Question

A community newspaper asked the following question and surveyed a random sample of residents. “Do you think it should be legal or illegal for a child to use the Internet to harass another child?” Data were tabulated based on their political view and the response. A chi-square test was conducted to test whether the opinion and the political ideology are related. The chi-square test statistic was calculated to be 7.6645

	Conservative	Moderate	Liberal
Legal	27	22	14
Illegal	119	196	124
Not Sure	19	24	21

a. State the hypotheses:

H₀:

H₁:

b. Find the df:________________and the p-value (four decimal places): __________________________

c. If the test statistic χ² = 7.6645, state your conclusion at 0.05 significance level for the relationship of opinion and political view.

Answer 1

Solution:

Part a

Null hypothesis: H₀: There is no any relationship between the given two categorical variables opinion and the political view.

Alternative hypothesis: H₁: There is a relationship between the given two categorical variables opinion and the political view.

We are 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 = 3

Number of columns = c = 3

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

df = 4

α = 0.05

Critical value = 9.487729

(by using Chi square table or excel)

Part b

We are given

Test Statistic = Chi square = ∑[(O – E)^2/E] = 7.6645

χ² statistic = 7.6645

P-value = 0.1047

(By using Chi square table or excel)

P-value > α = 0.05

So, we do not reject the null hypothesis

Part c

There is not sufficient evidence to conclude that there is a relationship between the given two categorical variables opinion and the political view.