Question

A business owner had been working to improve employee relations in his company. Employees from three departments were asked if they were satisfied with the working conditions of the company. Test the hypothesis that satisfaction and department are independent at the 5% level of significance.
Finance Sales Human Resources Total
Satisfied 12 38 13 63
Dissatisfied 7 19 4 30
Total 19 57 17 93
a. (3 pts.) State the NULL and ALTERNATE HYPOTHESES
b. (6 pts.) Calculate the sample test statistic, Chi Square Χ2
c. (3 pts.) Using the appropriate degrees of freedom determine p-value and your conclusion regarding H0.
d. (3 pts.) Interpret the test result in the context of the application.

Answer 1

a)

Hypotheses are:

H0: Satisfaction and department are independent.

Ha: Satisfaction and department are not independent.

(b)

Expected frequencies will be calculated as follows:

Following table shows the expected frequencies:

	Finance	Sales	Human Resources	Total
Satisfied	12.871	38.613	11.516	63
Dissatisfied	6.129	18.387	5.484	30
Total	19	57	17	93

Following table shows the calculations for chi square test statistics:

O	E	(O-E)^2/E
12	12.871	0.058941885
7	6.129	0.12377892
38	38.613	0.009731671
19	18.387	0.020436667
13	11.516	0.191234456
4	5.484	0.40157841
Total		0.805702009

Following is the test statistics:

c)

Degree of freedom: df =( number of rows -1)*(number of columns-1) = (2-1)*(3-1)=2

The p-value is: 0.6683

Conclusion: Since p-value is not less than 0.05 so we fail to reject the null hypothesis.

Excel function used for p-value: "=CHIDIST(0.806,2)"

d)

That is we can conclude that satisfaction and department are independent.