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

• 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=

• Calculate the degrees of freedom for the between group sum of squares. Then, use this quantity to calculate the mean square between (6 pts).

• If the F statistic calculated for these data is 8.49, what is the value of the mean square within n(4 pts)?

• 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).

• 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)?