	40
40 up to 60	73	46	21
60 and older	47	18	29

State the decision rule. Use 0.02 significance level. (Round your answer to 3 decimal places.)

H₀: Age and pressure are not related.

H₁: Age and pressure are related.

Compute the value of chi-square. (Round your answer to 3 decimal places.)

What is your decision regarding H₀?

Answer 1

(a)

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

= (4 - 1) X (3 - 1)

= 6

= 0.02

From Table, critical value of = 15.033

Decision Rule:
Reject null hypothesis if > 15.033

(b)

Observed Frequencies:

	Low	Medium	High	Total
Less than 25	92	85	56	233
25 up to 40	86	63	40	189
40 up to 60	73	46	21	140
60 and older	47	18	29	94
Total	298	212	146	656

Expected Frequencies are calculated as follows:

	Low	Medium	High	Total
Less than 25	105.8445	75.2988	51.8567	233
25 up to 40	85.8567	61.0793	42.0640	189
40 up to 60	63.5976	45.2439	31.1585	140
60 and older	42.7012	30.3780	20.9207	94
Total	298	212	146	656

Test Statistic is got as follows:

Observed (O)	Expected (E)	(O - E)2/E
92	105.8445	1.811
85	75.2988	1.250
56	51.8567	0.331
86	85.8567	0.000
63	61.0793	0.060
40	42.0640	0.101
73	63.5976	1.390
46	45.2439	0.013
21	31.1585	3.312
47	42.7012	0.433
18	30.3780	5.044
29	20.9207	3.120
Total = =		16.865

So,

The value of chi-square = 16.865

(c)

Since calculated value of = 16.865 is greater than critical value of = 15.033, the difference is significant. Reject null hypothesis.

So,

Decision regarding H₀ :

Reject null hypothesis.