# Study Questions

### Chapter 9

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.)

 White0 Black Mean 13.66 12.87 Standard Deviation 2.93 2.95 N 3,277 630
1. Suppose for the moment that the black population has a mean educational level of 13.12 years with a standard deviation of 3.11. What is the appropriate test for determining whether the sample mean differs from the population mean?

2. What is the null hypothesis for the test you identified in Question #1?

3. What are the assumptions underlying the test you identified in Question #1?

4. Before calculating the statistic you identified in Question #1, first calculate the value of the standard error for this test.

5. Determine the Alpha (a) you wish to use and interpret what this means.

6. Suppose you wanted to reduce the risk of making a Type I error. How would you do this? How does this affect a Type II error?

7. Calculate the value of the test statistic you identified in Question #1.

8. Using the appendix in the back of your textbook, determine whether we are able to reject the hypothesis or not? What do you conclude?

9. In light of your answer to Question #6, are you at risk of committing a Type I or a Type II error? Explain.

10. Recall from Question #1 that we made an assumption about the population standard deviation. Suppose, however, that the population standard deviation is unknown. What is the appropriate test for determining whether our sample mean differs from the population mean? Again, the population of interest is the black population.

11. Before calculating the statistic you identified in Question #1, first calculate the value of the standard error for this test.

12. Calculate the value of the test statistic you identified in Question #9.

13. Calculate the degrees of freedom associated with the above test.

14. Using the appendix in the back of your textbook, determine whether we are able to reject the hypothesis or not? (Assume that alpha is set at .05 for a two-tailed test). What do you conclude?

15. Having made it through the above exercises, let's now determine whether there is a significant difference between mean levels of education for whites and blacks. What is the appropriate test in this case?

16. What is the null hypothesis that you need to test in order to determine whether there is a significant difference between mean levels of education for whites and blacks?

17. What is the value of the estimated standard error for this test? (Hint: use formula 9.5 in Chapter 9.)

18. Calculate the value of the test statistic you identified in Question #13.

19. Calculate the degrees of freedom associated with the above test.

20. Using the appendix in the back of your textbook, determine whether we are able to reject the hypothesis or not? (Assume that alpha is set at .05 for a two-tailed test). What do you conclude?