4. A researcher is interested in whether there is a significant difference between the mean age of marriage across three racial groups. Using the data provided below, conduct an F-test to determine whether you believe there is an association between race and average age at marriage. Note: The value of the mean square within (i.e. the SS within divided by the degrees of freedom within) is 36.87. Please show all steps in conducting this test, including writing your hypotheses, calculating the mean square between, calculating the F-statistic, deciding whether to reject the null, and explaining what this decision means. Race N Mean Black 113 25.39 White 904 22.99 Other 144 23.87 All Groups 1,161 23.33