Question

(1 point) A researcher is interested in whether the number of years of formal education is related to a person's decision to never smoke, continue to smoke, or quit smoking cigarettes. The data below represent the smoking status by level of education for residents of the United States 18 years or older from a random sample of 475 residents. Round all numeric answers to four decimal places.

		Smoking Status
Education Level	Current	Former	Never
Less than high school	25	21	40
High school	38	19	52
Some College	40	69	171

1. Select the name of the test that should be used to assess the hypotheses:

?0H0: "Smoking Status" is independent of "Education Level"

??HA: "Smoking Status" is not independent of "Education Level"

A. ?2X2 test of a single variance
B. ?2X2 test of independence
C. ?2X2 goodness of fit

2. Under the null hypothesis, what is the expected number for people with an education of Less than high school and a smoking status of Former?

3. Calculate the ?2X2 test statistic.

4.What was the contribution of Former smokers who attended Less than high school toward this test statistic?

5. What are the degrees of freedom for this test?

6. What is the p-value for this test?

7. Based on the p-value, we have:
A. little evidence
B. some evidence
C. very strong evidence
D. extremely strong evidence
E. strong evidence
that the null model is not a good fit for our observed data.

8. Which of the following is a necessary condition in order for the hypothesis test results to be valid? Check all that apply.

A. There must be at least 10 "yes" and 10 "no" observations for each variable.
B. The population data must be normally distributed.
C. There must be an expected count of at least 5 in every cell of the table.
D. There must be an observed count of at least 5 in every cell of the table.
E. The observations must be independent of one another.

Answer 1

Applying chi square test of independence:

Observed		column 1	column 2	column 3	Total
	row 1	25	21	40	86
	row 2	38	19	52	109
	row 3	40	69	171	280
	total	103	109	263	475
Expected	Ei=row total*column total/grand total	column 1	column 2	column 3	Total
	row 1	18.6500	19.7347	47.6168	86
	row 2	23.6358	25.0126	60.3516	109
	row 3	60.7158	64.2526	155.0316	280
	total	103	109	263	475
chi square    χ2	=(Oi-Ei)2/Ei	column 1	column 2	column 3	Total
	row 1	2.162	0.081	1.218	3.4616
	row 2	8.730	1.4453	1.1557	11.3306
	row 3	7.068	0.3508	1.6448	9.0636
	total	17.9597	1.8772	4.0189	23.8558
test statistic X2 =		23.8558

from above:

1)B:X2 test of independence

2)

expected number for people with an education of Less than high school and a smoking status of Former =19.7347

3)

test statistic X2 =

23.8558

4)

contribution of Former smokers who attended Less than high school toward this test statistic =0.0811

5)

degree of freedom(df) =(rows-1)*(columns-1)=

4

6)

p value =

0.0001

7)

D. extremely strong evidence

8)C. There must be an expected count of at least 5 in every cell of the table.

E. The observations must be independent of one another