Study Questions

Chapter 12

The 2006 General Social Survey contains information on the number of years of education that respondents have completed. The data are presented below. (Note: throughout the exercise, answers may vary due to rounding.)

  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 F-test.
  2. To test whether the mean level of education differs across groups, it is necessary to specify the null hypothesis that we intend to test. State the null hypothesis in both written and symbolic form.
  3. State the research hypothesis.
  4. The first quantity that we need to calculate is the between group sum of squares. Calculate and interpret this quantity.
  5. 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.
  6. Suppose that the value of the F-statistic is 104.65. Using this information and your answers from Questions #4-5, calculate the value of the sum of squares within. Interpret this quantity.
  7. 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?
  8. Given your work thus far, what is the critical value for an F-statistic of 104.65 with the associated degrees of freedom you calculated in Question #5, assuming an alpha level of .05?
  9. On the basis of your work thus far, can we reject the null hypothesis? If so, on what basis? If not, why not?
  10. What, if anything, are the results of these ANOVA procedures unable to tell us about the relationship between race and educational attainment?