Question

Provide an appropriate response. The contingency table below shows the results of a random sample of 200 registered voters that was conducted to see whether their opinions on a bill are related to their party affiliation. Party Opinion Approve Disapprove No Opinion Republican 42 20 14 Democrat 50 24 18 Independent 10 16 6 2 Find the chi-square test statistic, xó, to test the claim of independence. 9.483 8.030 ö 11.765 7.662

Answer 1

Answer: 8.030

Solution:

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 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 = 3

Number of columns = c = 3

Degrees of freedom = df = (r – 1)*(c – 1) = 2*2 = 4

α = 0.05

Critical value = 9.487729

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Observed Frequencies
	Opinion
Party	Approve	Disapprove	No Opinion	Total
Republican	42	20	14	76
Democrat	50	24	18	92
Independent	10	16	6	32
Total	102	60	38	200

Expected Frequencies
	Opinion
Party	Approve	Disapprove	No Opinion	Total
Republican	38.76	22.8	14.44	76
Democrat	46.92	27.6	17.48	92
Independent	16.32	9.6	6.08	32
Total	102	60	38	200

Calculations
(O - E)
3.24	-2.8	-0.44
3.08	-3.6	0.52
-6.32	6.4	-0.08

(O - E)^2/E
0.270836	0.34386	0.013407
0.202182	0.469565	0.015469
2.447451	4.266667	0.001053

Test Statistic = Chi square = ∑[(O – E)^2/E] = 8.03049

χ² statistic = 8.030

P-value = 0.090468

(By using Chi square table or excel)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that opinions on a bill are related to party affiliation.