Homework
Assignment #7 (due by 11:59pm CST on Saturday, November 21st)
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 (30
points):
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.
|
Race |
N |
Mean |
|
Black |
113 |
25.39 |
|
White |
904 |
22.99 |
|
Other |
144 |
23.87 |
|
All Groups |
1,161 |
23.33 |
1. Calculate
the value of the between group sum of squares (SSB, 10 pts).
|
Race |
Y bar for each group |
Total mean |
Group mean – Total mean |
Square of the difference |
The number of cases |
Nk*Square of the difference |
|
Black |
||||||
|
White |
||||||
|
Other |
||||||
|
Sum up= |
2. Calculate
the degrees of freedom for the between group sum of squares. Then, use this
quantity to calculate the mean square between (6 pts).
3. If the F
statistic calculated for these data is 8.49, what is the value of the mean
square within n(4 pts)?
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 (6 pts).
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
(4 pts)?
Problem set 2: Use the following data to answer questions 6-10 (30
points):
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.
|
Less |
Some |
College |
|
1 |
2 |
1 |
|
4 |
3 |
1 |
|
2 |
2 |
1 |
|
2 |
2 |
2 |
|
3 |
4 |
1 |
|
3 |
2 |
2 |
6. Find the
answers for the worksheet (10 pts).
|
Less |
Some |
College |
|
1 |
2 |
1 |
|
4 |
3 |
1 |
|
2 |
2 |
1 |
|
2 |
2 |
2 |
|
3 |
4 |
1 |
|
3 |
2 |
2 |
|
Sum Y1= |
Sum Y2= |
Sum Y3= |
|
Mean Y1= |
Mean Y2= |
Mean Y3= |
|
Sum up square of Y1= |
Sum up square of Y2= |
Sum up square of Y3= |
|
K1= |
K2= |
K3= |
|
Total |
||
|
N = |
7. Calculate
the degrees of freedom for SSB and SSW (6 pts).
8. Calculate
Mean Square within and Mean Square between (6 pts).
9. What’s the
F statistic in this data (4 pts)?
10. Make
decision if alpha was set up at .05, and please use Appendix E (Page to discuss your decision making (4 pts).
Problem set 3: Use the following data to answer questions 11-15 (20
points):
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 |
195 |
22.47 |
|
High |
590 |
22.87 |
|
Junior |
86 |
23.71 |
|
Bachelor’s |
185 |
24.58 |
|
Graduate |
104 |
25.10 |
|
All |
1,161 |
23.33 |
11. Answer
the blanks in the worksheet (8 pts).
|
Highest Degree |
Y bar for each group |
Total mean |
Group mean – Total mean |
Square of the difference |
The number of cases |
Nk*Square of the difference |
|
Less |
||||||
|
High |
||||||
|
Junior |
||||||
|
Bachelor’s |
||||||
|
Graduate |
||||||
|
Sum up= |
12. Calculate
the value of the between group sum of squares (2 pts).
13. Calculate
the degrees of freedom for the between group sum of squares. Then, use this
quantity to calculate the mean square between (4 pts).
14. If the F
statistic is 6.10, use the data below to determine the value of the mean square
within (2 pts).
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 (4 pts).
Problem set 4: Use the following data to answer questions 16-17 (20
points):
We examine the relationship between educational attainment and
agreement to the statement, “Immigrants take jobs away from people who were
born in America” as measured in the GSS 2010. Responses to IMMJOBS are measured
according to the same five-point scale (as FINDEPDN in practice question #4 on
Page 409; see details in Figure 12.8 on page 410).
16. Set
alpha at .05 and test the null hypothesis of equal means (15 pts).
17. I f
alpha were set at .01, would your decision remain the same (5 pts)?
