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	40	21	38
High school	13	28	45
Some College	36	78	176

1

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 independence
C. X2X2 test of a single variance

2. Under the null hypothesis, what is the expected number for people with an education of Some college and a smoking status of Never?

3. Calculate the X2X2 test statistic.

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

Solution:

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

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

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

Answer: B. test of independence

2. Under the null hypothesis, what is the expected number for people with an education of Some college and smoking status of Never?

Answer: The expected number for people with an education of some college and smoking status of Never is:

3. Calculate the X2 test statistic.

Answer: The chi-square test statistic is:

The observed data is given below:

	Smoking Status
Education Level	Current	Former	Never	Total
Less than high school	40	21	38	99
High school	13	28	45	86
Some College	36	78	176	290
Total	89	127	259	475

The expected data can be calculated as:

4. What was the contribution of Never smokers who attended Some college toward this test statistic?

Answer:

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

Answer:

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

7. Based on the p-value, we have:
Answer: A. 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.
Answer: A. 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.