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

		Smoking Status
Education Level	Current	Former	Never
Less than high school	14	19	26
High school	25	14	38
Some College	32	58	124

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

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 ?2X2 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. strong evidence
B. very strong evidence
C. some evidence
D. little 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 at least 10 "yes" and 10 "no" observations for each variable.
B. The observations must be independent of one another.
C. The population data must be normally distributed.
D. There must be an observed count of at least 5 in every cell of the table.
E. There must be an expected count of at least 5 in every cell of the table.

Answer 1

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

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

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

A. test of independence

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

Expected value=

3. Calculate the test statistic.

In order to do this Let us first write the original numbers with their row and column totals. Also, we know that the expected frequency of any cell   where are the Row total of the ith row and column total of the jth row and T is the overall total. All these values are tabulated in the next table:

The original data Expected Frequencies

	Current	Former	Never	Row				Current	Former	Never	Row
<High	14	19	26	59			<High	11.96	15.34	31.39	58.69
High School	25	14	38	77			High School	15.62	20.02	41.36	77
Some college	25	58	124	207			Some college	43.41	55.64	114.95	214
Column	64	91	188	343			Column	70.99	91	187.7	349.69

Where are the Observed and Expected frequencies of the cell.

Now

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

This is the value corresponding to the last entry for the value 124   

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

Degrees of freedom (number of rows-1)*(number of columns-1)=(3-1)*(3-1)=2*2=4.

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

The p-value is 0.0081

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


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