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 375 residents. Round all numeric answers to four decimal places.

		Smoking Status
Education Level	Current	Former	Never
Less than high school	11	21	32
High school	28	15	36
Some College	37	60	135

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 High school and a smoking status of Never?  

3. Calculate the ?2X2 test statistic.

4.What was the contribution of Never smokers who attended 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. strong evidence
C. very strong evidence
D. some evidence
E. extremely 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 an observed count of at least 5 in every cell of the table.
B. The observations must be independent of one another.
C. There must be an expected count of at least 5 in every cell of the table.
D. There must be at least 10 "yes" and 10 "no" observations for each variable.
E. The population data must be normally distributed.

Answer 1

Applying chi square test of independence:

Observed		current	former	Never	Total
	less than high school	11	21	32	64
	high school	28	15	36	79
	some college	37	60	135	232
	total	76	96	203	375
Expected	Ei=row total*column total/grand total	current	former	Never	Total
	less than high school	12.9707	16.3840	34.6453	64.00
	high school	16.0107	20.2240	42.7653	79.00
	some college	47.0187	59.3920	125.5893	232.00
	total	76.00	96.00	203.00	375.00
chi square    χ2	=(Oi-Ei)2/Ei	current	former	Never	Total
	less than high school	0.299	1.301	0.202	1.8019
	high school	8.978	1.349	1.070	11.3977
	some college	2.135	0.006	0.705	2.8461
	total	11.4122	2.6561	1.9774	16.046
test statistic X2 =	16.0457

1)

X2 test of independence

2) expected number for people with an education of High school and a smoking status of Never =42.7653

3)

test statistic X2 =

16.0457

4)

contribution of Never smokers who attended High school toward this test statistic =1.0703

5)

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

4

6)

p value =0.0030

7)C. very strong evidence

8)

B. The observations must be independent of one anothe

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