Question

Among 1,000 managers with degrees in business administration, the following data have been accumulated as to their fields of concentration.

Major	Top Management	Middle Management	TOTAL
Management	280	220	500
Marketing	120	80	200
Accounting	150	150	300
TOTAL	550	450	1000

1.Determine if the position in management is independent of field (major) of concentration.

2.State the null and alternative hypotheses for a contingency table test if we want to determine if the position in management is independent of field (major) of concentration.

3.State the decision rule for the critical value approach. Let alpha = 0.01.

4.Calculate the expected frequency for the cell “Marketing” and “Middle Management.”

5.If the Chi Square statistic is 5.253 what is your conclusion?

Answer 1

Ans:

H₀:The position in management is independent of field (major) of concentration.

H_a:The position in management is not independent of field (major) of concentration.

Observed count(fo)
Major	Top Management	Middle Management	TOTAL
Management	280	220	500
Marketing	120	80	200
Accounting	150	150	300
TOTAL	550	450	1000
Expected count(fe)
Major	Top Management	Middle Management	TOTAL
Management	275	225	500
Marketing	110	90	200
Accounting	165	135	300
TOTAL	550	450	1000
Chi square=(fo-fe)^2/fe
Major	Top Management	Middle Management	TOTAL
Management	0.091	0.111	0.202
Marketing	0.909	1.111	2.020
Accounting	1.364	1.667	3.030
TOTAL	2.364	2.889	5.253

Chi square test statistic=5.253

df=(3-1)*(2-1)=2

critical chi square value=CHIINV(0.01,2)=9.210

Decision rule:

Reject H₀,if Chi square test statistic>9.210

As,chi square test statistic=5.253 is less than 9.210,we fail to reject the null hypothesis and we can conclude that the position in management is independent of field (major) of concentration.