Question

Center Chevrolet had been working to improve employee relations in the company. Employees from three departments were asked if they were satisfied with the working conditions of the company. Are the employees satisfied with the company? The results are shown in the following table. Do all hypotheses steps and number them neatly! The OBT is .478

	Finance	Sales	Mechanic
Satisfied	12	8	9
Dissatisfied	10	4	6

Answer 1

Solution:

Here, we have to use chi square test for independence of two categorical variables.

Step 1

Null hypothesis: H₀: Two categorical variables satisfaction and department are independent.

Alternative hypothesis: H_a: Two categorical variables satisfaction and department are dependent.

Step 2

We assume the level of significance = α = 0.05

Step 3

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

E = row total * column total / Grand total

Calculation tables for test statistic are given as below:

Observed Frequencies
	Department
Satisfied?	Finance	Sales	Mechanic	Total
Satisfied	12	8	9	29
Dissatisfied	10	4	6	20
Total	22	12	15	49

Expected Frequencies
	Department
Satisfied?	Finance	Sales	Mechanic	Total
Satisfied	13.02041	7.102041	8.877551	29
Dissatisfied	8.979592	4.897959	6.122449	20
Total	22	12	15	49

Calculations
(O - E)
-1.02041	0.897959	0.122449
1.020408	-0.89796	-0.12245

(O - E)^2/E
0.079969	0.113535	0.001689
0.115955	0.164626	0.002449

Test Statistic = Chi square = ∑[(O – E)^2/E] = 0.478224

χ² statistic = 0.478

Step 4

We are given

Number of rows = r = 2

Number of columns = c = 3

Degrees of freedom = df = (r – 1)*(c – 1) = 1*2 = 2

α = 0.05

Critical value = 5.991465

(by using Chi square table or excel)

Step 5

P-value = 0.787327

(By using Chi square table or excel)

Step 6

Decision:

P-value > α = 0.05

So, we do not reject the null hypothesis

Step 7

Conclusion:

There is sufficient evidence to conclude that two categorical variables satisfaction and department are independent.

We conclude that satisfaction of the employee does not depend on department.