Question

A poll classified respondents by gender and political​ party, as shown in the table. We wonder if there is evidence of an association between gender and party affiliation.​ (Assume a significance level of alpha=0.05​)

D R I

Male 36 45 25

Female 51 38 13

calculate chi-square statistic x²=

Answer 1

Solution:

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

Null hypothesis: H₀: Two categorical variables are independent.

Alternative hypothesis: H_a: Two categorical variables are dependent.

We assume/given level of significance = α = 0.05

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 = 0.05

Critical value = 5.991465

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Observed Frequencies
	Column variable
Row variable	Democratic	Republic	Independent	Total
Male	36	45	25	106
Female	51	38	13	102
Total	87	83	38	208

Expected Frequencies
	Column variable
Row variable	Democratic	Republic	Independent	Total
Male	44.33653846	42.29807692	19.36538462	106
Female	42.66346154	40.70192308	18.63461538	102
Total	87	83	38	208

Calculations
(O - E)
-8.33654	2.701923	5.634615
8.336538	-2.70192	-5.63462

(O - E)^2/E
1.567508	0.172594	1.639466
1.628979	0.179362	1.703759

Test Statistic = Chi square = ∑[(O – E)^2/E] = 6.891667643

χ² = 6.891667643

P-value = 0.03187817

(By using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that there is an association between gender and party affiliation.​