Question

You are interested in the relationship, if any, between reward and gender on the productivity of your employees. To test your suspicion that the variables are independent, you divide 100 employees into two groups of 50 males and 50 females. After each member of either group is rewarded, you record their change in productivity with the following results:

Productivity                            

Decreases                      No Change                       Increases

Males	30	15	5
Females	20	15	15

1. What is the critical value at the .05 level of significance?

2. What is the test statistic?

3. At an .05 level of significance, does the data indicate that the variables are dependent or independent?

Answer 1

The Expected value data are in the table below. Each Cell = Row total * Column Total/N. N = 100

Observed
	Decreases	No Change	Increases	Total
Male	30	15	5	50
Female	20	15	15	50
Total	50	30	20	100
Expected
	Decreases	No Change	Increases	Total
Male	25.0000	15.0000	10.0000	50
Female	25.0000	15.0000	10.0000	50
Total	50	30	20	100

The degrees of freedom, df = (r – 1) * (c -1) = (2 - 1) * (3 - 1) = 2

The Hypothesis:

H0: There is no relation between Gender and their Productivity after getting a reward.

Ha: There is a relation between Gender and their Productivity after getting a reward.

________________________________________

(a) The Critical Value:   The critical value at = 0.05,df = 2

critical = 5.992

(b) The Test Statistic: The table below gives the calculation of .

Number	Observed	Expected	(O-E)	(O-E)2	(O-E)2/E
1	30	25.000	5.000	25.000	1.000
2	20	25.000	-5.000	25.000	1.000
3	15	15.000	0.000	0.000	0.000
4	15	15.000	0.000	0.000	0.000
5	5	10.000	-5.000	25.000	2.500
6	15	10.000	5.000	25.000	2.500
			Total		7.0

test = 7.0

(c) The Decision:    Since test (7) is >critical (5.992), We Reject H0.

The Conclusion: There is sufficient evidence at the 95% significance level to conclude that there is a relation between Gender and their Productivity after getting a reward i.e the variables are dependent.

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