Please study Ch12 to finish this homework assignment. You can calculate the answers following steps in the textbook (Five Steps in Hypothesis Testing: A Summary on Page 397-98)practice and weekly materials on BlackBoard. Also, please familiar with how to interpret the results using your own words following each definitions (See interpretation on Page 399-400). Please continue to remind yourself about the issue of rounding error and should develop a general classroom rule to round to a specific decimal point (i.e., 2 decimal points) for all calculations.
Problem set 1: Use the following data to answer questions 1-5
A researcher is interested in whether there is a significant difference between the mean age of marriage across three racial groups . Based on the data below, answer these questions.
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Race
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N
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Mean
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Black
|
113
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25.39
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White
|
904
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22.99
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Other
|
144
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23.87
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All Groups
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1,161
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23.33
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1. Calculate the value of the between group sum of squares (SSB, ).
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Race
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Y bar for each group
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Total mean
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Group mean - Total mean
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Square of the difference
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The number of cases
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Nk*Square of the difference
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Black
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|
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|
|
|
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White
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|
|
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|
|
|
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Other
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|
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|
|
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|
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Sum up=
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2. Calculate the degrees of freedom for the between group sum of squares. Then, use this quantity to calculate the mean square between
3. If the F statistic calculated for these data is 8.49, what is the value of the mean square within n
4. Following answer of #3, calculate the within group sum of squares and the number of degrees of freedom for the within group sum of squares
5. Imagine you are interested in whether there is a significant difference between the mean age of marriage across educational groups. If the critical value for an F statistic of 8.49 is 2.99, are these results statistically significant or not
Problem set 2: Use the following datato answer questions 6-10 :
We take another look at health based on the practice question on Page 408, this time examining the relationship between educational attainment and perceived quality of health care. Data for three groups are presented based on the HINTS2012 data set. Present the five-step model for these data, using alpha = .01. QUALITYCARE is measured on a five-point scale: 1-excellenet, 2-very good, 3-good, 4-fair, and 5-poor. Note how a lower score indicates a higher quality of care.
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Less Than High School
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Some College
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College Graduate
|
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1
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2
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1
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4
|
3
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1
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2
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2
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1
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2
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2
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2
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3
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4
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1
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3
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2
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2
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6. Find the answers for the worksheet (10 pts).
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Less Than High School
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Some College
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College Graduate
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1
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2
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1
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4
|
3
|
1
|
|
2
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2
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1
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2
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2
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2
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3
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4
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1
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3
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2
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2
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Sum Y1=
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Sum Y2=
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Sum Y3=
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Mean Y1=
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Mean Y2=
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Mean Y3=
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Sum up square of Y1=
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Sum up square of Y2=
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Sum up square of Y3=
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K1=
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K2=
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K3=
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Total mean =
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N =
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7. Calculate the degrees of freedom for SSB and SSW
8. Calculate Mean Square within and Mean Square between
9. What's the F statistic in this data
10. Make decision if alpha was set up at .05, and please use Appendix E (Page to discuss your decision making
Problem set 3: Use the following data to answer questions 11-15 :
Imagine you are interested in whether there is a significant difference between the mean age of marriage across educational groups. Use the data in the accompanying table to calculate question 11 to 15.
|
Highest Degree
|
N
|
Mean
|
|
Less than high school
|
195
|
22.47
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High school
|
590
|
22.87
|
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Junior college
|
86
|
23.71
|
|
Bachelor's degree
|
185
|
24.58
|
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Graduate degree
|
104
|
25.10
|
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All Groups
|
1,161
|
23.33
|
11. Answer the blanks in the worksheet (8 pts).
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Highest Degree
|
Y bar for each group
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Total mean
|
Group mean - Total mean
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Square of the difference
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The number of cases
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Nk*Square of the difference
|
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Less than high school
|
|
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High school
|
|
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|
|
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Junior college
|
|
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|
|
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Bachelor's degree
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|
|
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Graduate degree
|
|
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Sum up=
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12. Calculate the value of the between group sum of squares .
13. Calculate the degrees of freedom for the between group sum of squares. Then, use this quantity to calculate the mean square between .
14. If the F statistic is 6.10, use the data below to determine the value of the mean square within .
15. If the value of the mean square within for these data is 36.87, calculate the within group sum of squares and the number of degrees of freedom for the within group sum of squares .
Problem set 4: Use the following data to answer questions 16-17 :
1. Set alpha at .05 and test the null hypothesis of equal means .
2. I f alpha were set at .01, would your decision remain the same ?