Question Description
I’m working on a statistics question and need an explanation to help me study.
1.Use the following sample of 32 GSS cases to analyze the relationship between social class and health assessment. Health is measured according to a fourpoint scale: 1 = excellent, 2 = good, 3 = fair, and 4 = poor. Four social classes are reported here: lower, working, middle, and upper.
Lower Class 
Working Class 
Middle Class 
Upper Class 
3 
2 
2 
2 
2 
1 
3 
1 
2 
3 
1 
1 
2 
2 
1 
2 
3 
2 
2 
1 
3 
2 
3 
1 
4 
3 
3 
1 
4 
3 
1 
2 
a. Using this data, fill in the following table:
Lower Class 
Working Class 
Middle Class 
Upper Class 

n_{1} = 
n_{2} = 
n_{3} = 
n_{4} = 

Sample mean (Y_{1}) = 
Sample mean (Y_{2}) = 
Sample mean (Y_{3}) = 
Sample mean (Y_{4}) = 

Sample variance (S_{1}) = 
Sample variance (S_{2}) = 
Sample variance (S_{3}) = 
Sample variance (S_{4}) = 

Sample SD (S^{2}_{1}) = 
Sample SD (S^{2}_{2}) = 
Sample SD (S^{2}_{3}) = 
Sample SD (S^{2}_{4}) = 

Sum of scores (EY_{1}) = 
Sum of scores (EY_{2}) = 
Sum of scores (EY_{3}) = 
Sum of scores (EY_{4}) = 

Sum of scores^{2} (EY^{2}_{1})= 
Sum of scores^{2} (EY^{2}_{2})= 
Sum of scores^{2} (EY^{2}_{3})= 
Sum of scores^{2} (EY^{2}_{4})= 

Mean of all respondents (Y) = 

N = 

1
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b. Calculate the betweengroup sum of squares (SSB). SSB = ___________________________________________
 Calculate degrees of freedom (df_{b}). df_{b} = ________________________________________________________
 Calculate the mean square between (MSB). MSB = ________________________________________________
 Calculate the withingroup sum of squares (SSW). SSW = ___________________________________________
 Calculate degrees of freedom (df_{w}). df_{w} = ________________________________________________________
 Calculate the mean square within (MSW). MSW = ________________________________________________
 Calculate the F statistic. F = _________________________________________________________________
 Will we reject or fail to reject the null hypothesis using an alpha = .05? __________________________________
2
QUESTION 2
 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, calculate the between group sum of squares (SSB).
Race 
N 
Mean 
Black 
113 
25.39 
White 
904 
22.99 
Other 
144 
23.87 
All Groups 
1,161 
23.33 
QUESTION 3
Using the data from Question #2, calculate the degrees of freedom between (df_{b}).
QUESTION 4
Using the data from Question #2, calculate the mean square between (MSB).
QUESTION 5
If the mean square within calculated for this data is 36.87, what is the value of the F statistic?
QUESTION 6
If alpha is .05 and df_{w} is 1,158, will you reject or fail to reject the null hypothesis?
QUESTION 6
The 2006 General Social Survey contains information on the number of years of education that respondents have completed. The data are presented below.
White 
Black 
Other 
Total Sample 

Mean 
13.66 
12.87 
11.69 
13.29 
Standard deviation 
2.93 
2.95 
4.36 
3.23 
N 
3,277 
630 
592 
4,499 
1.Specify the assumptions required in order to employ ANOVA procedures and conduct an Ftest and state the null and research hypotheses.
2.Calculate the between group sum of squares.
3.Next, we need to calculate the sum of squares within. However, as you probably noticed, this would be quite a cumbersome task considering the number of observations in the data set. Instead, let’s work backwards to arrive this quantity. Begin by calculating the degrees of freedom for the sum of squares between and the sum of squares within.
4.Suppose that the value of the Fstatistic is 104.65. Using this information and your answers from Questions #45, calculate the value of the sum of squares within.
5.Although you calculated these values indirectly in arriving at your answer to Question #6, what are the values of the mean square between and the mean square within?
6.Given your work thus far, what is the critical value for an Fstatistic of 104.65 with the associated degrees of freedom you calculated in Question #5, assuming an alpha level of .05? On the basis of your work thus far, can we reject the null hypothesis?