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

We want to determine if the position in management is independent of field (major) of concentration.

a.	Compute the test statistic.
b.	Using the p-value approach at 90% confidence, test to determine if management position is independent of major.
c.	Using the critical value approach, test the hypotheses.  Let alpha = 0.10.

Answer 1

( a )

Observed Frequencies

	B1	B2	Total
A1	280	220	500
A2	120	80	200
A3	150	150	300
Total	550	450	1000

Expected Frequencies

	B1	B2	Total
A1	275	225	500
A2	110	90	200
A3	165	135	300
Total	550	450	1000

Compute Chi-square

test statistic = 5.2525

( b )

Compute the degrees of freedom (df).
df=(3-1)⋅(2-1)=2

for 2 df, p(χ2≥5.2525)=0.0723

Since the p-value(0.0723) < 0.10

we reject the null hypothesis H0.

management position is not independent of major

( c )

At alpha = 0.10 ,df = 2

Chi square critical value = 4.605

Chi square cal > chi square c .v

i.e.,  5.2525 >   4.605

we reject the null hypothesis H0.

management position is not independent of major