1. Describe what a sequence is. (p. 14-55

2. Clearly describe what the runs test for randomness is used for. (p. 14-55

3. Explain what a run is. (p. 14-55

4. What does it mean if the number of runs in a sequence is too low or too high? (p. 14-56

1. , the number of observations having the first distinct outcome
2. , the number of observations having the second distinct outcome
4. , the number of runs in the sequence

5. M M F F F M F M F M M M M F M M M

6. N N N N N N P P P P P P P P N N N N N N N

7. T F T F T F F T T F T F T F T T F T F T F T F F F T F T F T F T F F T F T F T T T F

8. Y Y N N Y Y Y N N Y Y N N N Y N N N N Y Y N N Y Y Y N N N N Y Y N N N N N Y Y Y Y Y Y Y

9. Find and for the sequence in Exercise 5 for level of significance .

10. Find and for the sequence in Exercise 6 for level of significance .

11. Find the critical value for the sequence in Exercise 7 for level of significance .

12. Find the critical value for the sequence in Exercise 8 for level of significance .

13. For the sequence in Exercise 5

14. For the sequence in Exercise 6

15. For the sequence in Exercise 7

16. For the sequence in Exercise 8

1. State the hypotheses.
2. Find the critical values.
3. Calculate the test statistic.
4. State the conclusion and the interpretation.

17. Use the sequence in Exercise 5, the critical values in Exercise 9, the test statistic in Exercise 13, and level of significance .

18. Use the sequence in Exercise 6, the critical values in Exercise 10, the test statistic in Exercise 14, and level of significance .

19. Use the sequence in Exercise 7, the critical value in Exercise 11, the test statistic in Exercise 15, and level of significance .

20. Use the sequence in Exercise 8, the critical value in Exercise 12, the test statistic in Exercise 16, and level of significance .

21. Florida Lottery Winners. The following sequence represents whether there is one (A) or more than one (B) winning ticket for the Florida Lotto Jackpot lottery for the year 2008. Test whether the A/B sequence is random, using level of significance .

22. Boston Red Sox. The following sequence represents the last 15 games of the 2013 regular season, showing whether the Red Sox won (W) or lost (L) the game. Test whether the sequence is random, using level of significance .

23. Nobel Prize Winners. The following sequence represents the nationality of the Nobel Prize in Economics winners (2000–2013), with A representing an American and O representing all other nationalities.¹⁴ Test whether the sequence is random, using level of significance .

24. Super Bowl Winners. The following sequence represents the conference of the Super Bowl winners from 1967 to 2014, where A represents the American Football Conference and N represents the National Football Conference.¹⁵ Test whether the sequence is random, using level of significance .

25. Douglas Fir Trees: Annual Growth Versus Age. The following scatterplot depicts the residuals versus the fits from a regression of the annual growth of Douglas fir trees versus the age of the tree.¹⁶ Proceeding from left to right, classify each residual as either above zero (A) or below zero (B). Then perform the runs test to determine whether the independence assumption is violated, using level of significance .

26. Women's Pulse Rates versus Temperature. The following scatterplot depicts the residuals versus the fits from a regression of pulse rates versus body temperatures for a random sample of 20 women. Proceeding from left to right, classify each residual as either above zero (A) or below zero (B). Then perform the runs test to determine whether the independence assumption is violated, using level of significance .