Question

The president of a company asked a random sample of employees how they felt about the work they were doing. The following table gives a breakdown of their responses by gender. Does the data provide enough evidence to conclude that the level of job satisfaction is related to gender? Use alpha = .10

Gender	Very Interesting	Fairly Interesting	Not Interesting
Male	70	41	9
Female	35	34	11

The null hypothesis

1. Would have to be revised
2. No changes
3. Would not be rejected
4. Would be rejected

Answer 1

Solution:

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

Null hypothesis: H₀: The level of job satisfaction is not related to gender.

Alternative hypothesis: H_a: The level of job satisfaction is related to gender.

We are given level of significance = α = 0.10

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

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 = 0.10

Critical value = 4.60517

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Observed Frequencies
	Level of job Satisfaction
Gender	C1	C2	C3	Total
Male	70	41	9	120
Female	35	34	11	80
Total	105	75	20	200

Expected Frequencies
	Level of job Satisfaction
Gender	C1	C2	C3	Total
Male	63	45	12	120
Female	42	30	8	80
Total	105	75	20	200

Calculations
(O - E)
7	-4	-3
-7	4	3

(O - E)^2/E
0.777778	0.355556	0.75
1.166667	0.533333	1.125

Chi square = ∑[(O – E)^2/E] = 4.708333

P-value = 0.094973

(By using Chi square table or excel)

P-value < α = 0.10

So, we reject the null hypothesis

There is sufficient evidence to conclude that the level of job satisfaction is related to gender.

Answer:

The null hypothesis

4. Would be rejected