Question

Yes	No	Undecided
Employed	30	15	5
Unemployed	20	25	10

Use the table data to answer 9 -12.

Responses to a survey question are broken down according to employment and the sample results are given in the table. At the .10 significance level, test the claim that the response and employment status are independent.

Which of the following is the correct statement for the claim?

Group of answer choices

H1: Response and Employment status are dependent

Ho: Response and Employment status are independent

Ho: Response and Employment status are dependent

H1: Response and Employment status are independent

Question 10

The p-value is:

Group of answer choices

.0156

.0722

.2364

.0513

Question 11

The test statistic is:

37.541

25.963

5.942

12.588

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Question 12

The conclusion for this test is:

Fail to reject Ho which says that there is sufficient evidence to support the claim that response and employment status are dependent

Fail to reject Ho which says there is insufficient evidence to warrant rejection of the claim that response and employment status are independent

Reject Ho which says there is sufficient evidence to warrant rejection of the claim that response and employment status are independent

Reject Ho which says that there is sufficient evidence to supoort the claim that response and employment status are dependent

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: H_a: Two variables are dependent.

We assume/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 = 4.605170186

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Observed Frequencies
	Response
Employment	Yes	No	Undecided	Total
Employed	30	15	5	50
Unemployed	20	25	10	55
Total	50	40	15	105

Expected Frequencies
	Response
Employment	Yes	No	Undecided	Total
Employed	23.80952381	19.047619	7.142857143	50
Unemployed	26.19047619	20.952381	7.857142857	55
Total	50	40	15	105

Calculations
(O - E)
6.190476	-4.04762	-2.14286
-6.19048	4.047619	2.142857

(O - E)^2/E
1.609524	0.860119	0.642857
1.463203	0.781926	0.584416

Test Statistic = Chi square = ∑[(O – E)^2/E] = 5.942045455

χ² statistic = 5.942045455

P-value = 0.051250868

(By using Chi square table or excel)

P-value < α = 0.10

So, we reject the null hypothesis

Reject Ho which says there is sufficient evidence to warrant rejection of the claim that response and employment status are independent.