Question

# A researcher is interested in whether there is a significant difference between the mean age of...

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 118 21.57 White 882 24.59 Other 120 28.39 All Groups 1,120 24.68

1. Calculate the value of the between group sum of squares (SSB, 20 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 21.57 24.68 White 24.59 24.68 Other 28.39 24.68 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 15.29, what is the value of the mean square within (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 15.29 is 2.99, are these results statistically significant or not (4 pts)?

1.

 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 21.57 24.68 -3.11 9.6721 118 1141.3078 White 24.59 24.68 -0.09 0.0081 882 7.1442 Other 28.39 24.68 3.71 13.7641 120 1651.692 Sum up=2800.144

2. Degrees of freedom for the between group sum of squares=3-1=2

Sum of square between=SSB=2800.144

Mean square between=MSB=SSB/2= 2800.144/2=1400.072

3. F=MSB/MSW= 15.29, or, MSW=1400.072/15.29=91.5678

where MSW=mean square within=91.5678

4. The number of degrees of freedom for the within group sum of squares=1120-3= 1117

SSW=sum of square within=1117*91.5678=102281.2.

5. Yes, this is statistically significant F statistic= 15.29 >2.99.