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 0.01 significance level, is there a relationship between job pressure and age?

	Degree of Job Pressure
Age (years)	Low	Medium	High
Less than 25	20	18	22
25 up to 40	50	46	44
40 up to 60	58	63	59
60 and older	34	43	43

State the decision rule. Use 0.01 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

Solution-:

Let, A= Degree of Job Pressure and B=Age (Years) Given :

Here, we want to test

Age and pressure are not related.

Vs

Age and pressure are related.

The given frequencies table are observed frequencies

	Degree of Job Pressure
Age (Years)	Low	Medium	High	Total
Less than 25	20	18	22	60
25 up to 40	50	46	44	140
40 up to 60	58	63	59	180
60 and older	34	43	43	120
Total	162	170	168	500

The corresponding expected frequencies are obtained using formula

for i=1,2,3,4 ;j=1,2,3

Note: are not to be rounded-off to the integers.

The given frequencies table are expected frequencies

	Degree of Job Pressure
Age (Years)	Low	Medium	High
Less than 25	19.44	20.4	20.16
25 up to 40	45.36	47.6	47.04
40 up to 60	58.32	61.2	60.48
60 and older	38.88	40.8	40.32

Table for

	Degree of Job Pressure
Age (Years)	Low	Medium	High
Less than 25	20.576	15.882	24.008
25 up to 40	55.115	44.454	41.156
40 up to 60	57.682	64.853	57.556
60 and older	29.733	45.319	45.858

The test statistic is

  

  

Table value :-

( From statistical table or By using MS-Excel Command "=CHIINV(0.01,6)" )

Decision Rule:-

Here hence we accept (Or fail to reject ) at l.o.s.

Conclusion:- We conclude that , Age and pressure are not related.