Question

use the following contingency table

	a	b	c	total
1	15	30	45	90
2	40	45	50	135
total	55	75	95	225

a. compute the expected frequency for each cell

b. compute x^2stat. is it significant at a=0.01

Answer 1

Solution:

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

Null hypothesis: H0: Two variables are independent.

Alternative hypothesis: Ha: Two variables are dependent.

We assume level of significance = α = 0.01

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 = 0.01

Critical value = 9.21034

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Observed Frequencies
	Column variable
Row variable	a	b	c	Total
1	15	30	45	90
2	40	45	50	135
Total	55	75	95	225

(Part a answer)

Expected Frequencies
	Column variable
Row variable	a	b	c	Total
1	22	30	38	90
2	33	45	57	135
Total	55	75	95	225

Calculations
(O - E)
-7	0	7
7	0	-7

(O - E)^2/E
2.227273	0	1.289474
1.484848	0	0.859649

Test Statistic = Chi square = ∑[(O – E)^2/E] = 5.861244

(Part b answer)

χ2 statistic = 5.861244

P-value = 0.053364

(By using Chi square table or excel)

P-value > α = 0.01

So, we do not reject the null hypothesis

This test is not significant at α = 0.01.