Question

Answer questions 21 – 23 based on the following. Among 1,000 managers with degrees in business administration, the following data have been accumulated as to their fields of concentration:

	Position in Management	Position
major	Top management	Middle Management
Management	300	200
Marketing	200	0
Accounting	100	200

Test, using α = 0.01, to determine if their position in management is independent of their major.

21. What is your test statistic? a. -0.11 b. 25,600 c. 222.22 d. 14.91

22. Compute the critical value. a. 0.02 b. 0.00 c. 4.61 d. 9.21 e. 16.81

23. What is your conclusion? a. Reject the null at the 1% level b. Fail to reject the null at the 1% level c. Reject the null at the 0.5% level d. Fail to reject the null at the 0.5% level

Answer 1

The observed and expected value table is as below

Observed
	Moderate	Heavy	Total
High School	300	200	500
College	200	0	200
Graduate	100	200	300
Total	600	400	1000
Expected
	Moderate	Heavy	Total
High School	300.00	200.00	500
College	120.00	80.00	200
Graduate	180.00	120.00	300
Total	600.00	400.00	1000

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(21) The Test Statistic:

Number	Observed	Expected	(O-E)	(O-E)2	(O-E)2/E
A	300	300.00	0.00	0	0
B	200	120.00	80.00	6400	53.33333
C	100	180.00	-80.00	6400	35.55556
D	200	200.00	0.00	0	0
E	0	80.00	-80.00	6400	80
F	200	120.00	80.00	6400	53.33333
Total					222.22

Option c: 222.22

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(22) The critical value at = 0.01, df = (r - 1) * (c - 1) = (2 - 1) * (3 - 1) = 2 is Option d: 9.21

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(23) Since test is > critical, We Option a: Reject the null at the 1% level

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