## Statistics- Homework Assignment #7

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 â 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: 1âexcellenet,

2âvery good, 3âgood, 4âfair, and 5âpoor. Note how a lower score indicates a

higher quality of care.

Less

Than High School

Some

College

College

Graduate

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

Than High School

Some

College

College

Graduate

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

mean =

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. Whatâs 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

than high school

195

22.47

High

school

590

22.87

Junior

college

86

23.71

Bachelorâs

degree

185

24.58

Graduate

degree

104

25.10

All

Groups

1,161

23.33

11. Answer

the blanks in the worksheet (8 pts).

Highest Degree

Y bar for each group

Total mean

Group mean â Total mean

Square of the difference

The number of cases

Nk*Square of the difference

Less

than high school

High

school

Junior

college

Bachelorâs

degree

Graduate

degree

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, âImmigrants take jobs away from people who were

born in Americaâ 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).

.0/msohtmlclip1/01/clip_image002.jpg”>

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)?

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