Question

8) (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 200 residents. Round all numeric answers to four decimal places.

		Smoking Status
Education Level	Current	Former	Never
Less than high school	15	9	14
High school	6	11	21
Some College	26	27	71

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

H0H0: "Smoking Status" is independent of "Education Level"

HAHA: "Smoking Status" is not independent of "Education Level"

A. X2X2 goodness of fit
B. X2X2 test of a single variance
C. X2X2 test of independence

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 X2X2 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. some evidence
B. strong evidence
C. little evidence
D. extremely strong evidence
E. very 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 population data must be normally distributed.
C. The observations must be independent of one another.
D. There must be at least 10 "yes" and 10 "no" observations for each variable.
E. There must be an expected count of at least 5 in every cell of the table.

Answer 1

1)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	current	former	Never	Total
	less than HS	8.9300	8.9300	20.1400	38.00
	HS	8.9300	8.9300	20.1400	38.00
	some college	29.1400	29.1400	65.7200	124.00
	total	47.00	47.00	106.00	200.00
chi square    χ2	=(Oi-Ei)2/Ei	current	former	Never	Total
	less than HS	4.1260	0.0005	1.8719	5.9984
	HS	0.9614	0.4798	0.0367	1.4779
	some college	0.3384	0.1572	0.4242	0.9197
	total	5.4257	0.6375	2.3328	8.396
test statistic X2 =		8.3960

1)

C. X2 test of independence

2) expected number for people with an education of Less than high school and a smoking status of Former =8.9300

3)

X2 test statistic =8.3960

4)

contribution of Former smokers who attended Less than high school toward this test statistic=0.0005

5)

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

4

6)

p value =

0.0781

7)

A. some evidence

8)

C. The observations must be independent of one another.

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